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Publication Number: FHWA-RD-02-095

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Figure 1: Chart. Flowchart for Phase 1 - Initiation and Planning. This chart presents a flowchart with boxes representing steps in the process. Step 1 is "Identify need for the specification or specifications within the agency." This step includes three points:

1.1 Problems that need to be solved?

1.2 Innovative or progressive ideas?

1.3 Industry suggested need to improve?

After step 1 is complete, step 2, "Define goals and expectations," can begin. The subtasks in this step are:

2.1 Identify benefits to agency and industry

2.2 What is expected of the final product?

2.3 Define criteria for success

The third step is "Reach agency consensus." The subtasks in this step are:

3.1 Obtain/verify top management commitment and support

3.2 Choose task force leaders and agency members

3.3 Build consensus within task force

3.4 Set target date for initial draft specification

After step 3 is finished, step 4, "Understand 'Best Practices,'" can begin. This step's subtasks are:

4.1 Review the literature

4.2 Learn other States' experiences

Step 5 is then, "Confirm interest and commitment." This step involves reconfirming top management commitment and support. Step 6, "Establish industry contact," follows. Subtasks in step 6 are:

6.1 Present concepts to selected industry leaders, present potential benefits to industry and agency

6.2 Select industry representatives for task force

After step 6 is complete, step 7, "Hold first joint agency–industry task force meeting," can begin. This step involves eight subtasks:

7.1 Present concepts

7.2 Build consensus among members

7.3 Establish short-term and long-term goals

7.4 Establish deadline for trial specification

7.5 Establish schedule for the initiative

7.6 Determine if outside expertise is needed

7.7 Set frequency of task force meetings

7.8 Make specific work assignments

Finally, an arrow leaves step 7, indicating that the process can continue to Phase 2: Specification Development.

 

Figure 2: Chart. Flowchart for Phase 2—Specification Development.

This chart presents a flowchart with boxes representing steps in the process. The first step is to "Select material or materials and/or construction specifications to develop." Step 2, "Procure outside assistance, if required (see Phase I, Item 7.6)," follows. After step 2 is completed, step 3, "Recognize need to identify current practices," can begin. After step 3 is finished, both step 4, "Search the literature (for specific material or materials selected)," and step 5, "Contact/interview other agencies and associations (for specific material or materials selected)," can begin simultaneously. Both these steps must be completed before step 6, "Develop outline for the QA specification," can begin, with the following examples given: General Information, Definitions, Quality Assurance, Quality Control, Acceptance, Payment and Conflict Resolution. Step 7 is to "Develop introductory information for the QA specification." Next, is step 8, "Begin to develop procedures," which includes the following examples: Responsibilities of agency and contractor, and Requirements for technician and laboratory qualification. The flowchart concludes with arrows leaving step 8, indicating that both step 9, "Develop QC procedures and requirements," and step 19, "Develop acceptance procedures and requirements," can begin.

The flowchart continues, beginning with step 9, "Develop QC procedures and requirements." After step 9 is completed, both steps 10, "Establish QC requirements," and 11, "Determine quality characteristics to measure," can begin. Step 10 includes the following examples of QC requirements: QC plan, Qualified Technicians, Qualified Laboratories, Control Charts and Action Criteria. After step 11 is completed, step 12 indicates that steps 13 through 17 are to be completed for each QC quality characteristic. The steps, in order, are as follows. Step 13 is "Evaluate available data." Step 14 is to decide if there are sufficient valid data available. If the answer is no, then step 15, "Obtain data," is performed, and the process returns to step 13. If the answer is yes, then the process proceeds to step 16, "Determine sampling and testing procedures and test frequency." Step 17 asks whether or not the quality characteristic should be used for QC. If the answer is no, the quality characteristic is either eliminated or considered for acceptance testing. If the answer is yes, then the process proceeds to step 18, in which QC procedures and requirements are completed. This is not achieved until both steps 9 and 17 are completed. The flowchart concludes with an arrow leaving step 18, indicating that step 42, "Finalized initial draft specification," is the next step in the process.

The flowchart continues, from step 8, "Begin to develop procedures," this time to step 19, "Develop acceptance procedures and requirements." From step 19, step 20 asks, "Will contractor tests be used in the acceptance decision?" If the answer is no, the process proceeds to step 23, which is described below. If the answer is yes, the process proceeds to step 21, "Use contractor to do acceptance testing with agency doing verification testing." After step 21 is completed, step 22, "Develop verification procedures," begins with the following examples of procedures given: F-test and T-test, allowable differences between tests and frequency of comparisons. After step 22 is completed, both step 42, "Finalized initial draft specification," and step 23, "Determine quality characteristics to measure," can begin. From step 23, step 24 indicates that steps 25 through 36 are to be completed for each acceptance quality characteristic. Step 25, "Evaluate available data," follows step 24. After step 25 is completed, step 26 is to decide if sufficient data are available. If the answer is no, then step 27, "Obtain data," is performed, and the process returns to step 25. If the answer is yes, then the process proceeds directly to step 28, "Analyze data for statistical parameters and distribution." After step 28 is completed, step 29 asks whether or not the quality characteristic is valid for acceptance. If the answer is no, the quality characteristic either is considered for QC testing or eliminated. If the answer is yes, the flowchart moves to step 30, which asks whether to use the characteristic for payment determination.

If the answer to step 30 is yes, then the process proceeds to step 32, "Determine the quality measure to use." From step 32, the process proceeds to step 34, "Determine specification limits, decide on AQL and RQL." After step 34 is completed, the process proceeds to step 37, "Decide pay relationships" such as Performance-related pay, Incentive/Disincentive, Minimum pay provisions, Remove/replace provisions and Retest provisions. The process then proceeds to step 38, "Determine sample size, lot size, sublot size." If the answer to step 30 is no, then the process proceeds to step 31, "Use as a Screening (pass/fail) test." The process then proceeds to step 33, "Determine the quality measure to use." The process then proceeds to step 35, "Determine specification limits, decide on AQL and RQL." After step 35 is completed, the process continues to step 36, "Determine acceptance/rejection procedures, including rework provisions." The process then proceeds to step 38, "Determine sample size, lot size, sublot size." Step 39, "Develop OC curve and evaluate risks," follows from step 38.

Step 40 then asks "Are risks acceptable?" If the answer is no, then the process proceeds to step 41, "Modify specification limits, acceptance limits, pay schedule, sample size, and/or lot size." After this is done, the process returns to step 39, "Develop OC curve and evaluate risks," and step 40, "Are risks acceptable?" until the answer is yes. The process then proceeds to step 42, "Finalized initial draft specification." Step 42 also has arrows pointing to it, indicating that step 18, "QC procedures and requirements completed" and step 22, "Develop validation/verification procedures," also must be completed before step 42 can be completed.

 

Figure 3: Chart. Flowchart for Phase 3 Implementation. This chart presents a flowchart with boxes representing steps in the process. Step 1, "Simulate specification," is divided into five subtasks:

1.1. Use several projects under construction or recently completed

1.2. Be sure random sampling was used

1.3. Use same sampling and testing procedures as decided upon in Phase 2

1.4. Analyze simulated payment factor data

1.5. Revise or fine–tune as necessary for a Draft Special Provision

Step 2, "Begin/continue technician qualification training," is divided into two subtasks:

2.1. Include training in sampling and testing procedures

2.2. Include training in basic statistical procedures

Step 3, "Try specification on a limited number of pilot projects," is divided into three subtasks:

3.1. Let projects using Draft Special Provision (Item 1.5)

3.2. Apply only a percentage of the disincentives

3.3. Bid prices may not reflect future project prices

Step 4 is to "Analyze pilot project results." After step 4 is completed, step 5 asks whether major revisions to the draft specification are needed. If the answer is yes, then the process proceeds to step 6, "Prepare new draft special provision." The process then returns to steps 3, 4, 5, and 6 until no major revisions are needed. The process then proceeds to step 7, "Phase in projects agency-wide," which has two subtasks:

7.1. Phase in until all major projects are included

7.2. Phase in payment factors

The flowchart concludes with step 8, "Ongoing monitoring of specification performance," which has six subtasks:

8.1. Look at quality levels achieved each year

8.2. Look for administrative problems

8.3. Consider contractor concerns

8.4. Identify technology changes

8.5. Tie results into the pavement management system

8.6. Compare with established criteria for success

Figure 4: Chart. Flowchart for Phase 1—Initiation and Planning. This chart presents a flowchart with boxes representing steps in the process. Step 1 is "Identify need for the specification or specifications within the agency." This step includes three subtasks:

1.1 Problems that need to be solved?

1.2 Innovative or progressive ideas?

1.3 Industry suggested need to improve?

After step 1 is complete, step 2, "Define goals and expectations," can begin. The subtasks in this step are:

2.1 Identify benefits to agency and industry

2.2 What is expected of the final product?

2.3 Define criteria for success

The third step is "Reach agency consensus." The subtasks in this step are:

3.1 Obtain/verify top management commitment and support

3.2 Choose task force leaders and agency members

3.3 Build consensus within task force

3.4 Set target date for initial draft specification

After step 3 is finished, step 4, "Understand 'Best Practices,'" can begin. This step's subtasks are:

4.1 Review the literature

4.2 Learn other States' experiences

Step 5 is then, "Confirm interest and commitment." This step involves reconfirming top management commitment and support. Step 6, "Establish industry contact," follows. Subtasks in step 6 are:

6.1 Present concepts to selected industry leaders, present potential benefits to industry and agency

6.2 Select industry representatives for task force

After step 6 is complete, step 7, "Hold first joint agency–industry task force meeting," can begin. This step involves eight subtasks:

7.1 Present concepts

7.2 Build consensus among members

7.3 Establish short-term and long-term goals

7.4 Establish deadline for trial specification

7.5 Establish schedule for the initiative

7.6 Determine if outside expertise is needed

7.7 Set frequency of task force meetings

7.8 Make specific work assignments

Finally, an arrow leaves step 7, indicating that the process can continue to Phase 2: Specification Development.

Figure 5: Chart. Flowchart for Initial Portion of Phase 2. This chart presents a flowchart with boxes representing steps in the process. The first step is to "Select material or materials and/or construction specifications to develop." Step 2, "Procure outside assistance, if required (see Phase I, Item 7.6)," follows. After step 2 is completed, step 3, "Recognize need to identify current practices," can begin. After step 3 is finished, both step 4, "Search the literature (for specific material or materials selected)," and step 5, "Contact/interview other agencies and associations (for specific material or materials selected)," can begin simultaneously. Both these steps must be completed before step 6, "Develop outline for the QA specification," can begin. Step 6 includes the following examples of items to include in the outline: General Information, Definitions, Quality Assurance, Quality Control, Acceptance Payment and Conflict Resolution. Step 7 is to "Develop introductory information for the QA specification," for example, Responsibilities of agency and contractor and Requirements for technician and laboratory qualification. Next, step 8, "Begin to develop procedures," can begin. The flowchart concludes with arrows leaving step 8, indicating that both step 9, "Develop QC procedures and requirements," and step 19, "Develop acceptance procedures and requirements," can begin.

Figure 6: Chart. Flowchart for QC Portion of Phase 2. This chart presents a flowchart with boxes representing steps in the process. The flowchart begins with an arrow from step 8, "Begin to develop procedures," leading into step 9, "Develop QC procedures and requirements." After step 9 is completed, both step 10, "Establish QC requirements," and step 11, "Determine quality characteristics to measure," can begin. Step 10 includes the following examples of requirements: QC Plan, Qualified Technicians, Qualified Laboratories, Control Charts and Action Criteria. After step 11 is completed, step 12 indicates that steps 13 through 17 are to be completed for each QC quality characteristic. The steps, in order, are as follows. Step 13 is "Evaluate available data." Step 14 is to decide if there are sufficient valid data available. If the answer is no, then step 15, "Obtain data," is performed, and the process returns to step 13. If the answer is yes, then the process proceeds to step 16, "Determine sampling and testing procedures and test frequency." Step 17 asks whether or not the quality characteristic should be used for QC testing. If the answer is no, the quality characteristic either is eliminated or considered for acceptance. If the answer is yes, then the process proceeds to step 18, in which QC procedures and requirements are completed. This is not achieved until both steps 10 and 17 are completed. The flowchart concludes with an arrow leaving step 18, indicating that step 42, "Finalized initial draft specification," is the next step in the process.

Figure 7: Chart. Flowchart for Acceptance Procedures Portion of Phase 2. This chart presents a flowchart with boxes representing steps in the process. The flowchart begins with an arrow from step 8, "Begin to develop procedures," leading to step 19, "Develop acceptance procedures and requirements." From step 19, step 20 asks, "Will contractor tests be used in the acceptance decision?" If the answer is no, the process proceeds to step 23, which is described below. If the answer is yes, the process proceeds to step 21, "Use contractor to do acceptance testing with agency doing verification testing." After step 21 is completed, step 22, "Develop verification procedures," begins, with examples of procedures given as F-Test and T-Test, allowable differences between tests and frequency of comparisons. After step 22 is completed, step 23, "Determine quality characteristics to measure," can begin. Step 42, "Finalized initial draft specification," also follows step 22, and is described below. From step 23, step 24 indicates that steps 25 through 36 are to be completed for each acceptance quality characteristic. Step 25, "Evaluate available data," follows step 24. After step 25 is completed, step 26 is to decide if sufficient valid data are available. If the answer is no, then step 27, "Obtain data," is performed, and the process returns to step 25. If the answer is yes, then the process proceeds directly to step 28, "Analyze data for statistical parameters and distribution." After step 28 is completed, step 29 asks whether the quality characteristic is valid for acceptance. If the answer is no, the quality characteristic either is considered for QC testing or eliminated. If the answer is yes, the flowchart moves to step 30, which asks whether to use the characteristics for payment determination.

Figure 8: Diagram. Components of Variance for Independent Samples. This diagram represents four cores obtained by a contractor from a pavement, along with one core obtained independently by the agency. The chart indicates that all five cores have variability components of material, process, sampling, and testing.

Figure 9: Diagram. Components of Variance for Split Samples. This diagram represents three cores obtained by a contractor from a pavement, along with two cores that were obtained from the same sample location, with one to be tested by the contractor and the other by the agency. The diagram indicates that the two cores obtained from the same location and split between the contractor and agency only have one component of variability, testing, while the others have all four variability components.

 

Equation 1: T equals a quotient with the numerator consisting of the absolute value of X bar subscript D, which is the average of the differences between the split sample test results, while the denominator is the quotient of S subscript D (the standard deviation of the differences between the split sample test results) divided by the square root of N (the number of split samples).

Equation 2: T equals a quotient with the numerator consisting of the absolute value of X bar subscript D, which is the average of the differences between the split sample test results, while the denominator is the quotient of S subscript D (the standard deviation of the differences between the split sample test results) divided by the square root of N (the number of split samples). This equals the quotient with 0.06 in the numerator and 0.05 divided by the square root of 10 in the denominator. This equals 3.795.

Figure 10: Chart. Simple Example of an OC Curve for a Statistical Test Procedure. The chart plots Probability of Not Detecting a Difference on the vertical axis versus the Actual Difference on the horizontal axis. Three curves are shown representing sample sizes of N equals 2, N equals 4, and N equals 10. The curves show that, when the actual difference is 0, the probability of not detecting a difference is 0.95 for all three N values. For an actual difference of 1.0, the probabilities of not detecting a difference are about 0.93, 0.70, and 0.20 for N values of 2, 4, and 10 respectively. For an actual difference of 2.0, these probabilities drop to approximately 0.82, 0.25, and 0 for N values of 2, 4, and 10, respectively. Finally, for an actual difference of 3.0, the probabilities fall to approximately 0.72, 0.04, and 0 for N values of 2, 4, and 10, respectively.

Equation 3: The square of S subscript P, which is the pooled estimate for the within-lot process variance, equals a quotient. The numerator of this quotient consists of the quantity N subscript 1 (the number of values for lot 1) minus 1 multiplied by the square of S subscript 1 (the variance for lot 1). This is added to the quantity N subscript 2 (the number of values for lot 2) minus 1 multiplied by the square of S subscript 2 (the variance for lot 2). This continues until the final quantity in the numerator is the quantity N subscript K (where K is the number of lots in the project) minus 1 multiplied by the square of S subscript K. The denominator of the quotient is the sum of N subscript 1 plus N subscript 2, etcetera, continuing until N subscript K. K is then subtracted from this sum.

Equation 4: The square of Sigma hat subscript combined, which is the estimated combined process center and within-process variance, equals the square of Sigma hat subscript center (the estimated process center variance) plus the square of Sigma hat subscript process (the estimated within-process variance).

Equation 5: Sigma hat subscript combined, which is the estimated combined standard deviation, equals the square root of the square of Sigma hat combined.

Equation 6: The square of Sigma hat subscript combined equals 1.817 plus 4.840, which then equals 6.657.

Equation 7: Sigma hat subscript equals the square root of 6.657, which then equals 2.58.

Equation 8: The square of Sigma hat subscript combined equals 0.75 squared plus 2.75 squared, which then equals 8.125.

Equation 9: Sigma hat subscript equals the square root of 8.125, which then equals 2.85.

Figure 11: Chart. Flowchart for Acceptance and Payment Portion of Phase II. This chart presents a flowchart with boxes representing steps in the process. The flowchart begins with an arrow from step 29 "Is quality characteristic valid for acceptance?" leading into step 30 that asks whether or not to use the quality characteristics for payment determination. If the answer to step 30 is yes, then the process proceeds to step 32, "Determine the quality measure to use."Examples given of quality measures are PWL, PD and AAD. From step 32, the process proceeds to step 34, "Determine specification limits, decide on AQL and RQL." After step 34 is completed, the process proceeds to step 37, "Decide pay relationships." Examples given of pay relationships are Performance-related pay, Incentive/disincentive, Minimum pay provisions, Remove/replace provisions and Retest provisions. The process then proceeds to step 38, "Determine sample size, lot size, sublot size." If the answer to step 30 is no, then the process proceeds to step 31, "Use as a screening (pass/fail) test." The process then proceeds to step 33, "Determine the quality measure to use." The process then proceeds to step 35, "Determine specification limits, decide on AQL and RQL." After step 35 is completed, the process continues to step 36, "Determine acceptance/rejection procedures, including rework provisions." The process then proceeds to step 38, "Determine sample size, lot size, sublot size." Step 39, "Develop OC curve and evaluate risks," follows from step 38.

Equation 10: Z equals a quotient with the numerator consisting of X minus Mu and the denominator consisting of Sigma.

Figure 12: Diagram. Illustration of the Calculation of the Z–statistic. This diagram shows a bell-shaped curve that represents a normal distribution. There is a vertical line at the center indicating an axis of symmetry about the mean, which is designated Mu. Near the right end of the curve is another vertical line that represents an X with a positive Z value. An arrow from the mean to this X value is labeled with the equation Z equals the quotient with X minus Mu in the numerator and with Sigma in the denominator. In the left half of the curve is another vertical line that represents an X with a negative Z value. An arrow from the mean to this X value is labeled with the equation Z equals the quotient with X minus Mu in the numerator and with Sigma in the denominator.

Equation 11: Q subscript L equals a quotient with X bar minus LSL in the numerator and with S in the denominator.

Equation 12:Q subscript U equals a quotient with USL minus X bar in the numerator and with S in the denominator.

Equation13: PWL subscript T equals PWL subscript U, plus PWL subscript L, minus 100.

Equation 14: Q subscript L equals a quotient with 25000 minus 21000 in the numerator and with 3400 in the denominator. This quotient then equals 1.18.

Figure 13: Diagram. Illustration of Positive Quality Index Values. This diagram Illustration of Positive Quality Index Values, is an illustration of positive Q values. There is a bell-shaped curve that represents a normal distribution with a vertical line that represents the mean, which is labeled X bar. Near the right end of the curve is another vertical line that represents USL. An arrow from the USL to the mean is labeled with the product Q subscript U multiplied by S. In the left half of the curve is another vertical line that represents LSL. An arrow from the LSL to the mean is labeled with the product Q subscript L multiplied by S. Illustration of a Negative Quality Index Value,

Figure 14: Diagram. Illustration of a Negative Quality Index Value. This diagram is an illustration of a negative Q value. There is a bell-shaped curve that represents a normal distribution with a vertical line that represents the mean, which is labeled X bar. Near the right end of the curve is another vertical line that represents USL. Between the mean and the USL there is another vertical line that represents the LSL. An arrow from the LSL to the mean is labeled with the product Q subscript L multiplied by S.

Figure 15: Diagram. Relationship between PWL and PD. There is a bell-shaped curve that represents a normal distribution. At the right edge of the curve is a line that represents the USL. Between the left edge and the center of the curve is another vertical line that represents the LSL. The area under the curve between the LSL and USL vertical lines is shaded and labeled as PWL. The area under the curve to the left of the LSL is not shaded and is labeled as PD.

Equation 15: AAD equals the quotient of a numerator consisting of the absolute value of the sum of X subscript I, minus T, and the denominator consisting of N.

Equation 16: CI equals the square root of the quotient of a numerator consisting of the sum of the square of the quantity X subscript I, minus T, and the denominator consisting of N.

Figure 16: Diagram. Illustration of the Moving Average. This diagram illustrates how a moving average of size n equals 4 works. There are six consecutive values, represented as X subscript 1 to X subscript 6. A line underscores the first four X values and indicates that these represent X bar subscript M1 and R subscript M1. Another line overscores X values 2 through 5 and indicates that these represent X bar subscript M2 and R subscript M2. Another bar underscores X values 3 through 6 and indicates that these represent X bar subscript M3 and R subscript M3.

Figure 17: Diagram. AQL Materialfor Example 6–1. There is a bell-shaped curve that represents a normal distribution with a vertical line that represents the mean, which is labeled Mu equals JMF. There are two more vertical lines that are equal distances from the mean. These distances are labeled as 1.645 times Sigma. The line on the left of the mean is labeled LSL while the one on the right is labeled USL. The standard deviation for the curve is labeled Sigma equals 0.18. The area under the curve between the LSL and the USL lines is shaded and is labeled 90 PWL.

Figure 18: Diagram. RQL Materialfor Example 6–1. There is a bell-shaped curve that represents a normal distribution with a vertical line that represents the mean, which is labeled Mu. About halfway between the mean and the right edge of the curve is another vertical line labeled JMF. An arrow from the JMF to the mean is labeled 0.25 percent. The standard deviation for the curve is labeled as Sigma equals 0.18. There are two more vertical lines that are equal distances of 0.30 percent from the JMF line. The line to the left of the JMF is also just to the left of the mean line and is labeled LSL. The line to the right of the JMF line is at the right edge of the normal curve and is labeled USL. The area under the curve between the LSL and the USL lines is shaded and labeled 61 PWL.

Figure 19: Diagram. AQL Materialfor the Example. There is a bell-shaped curve that represents a normal distribution with a standard deviation that is approximately equal to 1.1 percent. Near the right edge of the curve is a vertical line that is labeled 7.0 percent Satisfactory Value. The area under the curve to the right of this line is shaded and is labeled 10 PD. The area under the curve to the left of the vertical line is not shaded and is labeled 90 PWL (AQL). A little beyond the right edge of the curve is another vertical line that is labeled 10 percent Critical Value.

Figure 20: Diagram. RQL Materialfor the Example. There is a bell-shaped curve that represents a normal distribution with a vertical line that represents the mean, which is labeled 6.7 percent. The standard deviation for the curve is labeled as Sigma and is approximately equal to 1.1 percent. At the right edge of the curve is another vertical line that is labeled 10 percent Critical Value. The distance between the mean and this line is given as 3 multiplied by Sigma. Slightly to the right of the mean is another vertical line that is labeled 7.0 percent Satisfactory Value. The area under the curve to the right of this line is shaded and is labeled 40 PD. The area under the curve to the left of this line is not shaded and is labeled 60 PWL (RQL).

Equation 17: Z subscript 50 equals a quotient consisting of a numerator with 50 minus 75 and a denominator with 12.5. This quotient is then equal to negative 2.0. Also Equation 17: Z subscript 100 equals a quotient consisting of a numerator with 100 minus 75 and a denominator with 12.5. This quotient is then equal to positive 2.0.

Figure 21: Diagram. AQL Population for the Screening Test Example. There is a bell-shaped curve that represents a normal distribution with a standard deviation that is labeled as Sigma and equals 12.5 millimeters. A vertical line that represents the mean is labeled Mu equals 75 millimeters and is also labeled Target equals 75 millimeters. . There are two more vertical lines that are equal distances from the mean and near the edges of the curve. The line near the left edge is labeled LSL equals 50 millimeters, while the line near the right edge is labeled USL equals 100 millimeters. An arrow that runs from the mean line to the USL line is labeled plus 25 millimeters. Another arrow that runs from the mean to the LSL line is labeled minus 25 millimeters. The areas under the curve to the left of the LSL and to the right of the USL are shaded.

Figure 22. RQL Population for the Screening Test Example. There is a bell-shaped curve that represents a normal distribution with a standard deviation that is labeled as Sigma and equal to 12.5 millimeters. A vertical line that represents the mean is labeled Mu equals 100 millimeters and is also labeled USL equals 100 millimeters. Outside the left edge of the curve is another vertical line that is labeled LSL equals 50 millimeters. Midway between the LSL and the mean is another vertical line that is labeled Target equals 75 millimeters. An arrow that runs from the target line to the LSL line is labeled minus 25 millimeters. Another arrow that runs from the target to the USL line is labeled plus 25 millimeters. The area under the curve to the left of the USL is shaded.

Equation 18: PF equals 55 plus the product that results from multiplying 0.5 by PWL.

Figure 23: Chart. Example of Stepped and Continuous Payment Schedules. This chart plots "Pay Factor (Percent)" on the vertical axis against "PWL" on the horizontal axis. The vertical axis ranges from 50 to 110 and the horizontal axis ranges from 0 to 100. The continuous payment schedule is represented by a straight line that begins at a pay factor value of 55 for 0 PWL and increases to a pay factor value of 105 for 100 PWL. The stepped payment schedule begins at a pay factor value of 70 for 0 PWL and, in three pay factor increments, increases to a pay factor value of 100 for 100 PWL. Each increment is of a decreasing value.

Equation 19: PAYADJ equals a quotient with the numerator consisting of the quantity R raised to the D power, minus the quantity R raised to the E power. This result is then multiplied by C. The denominator consists of 1 minus the quantity R raised to the O power.

NO NUMBER Equation: PAYADJ equals a quotient consisting of a numerator with the quantity 0.963 raised to the tenth power, minus the quantity of 0.963, which has been raised to the eighth power. This quantity is then multiplied by 23.92 dollars. The denominator of the quotient consists of raising 0.963 to the tenth power and then subtracting the result from 1. This quotient is then equal to minus 4.09 dollars per square meter.

Equation 20: EXPLIF equals C subscript 0, plus the product that results from multiplying C subscript 1 by PD subscript VOIDS, plus the product that results from multiplying C subscript 2 by PD subscript THICK, plus the product that results from multiplying C subscript 3 by PD subscript VOIDS by PD subscript THICK.

Equation 21: EXPLIF equals 22.9 minus the product that results from multiplying 0.163 by PD subscript VOIDS minus the product that results from multiplying 0.135 by PD subscript THICK, plus the product that results from multiplying 0.000961 by PD subscript VOIDS by PD subscript THICK.

Equation 22: EXPLIF equals the quantity A multiplied by the quantity E that has been raised to the power represented by taking the negative of the following series: the product of B subscript 1 multiplied by PD subscript 1, plus the product of B subscript 2 multiplied by PD subscript 2. This series continues until the product of B subscript K multiplied by PD subscript K.

Equation 23: The natural log of EXPLIF equals the natural log of A minus the product that results from multiplying B subscript 1 by PD subscript VOIDS, minus the product that results from multiplying B subscript 2 by PD subscript THICK, minus the product that results from multiplying B subscript 3 by PD subscript SMOOTH.

Equation 24: EXPLIF equals 13.8 multiplied by E that has been raised to the power represented by the negative of the following: the product of 0.0126 multiplied by PD subscript VOIDS, plus the product of 0.0107 multiplied by PD subscript THICK, plus the product of 0.00924 multiplied by PD subscript SMOOTH.

Equation 25: PF equals the product that results from multiplying 0.2 by AV, plus the product that results from multiplying 0.1 by VMA, plus the product that results from multiplying 0.1 by AC plus the product that results from multiplying 0.6 by DEN.

Equation 26: PF equals the product that results from multiplying 0.35 by AV, plus the product that results from multiplying 0.1 by VMA, plus the product that results from multiplying 0.2 by AC plus the product that results from multiplying 0.35 by DEN.

Equation 27: PD star equals the product that results from multiplying 0.807 by PD subscript VOIDS, plus the product that results from multiplying 0.669 by PD subscript THICK, minus the product that results from multiplying 0.00476 by PD subscript VOIDS by PD subscript THICK.

Figure 24: Diagram. Examples of Random and Stratified Random Sampling. At the top of this diagram is a rectangle that represents a pavement lot. In the left half of this rectangle are five circles that represent randomly selected coring locations on the pavement. In the bottom half of the figure, the same rectangle has been divided into five equal-sized segments to represent five sublots. A circle is shown within each sublot to represent a random sample location within the sublot.

Figure 25: Chart. Flowchart for Risk Analysis Portion of Phase II. The flowchart begins with an arrow from step 38, "Determine sample size, lot size, sublot size," leading to step 39, "Develop OC curves, EP curve and evaluate risks." After step 39 is completed, step 40 then asks "Are risks acceptable?" If the answer is no, then the process proceeds to step 41, "Modify specification limits, acceptance limits, pay schedule, sample size, and/or lot size." After step 41 is completed, the process returns to performing steps 39 and 40, until the outcome is yes. The process then proceeds to step 42, "Finalized initial draft specification." Step 42 also has arrows pointing to it, indicating that step 18, "QC procedures and requirements completed" and step 22, "Develop validation/verification procedures," must also be performed before step can be completed. The flowchart concludes with an arrow from step 42, indicating that "Proceed to Phase III: Implementation" is the next stage in the process.

Figure 26: Diagram. Typical Operating Characteristic (OC) Curve for an Accept/Reject Acceptance Plan. This chart plots "Probability of Acceptance" ranging from 0 percent to 100 percent on the vertical axis against "Level of Quality" on the horizontal axis. The plot shows an elongated S-curve that increases from 0 probability of acceptance near the left edge of the horizontal axis to 100 percent probability of acceptance near the right edge of the horizontal axis. On the horizontal axis, the RQL is noted with a vertical line that extends upwards to meet the curve.At this point of intersection, there is also a horizontal line that extends to meet the vertical axis at a probability of acceptance value of approximately 10 percent. This probability of acceptance is labeled "Agency's Risk, b." On the horizontal axis the AQL is noted with a vertical line that extends upwards to meet the curve. At this point of intersection, there is also a horizontal line that extends to meet the vertical axis at a probability of acceptance value of approximately 90 percent. The difference between this probability of acceptance and 100 percent is labeled "Contractor's Risk, a."

Figure 27: Diagram. Typical Operating Characteristic (OC) Curves for an Acceptance Plan with Payment Adjustments. There is a plot with "Probability of Receiving greater than or equal to PF" ranging from 0 percent to 100 percent on the vertical axis. The horizontal axis is Level of Quality. The plot shows five elongated S-curves that each increase from 0 probability of acceptance near the left edge of the horizontal axis to 100 percent probability of acceptance near the right edge of the horizontal axis. From highest to lowest, these curves are labeled "PF equals 0.70," "PF equals 0.80," "PF equals 0.90," "PF equals 1.00," and "PF equals 1.04," respectively. On the horizontal axis, the RQL is noted with a vertical line that extends as far as the point indicating almost 100 percent probability of receiving payment factor equal to or greater than one. At the point this line intersects with the "PF equals 1.00" curve, there is a horizontal line that extends to meet the vertical axis at a probability value of approximately 6 percent. This probability is labeled "b." On the horizontal axis, the AQL is noted with a vertical line that extends as far as the point indicating almost 100 percent probability of receiving payment factor equal to or greater than one. At the point this line intersects with the "PF equals 1.00"curve, there is a horizontal line that extend to meet the vertical axis at a probability value of approximately 66 percent. The difference between this probability and 100 percent is labeled "a."

Figure 28: Diagram. Typical Expected Payment (EP) Curve. This chart plots "Expected Payment, percent" ranging from 50 to 110 on the vertical axis against "Level of Quality" on the horizontal axis. An elongated S-curve is shown that increases from 0 near the left edge of the horizontal axis to 100 near the right edge of the horizontal axis. On the horizontal axis, the RQL is noted with a vertical line that extends upwards to meet the curve. At this point of intersection, there is also a horizontal line that extends to meet the vertical axis at an expected payment value of approximately 70 percent. Also on the horizontal axis, the AQL is noted with a vertical line that extends upwards to meet the curve. At this point of intersection, there is also a horizontal line that extends to meet the vertical axis at an expected payment value of approximately 100 percent. There is also a horizontal line that runs from the highest right edge of the curve to a value of 102 on the vertical axis. This point is labeled "Maximum Payment Factor equals 102 percent."

Figure 29: Diagram. AQL Population for Simplified a and b Risks Example. There is a bell-shaped curve that represents a normal distribution with a vertical line at the center that indicates the mean. This line is labeled "Mu equals 6.00 percent" and is also labeled "Target equals 6.00 percent." The standard deviation for the curve is labeled "Sigma equals 0.20 percent."

Figure 30: Diagram. RQL Populations for Simplified a and b Risks Example. There are two bell-shaped curves that are side by side with the right edge of the curve on the left slightly overlapping the left edge of the curve on the right. Where these curves intersect, there is a vertical line that is labeled "Target equals 6.00 percent." The horizontal center of the left curve has a vertical line that is labeled "Mu equals 5.60 percent." The horizontal center of the right curve has a vertical line that is labeled "Mu equals 6.40 percent." Between these two Mu values is an arc that is labeled "Or." The standard deviation for each of the two curves is labeled "Sigma equals 0.20 percent."

Figure 31: Diagram. Illustration of the a Risk for Simplified Example. There is a bell-shaped curve that represents a normal distribution with a vertical line that indicates the mean. This line is labeled "Mu equals 6.00 percent" and is also labeled "Target equals 6.0 percent." The standard deviation for the curve is labeled "Sigma equals 0.20 percent." Near the left edge of the curve is a vertical line labeled "LSL equals 5.60 percent." Near the right edge of the curve is a vertical line labeled "USL equals 6.40 percent." The areas under the curve to the left LSL and to the right of the USL are shaded and each labeled "one-half a."

Figure 32: Diagram. Illustration of the b Risk for Simplified Example. There is a bell-shaped curve that represents a normal distributionwith a vertical line that indicates the mean. This line is labeled "Mu equals 6.00 percent." and is also labeled "LSL equals 5.60 percent." The standard deviation of the curve is labeled "Sigma equals 0.20 percent." Near the right edge of the curve is a vertical line labeled "Target equals 6.00 percent." Outside the right edge of the curve is another vertical line labeled "USL equals 6.40 percent." The area under the curve to the right of the vertical line labeled "Mu equals 5.60 percent" is shaded. This shaded area is labeled "b."

Figure 33: Diagram. OC Curve for Simplified a and b Risks Example. There is a bell-shaped curve that is centered at a value ILL "CENTERED" of 6.0 on a horizontal axis that is labeled "Population Mean, percent." The curve extends along the horizontal axis from a value of approximately 5.0 to 7.0. The vertical axis is labeled "Probability of Acceptance, percent," and ranges from 0 to 100. The standard deviation of the curve is noted "Sigma equals 0.20 percent." The value of 5.6 on the horizontal axis is labeled "RQL" and from this point a vertical line extends up to the curve at which point a horizontal line extends to a value of approximately 50 on the vertical axis. The value of 6.0 on the horizontal axis is labeled "AQL" and from this point a vertical line extends up to the curve at which point a horizontal line extends to a value of approximately 95 on the vertical axis.

Figure 34: Diagram. Histogram of PWL Estimates for Simplified PWL Example. This chart plots "Frequency, percent" on the vertical axis against the "Number of Blue Marbles" on the horizontal axis. The scale of the vertical axis ranges from 0 to 30 in increments of 10. The scale of the horizontal axis ranges from 0 to 7 in increments of 1, with each increment having a bar above it to indicate frequency. Thus, for each of the blue marble counts labeled as 0, 1, 2, 3, 4, 5, 6, and 7 there are corresponding frequencies of 3, 15, 21, 27, 23, 7, 3, and 1, respectively. In the upper right hand corner of the chart, sample size is indicated as 10 and the average is indicated as equaling 2.9, or 29 percent.

Figure 35: Diagram. OC Curve from OCPLOT for the Accept/Reject Acceptance Plan Example. This chart plots "Acceptance Probability" on the vertical axis against "Percent Within Limits" on the horizontal axis. The scale of the vertical axis ranges from 0.0 to 1.0. The scale of the horizontal axis ranges from 100 on the far left to 0 on the far right of the axis. On the plot there is a reversed elongated S-curve that decreases from an acceptance probability of 1.0 on the vertical axis for a PWL of 100 on the horizontal axis to an acceptance probability of 0 for a PWL of approximately 25 on the horizontal axis. At a PWL value of 50 on the horizontal axis, the RQL is noted with a vertical line that extends up to meet the curve. At this point of intersection, there is also a horizontal line that extends to meet the vertical axis at an acceptance probability of approximately 0.16. At a PWL of 90 on the horizontal axis, the AQL is noted with a vertical line that extends up to meet the curve. At this point of intersection, there is a horizontal line that extends to meet the vertical axis at an acceptance probability of approximately 0.93.

Equation 28. PF equals 55 plus the product that results from multiplying 0.50 by the PWL.

Figure 36: Diagram. EP Curve from OCPLOT for the Payment Adjustment Acceptance Plan Example. This chart plots "Expected Pay Factor" axis on the horizontal axis against "Percent Within Limits" on the horizontal axis. The scale of the vertical axis ranges from 0 to 120. The scale of the horizontal axis ranges from 100 on the far left to 0 on the far right of the axis. On the plot a straight line representing an inverse linear relationship extends from a value of 105 on the vertical axis for a value of 100 on the horizontal axis to a value of 57.5 on the vertical axis for a value of 5 on the horizontal axis. On the horizontal axis, at a PWL value of 50, the RQL is noted with a vertical line that extends up to meet the curve. At this point of intersection, there is also a horizontal line that extends to meet the vertical axis at an expected pay factor of 80. On the horizontal axis, at a PWL of 90, the AQL is noted with a vertical line that extends upwards to meet the curve. At this point of intersection, there is also a horizontal line that extends to meet the vertical axis at an expected pay factor of 100.

Figure 37: Diagram. Histogram for an AQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 4. This shows two histograms, one for the distribution of "PWL Estimates" and below it, one for the distribution of "Pay Factors." The top histogram has a label stating "Performance at AQL." To the left of the histogram is noted that the PWL, then in parentheses, AQL, is equal to 90. The horizontal axis of the histogram has a scale that ranges from 0 to 100. There is no vertical axis as such but there is label to the left of the histogram that states "PWL Estimates." On the histogram are bars whose heights represent the relative frequency of PWL Estimates for each sample represented on the horizontal scale. The lowest estimated PWL corresponds to a horizontal axis value of approximately 43. Between the approximate values of 43 and 59 on the horizontal axis, are seven bars of a similar low PWL estimate. These bars are spread out unevenly at values of approximately 44, 45, 49, 52, 53, 55, 56, and 58. From a horizontal axis value of 59 to value of approximately 72, these bars are of the same low height. Between a horizontal axis value of approximately 73 and 99, the bars are of a slightly higher and fluctuating height. There is a very tall bar at the horizontal axis value of 100.

The second histogram displays a similar distribution and frequency as the first histogram. The scale of the second histogram's horizontal axis ranges from 0 to 110. Below the horizontal axis is a note that indicates that the average pay factor is equal to 100.0. There is no vertical axis as such but there is a label to the left of the histogram that states "Pay Factors." At horizontal axis values of approximately 76, 77, and 79 to 85, the bars are all of similar low heights. Between horizontal axis values of 86 and 99, the bars have slightly higher and fluctuating heights. There is a very tall bar that corresponds to a horizontal axis value of 105.

 

Figure 38: Diagram. Histogram for an RQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 4. This shows two histograms, one for the distribution of "PWL Estimates" and below it, one for the distribution of "Pay Factors." The top histogram has a label stating "Performance at RQL." To the left of the histogram is noted that the PWL, then in parentheses, RQL, is equal to 50. The horizontal axis of the histogram has a scale that ranges from 0 to 100. There is no vertical axis as such but there is label to the left of the histogram that states "PWL Estimates." On the histogram are bars whose heights represent the relative frequency of PWL Estimates for each sample represented on the horizontal scale. The distribution and frequency of the bars appear to be bell-shaped with the peak at around 45. The left and right tails of the curve extend to horizontal axis values of approximately 2 and 98. There are also tall bars that correspond to horizontal axis values of 0 and 100.

The second histogram displays a similar distribution and frequency as the first histogram. The scale of the second histogram's horizontal axis ranges from 0 to 110. Below the horizontal axis is a note that indicates that the average pay factor is equal to 80.0. There is no vertical axis as such but there is a label to the left of the histogram that states "Pay Factors." The distribution and frequency of the bars appear to be bell-shaped with the peak at around 77. The left and right tails of the curve extend to approximately 56 and 104 on the horizontal axis. There are also tall bars that correspond to horizontal axis values of approximately 55 and 105.

 

Figure 39: Diagram. Histogram for an AQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 20. This shows two histograms, one for the distribution of "PWL Estimates" and below it, one for the distribution of "Pay Factors." The top histogram has a label stating "Performance at AQL." To the left of the histogram is noted that the PWL, then in parentheses, AQL, is equal to 90. The horizontal axis of the histogram has a scale that ranges from 0 to 100. There is no vertical axis as such but there is label to the left of the histogram that states "PWL Estimates." On the histogram are bars whose heights represent the relative frequency of PWL Estimates for each sample represented on the horizontal scale. The distribution and frequency of the bars appear to indicate negative skewness in that the majority of the data are skewed towards the right and the tail is towards the left, with the peak at around 89 on the horizontal axis. The left and right tails of the curve extend to horizontal axis values of approximately 73 and 99.

The second histogram displays a similar distribution and frequency as the first histogram. The scale of the second histogram's horizontal axis ranges from 0 to 110. Below the horizontal axis is a note that indicates that the average pay factor is equal to 100.0. There is no vertical axis as such but there is a label to the left of the histogram that states "Pay Factors." The distribution and frequency of the bars appear to indicate negative skewness in that the majority of the data are skewed towards the right and the tail is towards the left, with the peak at around 99 on the horizontal axis. The left and right tails of the curve extend to approximately 56 and 104 on the horizontal axis.

 

Figure 40: Diagram. Histogram for an RQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 20. This shows two histograms, one for the distribution of "PWL Estimates" and below it, one for the distribution of "Pay Factors." The top histogram has a label stating "Performance at RQL." To the left of the histogram is noted that the PWL, then in parentheses, RQL, is equal to 50. The horizontal axis of the histogram has a scale that ranges from 0 to 100. There is no vertical axis as such but there is label to the left of the histogram that states "PWL Estimates." On the histogram are bars whose heights represent the relative frequency of PWL Estimates for each sample represented on the horizontal scale. The distribution and frequency of the bars appear to be bell-shaped with the peak at around 47. The left and right tails of the curve extend to horizontal axis values of approximately 33 and 75, with one additional low bar at about 84.

The second histogram displays a similar distribution and frequency as the first histogram. The scale of the second histogram's horizontal axis ranges from 0 to 110. Below the horizontal axis is a note that indicates that the average pay factor is equal to 80.0. There is no vertical axis as such but there is a label to the left of the histogram that states "Pay Factors." The distribution and frequency of the bars appear to be bell-shaped with the peak at around 80. The left and right tails of the curve extend to approximately 72 and 92 on the horizontal axis, with one additional bar of a low height at about 96.

Figure 41: Diagram. OC Curves for a Sample of Size 4 Using the Payment Relationship in Equation 28. This chart plots the "Probability of Receiving greater than or equal to PF" on the vertical axis against the "Population PWL, percent" on the horizontal axis. The scale of the vertical axis ranges from 0 to 100. The scale of the horizontal axis ranges from 0 to 100. There are five elongated S-curves plotted that each increase from 0 near the left edge of the horizontal axis to 100 near the right edge of the horizontal axis. From highest to lowest positions on the plot, these curves are labeled "PF equals 70 percent," "PF equals 80 percent," "PF equals 90 percent," "PF equals 100 percent," and "PF equals 104 percent," respectively. On the horizontal axis at a PWL of 50, the RQL is noted with a vertical line that extends upwards. As it does so, this line crosses the 104, 100, 90, 80, and 70 pay factor lines at probabilities of approximately 4, 5, 15, 45, and 90 respectively. On the horizontal axis, at a PWL of 90, the AQL is also noted with a vertical line that extends upwards. As it does so, this line crosses the 104, 100, 90, 80, and 70 pay factor lines at probabilities of approximately 48, 58, 90, 100, and 100, respectively.

Figure 42: Chart. Flowchart for Phase 3—Implementation. This chart presents a flowchart with boxes representing steps in the process. Step 1, "Simulate specification," is divided into the following five subtasks:

1.1. Use several projects under construction or recently completed

1.2. Be sure random sampling was used

1.3. Use same sampling and testing procedures as decided upon in Phase 2

1.4. Analyze simulated payment factor data

1.5. Revise or fine-tune as necessary for a Draft Special Provision

After step 1 is complete,

step 2, "Begin/continue technician qualification training" can begin. Step 2 is divided into two subtasks:

2.1. Include training in sampling and testing procedures

2.2. Include training in basic statistical procedures

The third step is "Try specification on a limited number of pilot projects." The subtasks in this step are:

3.1. Let projects using Draft Special Provision (Item 1.5)

3.2. Apply only a percentage of the disincentives

3.3. Bid prices may not reflect future project prices

After step 3 is complete, the process continues to step 4, "Analyze pilot project results." Step 5 asks whether major revisions to the draft specification are needed. If the answer is yes, then the process proceeds to step 6, "Prepare new draft special provision." The process then returns to steps 3, 4, 5, and 6 until no major revisions are needed. The process then proceeds to step 7, "Phase in projects agency-wide," which has two subtasks:

7.1. Phase in until all major projects are included

7.2. Phase in payment factors

The flowchart concludes with step 8, "Ongoing monitoring of specification performance," which has six subtasks:

8.1. Evaluate quality levels achieved each year

8.2. Look for administrative problems

8.3. Consider contractor concerns

8.4. Identify technology changes

8.5. Tie results into the pavement management system

8.6. Compare with established criteria for success

Equation 29: If PD is less than 50, then PA equals 3.0 minus the product of 0.3 multiplied by PD.

Equation 30: If PD is greater than or equal to 50, then PA equals 26.0 minus the product of 0.76 multiplied by PD.

Equation 31: EXPLIF equals C subscript zero, plus the product that results from multiplying C subscript 1 by PD subscript VOIDS, plus the product that results from multiplying C subscript 2 by PD subscript THICK, plus the product that results from multiplying C subscript 3 by PD subscript VOIDS by PD subscript THICK.

Equation 32: EXPLIF equals 22.9 minus the product that results from multiplying 0.163 by PD subscript VOIDS, then minus the product that results from multiplying 0.135 by PD subscript THICK, then plus the product that results from multiplying 0.000961 by PD subscript VOIDS by PD subscript THICK.

Equation 33. PD star equals the product that results from multiplying 0.807 by PD subscript VOIDS, then plus the product that results from multiplying 0.669 by PD subscript THICK, then minus the product that results from multiplying 0.00476 by PD subscript VOIDS by PD subscript THICK.

Figure 43: Diagram. Graph of Composite RQL Provision Given in Equation 33: This chart plots "PD subscript THICK" on the vertical axis against "PD subscripts VOIDS" on the horizontal axis. The scales of the vertical and horizontal axes range from 0 to 100. The values plotted are shown as a concave downward line that intersects the vertical axis at a PD subscript THICK value of approximately 95 for a PD subscript VOIDS value of 0 and extends to meet the horizontal axis at a PD subscript THICK value of 0 for a PD subscript VOIDS value of approximately 79. The region above the line is labeled "Rejectable," while the region below the line is labeled "Acceptable with Pay Adjustment."

Equation 34. For PD star of less than 40, PPA equals 10 minus the product that results from multiplying 0.67 by PD star

Equation 35. For PD star greater than or equal to 40, PPA equals 116 minus the product that results from multiplying 3.32 by PD star. The minimum value for PPA equals minus 100.

Equation 36. For PD subscript SMOOTH less than 2.0, PA equals 0.34 minus the product that results from multiplying 0.26 by PD subscript SMOOTH. The units are dollars per square meter.

Equation 37. For PD subscript SMOOTH greater than or equal to 2.0, PA equals 0.72 minus the product that results from 0.45 by PD subscript SMOOTH. The units are dollars per square meter.

Figure 44. Diagram. Outline of NJDOT Superpave Acceptance Procedure. This table is titled, "Base Course Air Voids and Surface Course Air Voids and Total Thickness" and lists multiple equations. The Compute Composite Quality Measure, noted as PD star, is shown to be equal to the product of 0.807 multiplied by PD subscript VOIDS, plus the product of 0.669 multiplied by PD subscript THICK, minus the product of 0.00476 multiplied by PD subscript VOIDS then multiplied by PD subscript THICK. There is a note after this equation that states "if base course, or no total thickness requirement, use PD subscript THICK equals 10 to compute PD star. Next, the Compute Percent Payment Adjustment, noted as PPA is shown to be based on the following components. For Mainline, Ramps and New Shoulders, if PD star is less than 40, then PPA equals 10 minus the product that results from multiplying 0.67 by PD star.

If PD star is greater than or equal to 40, then PPA equals 116 minus the product that results from multiplying 3.32 by PD star, with the minimum value of minus 100 percent. There is a note that indicates to retest if PD star is greater than or equal to 40, and to reject if PD star is greater than or equal to 65. For Existing Shoulders, it is the same as new shoulders except to multiply computed PPA by 0.5, with a minimum value of minus 100 percent. There is then a section titled "Surface Smoothness" and in parentheses, "Interim Procedure Until New Device is Selected." Under this title is the Compute Payment Adjustment, noted as PA and expressed in units of dollars per square meter. For this adjustment, if PD subscript SMOOTH is less than 2.0, then PA equals 0.34 minus the product that results from 0.26 multiplied by PD subscript SMOOTH.

If PD subscript SMOOTH is greater than or equal to 2.0, then PA equals 0.72 minus the product that results from 0.45 multiplied by PD subscript SMOOTH. There is a note that indicates to retest if PD subscript SMOOTH is greater than or equal to 2.0, and to reject if PD subscript SMOOTH is greater than or equal to 3.5.

Figure 45: Chart. Proposed Smoothness Acceptance Procedure Based on IRI. This is a flow chart that begins with the box "ARAN (Continuous Reporting)." This box then leads to a second box "Compute N subscript 100 and PD subscript 80." The next step asks the question "Is N subscript 100 greater than 0 or is PD subscript 80 greater than or equal to 30?" If the answer is "no," then the next step is to compute PA from PD subscript 80. This then leads to the final step, which is to "Apply PA." If the answer to the question is "yes," then the next step is for NJDOT to retest with the RSE. Then the chart proceeds to the question "Is the average PDL greater than or equal to 3.5 or is there a 100-foot section with PDL greater than or equal to 4.0?" If the answer is "no" the next step is to "Compute PA from PDL," which then leads to the final step, "Apply PA." If the answer to the question is "yes," then the next step provides the NJDOT with the following three options: The first is to require removal and replacement at expense of contractor. The second is to allow the contractor to remove and replace or accept payment reduction of minus 5,000 dollars per lane mile. The third option is to allow the contractor to submit corrective action plan but, if this is not accepted, then Option 1 or Option 2 applies. An arrow then leads to the statement "If removal and replacement or other corrective action is performed, testing process is repeated. Otherwise payment adjustment is applied."

Equation 38: EXPLIF equals A multiplied by E. E has been raised to the power that results from multiplying PD raised to the power of C by negative B.

Equation 39. EXPLIF equals 12 times E. E has been raised to the power that results from multiplying PD subscript 80 raised to the power of 0.992 by negative 0.0186.

Equation 40. PAYADJ equals a quotient with the numerator consisting of subtracting R raised to the E power from R raised to the D power. This result is then multiplied by C. The denominator consists subtracting R raised to the O power from 1.

Figure 46: Diagram. Proposed Smoothness Acceptance Procedure Based on IRI. This chart plots "Pay Adjustment" on the vertical axis against "PD subscript 80" on the horizontal axis. The unit of the vertical axis is 1,000 dollars per lane mile and the scale ranges from minus 150,000 dollars per lane mile to plus 50,000 dollars per land mile. There is a note adjacent to the vertical axis that states the following: 1,000 dollars per lane mile divided by 1.61 is equal to 1,000 dollars per lane kilometer. The scale of the horizontal axis ranges from is "PD subscript 80" ranging from 0 to 100. On the plot, there is a straight line representing a linear relationship that intersects the vertical axis at positive 12,500 dollars for a PD subscript 80 value of 0 and extends to a value of approximately minus 106,250 dollars for a PD subscript 80 value of 95. This line is labeled "PAYADJ equals 12,500 minus the product that results from multiplying 1250 by PD subscript 80." On the plot there is another line that is dashed and slightly concaves upwards. This line intersects the vertical axis at a value of approximately plus 18,000 dollars for a PD subscript 80 value of 0 and extends to a value of approximately minus 100,000 dollars for a PD subscript 80 value of 85. This line is labeled "Empirical Relationship."

Equation 41: PAYADJ equals 12,500 minus the product that results from multiplying 1250 by PD subscript 80.

Equation 42. PAYADJ equals 5,000 minus the product that results from multiplying 500 by PD subscript 80.

Equation 43. PAYADJ equals 3,000 minus the product that results from multiplying 2,308 by PDL.

Figure 47: Chart. Flowchart of 23 CFR 637B. The flow chart begins with a title box that states "Quality Assurance Program, 23 CFR 637b." An arrow leads from this box to a box directly beneath it that has its title,

"Applies to all NHS Projects, and program must include." The following elements are listed under this title:

1.     SHA central laboratory to be AAP (or comparable) by June 30, 1997

2.     All other laboratories to be qualified by June 29, 2000

3.     All personnel to be qualified by June 29, 2000"

Two arrows, each labeled as "mandatory," lead from this box to one of two parallel paths through the flow chart. The parallel paths are laid out on the left and right portions of the chart.

The mandatory path on the left portion of the flowchart begins with a box labeled "Material Acceptance Program." An arrow leads from this box to the next box that has its title,

"Program must include." The following elements are listed under this title:

1.     Frequency Guide

2.     Random Sample Locations

3.     Material Quality Attributes

4.     Validation through the IAP

Two arrows, each labeled "Option," lead from this box to one of two parallel paths. The path on the outer left begins with a box labeled "SHA Verification Sampling & Testing." An arrow leads from this box to a next box that states, "Conventional S&T and IAST criteria apply." The path on the inner right starts with a box labeled "SHA verification and Contractor Quality Control Sampling & Testing." An arrow leads from this box to a box that states the following:

"Program must include:

1.     Contractor Quality Control validated by independent SHA verification

2.     Dispute resolution system"

The two optional paths then converge into a single arrow that leads to a box that states, "Project Materials Certification to FHWA for non exempt projects only."

The mandatory path on the right portion of the flowchart beings with a box labeled "Independent Assurance Program." Two arrows, each labeled "Option" lead from this box to one of two parallel paths. The path on the outer right begins with a box that is labeled "Non-SHA administered." An arrow leads from this box to a box that states, "All laboratories must be AAP by June 29, 2000." The other option path, which is on the inner left, begins with a box labeled "SHA administered." An arrow leads from this box to converge with the arrow coming from the "All laboratories must be AAP by June 29, 2000" box. The single arrow that results from this convergence then leads to a box that states, "IAST frequency based on Time or Units." The process then proceeds to a box that states the following:

"Equipment evaluated by:

1.     Calibration

2.     Split or Proficiency samples"

This is followed by a box that states the following:

"Personnel evaluated by:

1.     Split or Proficiency Samples

2.     Limited Observations"

This is followed by a box that states, "Prompt laboratory comparison of IAST with the Acceptance Program." Two arrows, each labeled "Option," lead from this box to one of two paths. The path on the outer right edge begins with a box that states "System Basis of IAST," and then leads to "Annual Report to the FHWA." The path on the inner left edge starts with a box that states "Project Basis of IAST," and then leads to "Project Materials Certification to the FHWA for non-exempt projects only."

Equation 44: The square of S subscript C equals 0.061.

Equation 45: The square of S subscript A equals 0.097.

Equation 46: F equals a quotient with the square of S subscript A in the numerator and the square of S subscript C in the denominator. This quotient then equals a quotient with 0.097 in the numerator and 0.061 in the denominator. This then equals 1.59.

Equation 47: The square of S subscript C equals 1.036. 

Equation 48: The square of S subscript A equals 10.299.

Equations 49: F equals a quotient with the square of S subscript A in the numerator and the square of S subscript C in the denominator. This quotient then equals a quotient with 10.299 in the numerator and 1.036 in the denominator. This then equals 9.94.

Equation 50: X bar subscript C equals 6.10.

Equation 51: X bar subscript A equals 5.70.

Equation 52: There are two parts to this equation. (STATE THAT The FIRST PART first part of the equation is the equation itself, and the second part of the equation is the equation with actual values inserted. LGEBRA AND THE SECOND PART THE VALUES SUBTITUTED INIn the first part, the square of S subscript P equals a quotient. The numerator of this quotient consists of the addition of the following two terms. The first term is the product that results from multiplying the square of S subscript C by the quantity N subscript C minus 1. The second term is This is added to the product that results from multiplying the square of S subscript A by the quantity of N subscript A minus 1. The denominator of the quotient is the sum of N subscript C plus N subscript A minus 2.

In the second part, the square of S subscript P equals a quotient. The numerator of this quotient consists of the addition of the following two terms. The first term is the product that results from multiplying 0.061 by the quantity 12 minus 1. The second term is the product that results from multiplying 0.097 by the quantity 6 minus 1. The denominator of the quotient is 12 plus 6 minus 2. This quotient then equals 0.072.

Equation 53: There are two parts to this equation. The first part of the equation is the equation itself, and the second part of the equation is the equation with actual values inserted. In the first part, T equals a quotient. The numerator of this quotient consists of the absolute value of the quantity X bar subscript C minus X bar subscript A. The denominator of the quotient is the square root of the sum of two quotients. The numerator of the first quotient is the square of S subscript P and the denominator is N subscript C. The numerator of the second quotient is the square of S subscript P and the denominator is N subscript A.

In the second part, T equals a quotient. The numerator if this quotient consists of the absolute value of the quantity 6.10 minus 5.70. The denominator of the quotient is the square root of the sum of two quotients. The numerator of the first quotient is 0.072 and the denominator is 12. The numerator for the second quotient is 0.072 and the denominator is 6. The quotient then equals 2.981.

Equation 54: X bar subscript C equals 6.24. 

Equation 55: X bar subscript A equals 7.32.

Equation 56: There are two parts to this equation. The first part of the equation is the equation itself, and the second part of the equation is the equation with actual values inserted. In the first part, T equals a quotient. The numerator of this quotient consists of the absolute value of the quantity X bar subscript C minus X bar subscript A. The denominator of the quotient is the square root of the sum of two quotients. The numerator of the first quotient is the square of S subscript C and the denominator is N subscript C. The numerator for the second quotient is the square of S subscript A and the denominator is N subscript A.

In the second part, T equals a quotient. The numerator if this quotient consists of the absolute value of the quantity 6.24 minus 7.32. The denominator of the quotient is the square root of the sum of two quotients. The numerator of the first quotient is 1.036 and the denominator is 10. The numerator of the second quotient is 10.299 and the denominator is 5. The quotient then equals 0.734.

Equation 57: There are two parts to this equation. The first part of the equation is the equation itself, and the second part of the equation is the equation with actual values inserted. In the first part, F prime equals a principal quotient minus 2. The numerator of This principal quotient is the square of the sum of two quotients. The first quotient has the square of S subscript C in the numerator and N subscript C in the denominator. The second sub quotient has the square of S subscript A in the numerator and N subscript A in the denominator. The denominator of the main quotient is the sum of two quotients. The numerator of the first quotient consists of dividing the square of S subscript C by N subscript C, and then squaring the result. The denominator of the first quotient consists of N subscript C plus 1. The numerator of the second quotient consists dividing the square of S subscript A by N subscript A, and then squaring the result. The denominator of the second quotient consists of N subscript A plus 1.

In the second part, F prime equals a principal quotient minus 2. This is then equal to 4.61, which is rounded to 5. The numerator of the principal quotient is the square of the sum of two quotients. The first quotient has 1.036 in the numerator and 10 in the denominator. The second quotient has 10.299 in the numerator and 5 in the denominator. The denominator of the principal quotient is the sum of two quotients. The numerator of the first quotient consists of dividing 1.036 by 10, and then squaring the result. The denominator of the first quotient consists of 10 plus 1. The numerator of the second quotient consists of dividing 10.299 by 5. The denominator of the second quotient consists of 5 plus 1.

Figure 48: Diagram. Excel Results for Data from Example Problem 1. This is a diagram of a section of an excel computer spreadsheet. There are three columns labeled A, B, and C, respectively, with data only in columns A and B. Column A is labeled "Contractor," and lists the following values in each cell: 6.41, 6.23, 6.08, 6.55, 6.11, 5.97, 6.28, 6.07, 5.92, 5.76, 6.06, and 5.71. These cells correspond to rows 2 through 13, respectively. Column B is labeled "Agency," and lists the following values in each cell: 5.42, 5.78, 6.23, 5.38, 5.62, and 5.79. These cells correspond to rows 2 through 13, respectively. Below these values, one of the spreadsheet cells is labeled "F-test" and has a corresponding value of 0.48403927. Another cell is labeled "T-test" and has a corresponding value of 0.00985564.

Figure 49: Diagram. Excel Results for Data from Example Problem 2. This is a diagram of a section of an excel computer spreadsheet. There are three columns labeled A, B, and C, respectively, with data only in columns A and B. Column A. Column A is labeled "Contractor," and lists the following values in each cell: 6.42, 7.18, 5.04, 4.56, 7.12, 7.98, 6.32, 6.08, 5.92, and 5.78. These cells correspond to rows 2 through 11, respectively. Column B is labeled "Agency," and lists the following values in each cell: 7.52, 11.38, 9.2, 5.32, and 3.18. These cells correspond to rows 2 through 6, respectively. Below these values, one of the spreadsheet cells is labeled "F-test" and has a corresponding value of 0.00465863. Another cell is labeled "T-test" and has a corresponding value of 0.49995598.

Figure 50: Diagram. OC Surface for the D2S Test Method Verification Method (Assuming the smaller σ = σtest). This is a three-dimensional plot with "Mean Difference, in ssigma subscript test units," ranging from 0 to 3, on the horizontal axis. On the other horizontal axis, which is at a 45-degree angle from the first axis, is "Standard Deviation Ratio," ranging from 0 to 5. The vertical axis is labeled "Probability of Detecting a Difference, percent" and the scale ranges from 0 to 80. On these three axes is represented a surface that is almost rectangular in shape and is bounded by the following four corners. The corner in the lower right hand corner of the chart has values of 0 "Probability of Acceptance" for a "Mean Difference" of 0 and a "Standard Deviation Ratio" of 0. The corner in the upper right hand corner has values of 59 for a "Mean Difference" of 0 and a "Standard Deviation Ratio" of 5. The corner in the lower left hand corner of the chart has values of about 57 for a "Mean Difference" of 3 and a "Standard Deviation Ratio" of 0. The corner in the upper left hand corner of the chart has values of to about 59 for a "Mean Difference" of "Probability of Acceptance" of about 65 for a "Mean Difference" of 3 and a "Standard Deviation Ratio" of 5.

Figure 51. OC Curves for a Two-Sided T-Test, α = 0.05. This is a plot with "Standardized Difference, D," ranging from 0 to 3 on the horizontal axis, and with "Probability of Not Detecting a Difference, b," ranging from 0 to 1.0 on the vertical axis. There are 13 curves on the plot, one for each of the following N values, where N is sample size: 2, 3, 4, 5, 7, 10, 15, 20, 30, 40, 50, 75, and 100. All of the curves begin at a value of 0.95 "Probability of Not Detecting a Difference" for a "Standardized Difference" of 0. Each of the curves decreases in "Probability of Not Detecting a Difference" as the "Standardized Difference" increases. The curve for N equals 2 has the least steep slope and is at the top of the curves represented on the plot, while the curve for N equals 100 has the steepest slope and is the bottom curve represented. The curve for N equals 2 reaches a "Probability of Not Detecting a Difference" value of about 0.73 for a "Standardized Difference" of 3. The curve for N equals 3 reaches a "Probability of Not Detecting a Difference" value of about 0.31 for a "Standardized Difference" of 3. The curve for N equals 100 reaches a "Probability of Not Detecting a Difference" value of 0 for a "Standardized Difference" of about 0.5.

Figure 52: Diagram. OC Curves for a Two - Sided T-Test, α = equals 0.01. This is a plot with "Standardized Difference, D," ranging from 0 to 3.2 on the horizontal axis, and with "Probability of Not Detecting a Difference, b," ranging from 0 to 1.00 on the vertical axis. There are 12 curves on the plot, one for each of the following N values, where N is sample size: 3, 4, 5, 7, 10, 15, 20, 30, 40, 50, 75, and 100. All of the curves begin at a value of 0.99 "Probability of Not Detecting a Difference" for a "Standardized Difference" of 0. Each of the curves decreases in "Probability of Not Detecting a Difference" as the "Standardized Difference" increases. The curve for N equals 3 has the least steep slope and is at the top of the curves represented on the plot, while the curve for N equals 100 has the steepest slope and is at the bottom. The curve for N equals 3 reaches a "Probability of Not Detecting a Difference" value of about 0.72 for a "Standardized Difference" of 3.2. The curve for N equals 4 reaches a "Probability of Not Detecting a Difference" value of about 0.32 for a "Standardized Difference" of about 3.1. The curve for N equals 100 reaches a "Probability of Not Detecting a Difference" value of 0 for a "Standardized Difference" of about 0.5.

Figure 53: Diagram. OC Curves for the Two - Sided F-Test for Level of Significance, α = 0.05. This is a plot with "Lambda," ranging from 0 to 4.00 on the horizontal axis, and with "Probability of Accepting, H subscript zero," ranging from 0 to 1.00 on the vertical axis. There are 13 curves on the plot, one for each of the following N subscript X equals N subscript Y values: 3, 4, 5, 6, 7, 8, 9, 10, 16, 21, 31, 51, and 101. The curve for N equals 3 is placed highest on the plot and the curve for N equals 101 is placed lowest. All of the curves pass through a value of 0.95 "Probability of Accepting" for a "Lambda" value of 1.00. To the left of this point, each of the curves decreases steeply to reach a "Probability of Accepting" value of 0. The value of "Lambda" ranges from 0 for the curve for N equals 3 to approximately 0.62 for the curve N equals 101. To the right of this point, each of the curves more gently decreases to reach "Probability of Accepting" values between 0 and 0.69 and "Lambda" values between approximately 1.55 and 4.00. The curve for N equals 3 reaches a "Probability of Accepting" value of about 0.69 for a "Lambda" of 4.00. The curve for N equals 4 reaches a "Probability of Accepting" value of about 0.50 for a "Lambda" of 4.00. The curve for N equals 101 reaches a "Probability of Accepting" value of 0 for a "Lambda" of about 1.55.

Figure 54: Diagram. OC Curves for the Two Sided F-Test for Level of Significance, α = 0.01. This is a plot with "Lamda," ranging from 0 to 4.00 on the horizontal axis, and with "Probability of Accepting, H subscript zero," ranging from 0 to 1.00 on the vertical axis. There are 13 curves on the plot, one for each of the following N subscript X equal N subscript Y values: 3, 4, 5, 6, 7, 8, 9, 10, 16, 21, 31, 51, and 101. The curve for N equals 3 is placed highest on the plot and the curve for N equals 101 is placed lowest. All of the curves pass through a value of 0.99 "Probability of Accepting" for a "Lambda" value of 1.00. To the left of this point, each of the curves steeply decreases to reach a "Probability of Accepting" value of 0. The value of "Lambda" ranges from 0 for the curve for N equals 3 to approximately 0.60 for the curve N equals 101. To the right of this point, each of the curves more gently decreases to reach "Probability of Accepting" values between 0 and 0.92 and "Lambda" values between approximately 1.60 and 4.00. The curve for N equals 3 reaches a "Probability of Accepting" value of about 0.92 for a "Lambda" of 4.00. The curve for N equals 4 reaches a "Probability of Accepting" value of about 0.81 for a "Lambda" of 4.00. The curve for N equals 101 reaches a "Probability of Accepting" value of 0 for a "Lambda" of about 1.60.

Figure 55: Diagram. OC Curves for the Single Agency Test Method. This is a chart that plots the "Difference in Population Means, Delta equals Sigma divided into the quantity Mu subscript A minus Mu subscript B" on the horizontal axis against the "Probability of Detecting a Difference, 1 minus b" on the vertical axis. The scale of the horizontal axis ranges from 0.0 to 3.0 and the scale of the vertical axis ranges from 0 percent to 60 percent. There are six slightly upward concave curves on the plot, one for each of the following values of N: 5, 6, 7, 8, 9, and 10. Each curve begins at a "Probability of Detecting a Difference" value of about 3 percent for a "Difference in Population Means" value of 0. The curves are plotted with increasing slope as the "Difference in Population Means" value increases to 3.0. At the point that each curve reaches a "Difference in Population Means" value of 3.0, the "Probability of Detecting a Difference" values are approximately 33, 41, 45, 52, 53, and 57 percent for values of N equal to 5, 6, 7, 8, 9, and 10, respectively.

Figure 56: Diagram. Example Frequency Histogram. This is a plot with the values on the vertical axis ranging from 0 to 35. On the horizontal axis are 11 bars, corresponding to horizontal axis values of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, and 55 and to vertical axis values of approximately 2.5, 5, 10, 18, 28, 33, 25, 20, 11, 5, and 2.5, respectively. The histogram represents data that appears to be normally distributed: the heights of the bars are approximately symmetric about the center bar, which is the highest, and decrease almost equally out towards the bars with horizontal axis values of 5 and 55.

Figure 57: Diagram. Example of a Skewed Frequency Histogram. This is a plot with the values on the vertical axis ranging from 0 to 45. On the horizontal axis are 10 bars, corresponding to horizontal axis values of 82, 84, 86, 88, 90, 92, 94, 96, 98, and 100 and to vertical axis bars of approximately 2.5, 5, 11, 18, 27.5, 34.5, 42.5, 35, 25.5, and 24.5, respectively. The histogram appears to present data that is not normally distributed in that the majority of the data are skewed towards the right and the tail is towards the left, indicating negative skewness.

Figure 58: Diagram. Normal Probability Paper. This is a plot of graph paper with a normal arithmetic axis for the horizontal axis. The vertical axis, which runs from 0.01 percent to 99.99 percent, is scaled such that a Cumulative Distribution Function for a Normal Distribution will plot as a straight line. This is accomplished by plotting the vertical axis such that the increments between percentage points are small for values close to a value of 50 percent. These increments increase as the distance from a value of 50 increases. As the values become as small as 1 or as large as 99, the incremental distances between tenths of a percent increase slightly.

Figure 59: Diagram. Normal Probability Plot for Grouped Data Example. This is a plot of graph paper with a normal arithmetic axis, ranging from values of 80 to 120, for the horizontal axis. The vertical axis, which runs from 0.01 percent to 99.99 percent, is scaled such that a Cumulative Distribution Function for a Normal Distribution will plot as a straight line. This is accomplished by plotting the vertical axis such that the increments between percentage points are small for values close to a value of 50 percent. These increments increase as the distance from a value of 50 increases. As the values become as small as 1 or as large as 99, the incremental distances between tenths of a percent increase slightly. A straight line, starting at an X value of 84 and a Y valued of 0.6 tribution p and ending at an X value of approximately 121 and a Y value of 99.99 percent, is plotted on the axes. Four points are plotted that touch the line at approximate X values of 93, 100, 107, and 121. for respective Y values of approximately 15, 55, 91, and 99.99. At an X value of roughly 114 and a Y value of approximately 95.5 [Use the axis on the right. 95.5]another point is plotted that is below the line.

Figure 60: Diagram. Normal Probability Plot for Ungrouped Data Example. This is a plot of graph paper with a normal arithmetic axis, ranging from values of 80 to 120, for the horizontal axis. The vertical axis, which runs from 0.01 percent to 99.99 percent, is scaled such that a Cumulative Distribution Function for a Normal Distribution will plot as a straight line. This is accomplished by plotting the vertical axis such that the increments such that the increments between percentage points are small for values close to a value of 50 percent. These increments increase as the distance from a value of 50 increases. As the values become as small as 1 or as large as 99, the incremental distances between tenths of a percent become slightly larger. A straight line, starting at an X value of 84 and a Y valued of 1.8 and ending at an X value of 119 and a Y value of 99.7, is plotted on the axes. Nineteen points are also plotted that are close to the plotted line at X values ranging from 87 to 107. At an X value of 112 another point is plotted that is below the plotted line, with the line indicating a value of 96 and the point plotted at a value of 91. At an X value of 120 another point is plotted that is below the plotted line, with the line indicating a value of 99.7 and the point plotted at a value of 96.

Equation 66:Gamma subscript 1 equals the following quotient. The numerator of the quotient consists of the quantity X subscript I minus Mu, which is then raised to the third power. The denominator of the quotient is the product that results from multiplying the cube of Sigma by N and by 2.

Equation 67: G subscript 1 equals N multiplied by the following quotient. The numerator of the quotient consists of the quantity X subscript I minus X bar, which is then raised to the third power. The denominator of the quotient is the product of the cube of Sigma times the quantity N minus 1, which is then multiplied by the quantity N minus 2.

Equation 68:G subscripts 1 equals the product of two terms. The first term is a quotient with N in the numerator, and with the product of the quantities N minus 1 and N minus 2 in the denominator. The second term is the summation from I equals 1 to I equals N of a quotient raised to the third power. The quotient has X subscript I minus X bar in the numerator and S in the denominator.

Equation 69:Gamma subscripts 2 equals the following quotient. The numerator of the quotient consists of the quantity X subscript I minus Mu. This quantity is raised to the fourth power. The denominator of the quotient consists of N times the quantity Sigma raised to the fourth power. The quotient then has 3 subtracted from it.

Equation 70:G subscript 2 equals two quantities subtracted from one another. The first quantity is a quotient. The numerator of the quotient consists of N multiplied by the sum that results from N plus 1. This product is multiplied by the sum of a quotient with a numerator consisting of the quantity X subscript 1 minus X bar. This quantity is raised to the fourth power. The denominator consists of S raised to the fourth power multiplied by the quantities N minus 1, N minus 2, and N minus 3. From this first quantity the second quantity is subtracted. The second quantity consists of a quotient. The numerator of the quotient consists of 3 multiplied by the square of the quantity N minus 1. The denominator of the quotient consists of the quantity N minus 2 multiplied by the quantity N minus 3.

Equation 71: G subscript 2 equals two quantities subtracted from one another. The first quantity is the product of a quotient and a summation. The quotient has N multiplied by the quantity N plus 1 in the numerator. The denominator of the quotient consists of the product that results from multiplying N minus 1 by N minus 2 and by N minus 3. The quotient is multiplied by the sum from I equals 1 to I equals N of a quotient that is raised to the fourth power. The quotient has X subscript I minus X bar in the numerator and S in the denominator. From this first quantity the second quantity is subtracted. The second quantity consists of a quotient. The numerator of the quotient consists of 3 multiplied by the square of the quantity that results from N minus 1. The denominator of the quotient consists of the quantity that results from N minus 2 multiplied by the quantity that results from N minus 3.

Equation 72: PAYADJ equals the following quotient. The numerator of the quotient consists of C multiplied by the quantity that results from subtracting the term R raised to the E power from the term R raised to the D power. The denominator of the quotient consists of subtracting the R raised to the O power from 1.

Equation 73: NPV equals a quotient with C in the numerator. The denominator consists of the quantity 1 plus DISC. This quantity is then raised to the N power.

Equation 74. NPV equals a product that results from multiplying the quantity R raised to the N power by C.

Equation 73. This is a demonstration of equation 73, as discussed in the text above. NPV equals a quotient with C in the numerator. The denominator consists of the quantity 1 plus DISC. This quantity is then raised to the N power. This quotient is then equal to a quotient with C in the numerator and with 1.04 raised to the tenth power in the denominator. This quotient then equals 0.676 multiplied by C.

Equation 74: This is a demonstration of equation 74, as discussed in the text above. There are two parts to this equation. In the first part, R equals a quotient with 1 plus INF in the numerator and 1 Plus INT in the denominator. This quotient is then equal to a quotient with 1.04 in the numerator and 1.08 in the denominator. This quotient is then equal to 0.963.

In the second part, NPV equals the product that result from multiplying 0.963 raised to the tenth power by C. This product is then equal to 0.686 multiplied by C.

Unnumbered equation: PAYADJ equals a quotient. The numerator of the quotient consists of the product that results from multiplying negative 23.92 by a quantity. The quantity consists of 0.96296 raised to the twentieth power, from which is subtracted the quantity 0.96296 raised to the tenth power. The denominator of the quotient consists of subtracting the quantity 0.96296 raised to the tenth power from 1. This quotient is then equal to negative 16 dollars and 40 cents per square meter.

Unnumbered equation:PAYADJ equals the product that results form multiplying the quantity 0.96296 raised to the tenth power by negative 23.92. This product is then equal to negative 16 dollars and 40 cents per square meter.

Equation 75: DEBIT subscript 1, which represents overlay 1, equals the product that results from multiplying C by the quantity R that has been raised to the fifteenth power.

Equation 76: CREDIT subscript 1, which represents overlay 1, equals the product that results from multiplying C by the quantity R that has been raised to the twentieth power.

Equation 77: NETDEBIT subscript 1, which represents overlay 1, equals the product of C multiplied by the sum that results from subtracting the quantity R raised to the fifteenth power from the quantity R that has been raised to the twentieth power.

Equation 78: NETDEBIT subscript 2, which represents overlay 2, equals the product of C multiplied by the sum that results from subtracting the quantity R raised to the twenty-fifth power from the quantity R that has been raised to the thirtieth power.

Equation 79. There are two parts to this equation. In the first part, NETDEBIT subscript 3, which represents overlay 3, equals the product of C multiplied by the sum that results from subtracting the quantity R raised to the thirty-fifth power from the quantity R that has been raised to the fortieth power.

In the second part, NETDEBIT subscript 4, which represents overlay 4 equals etcetera, indicating that the series can continue along the same successive rescheduling.

Equation 80: NPV equals the product of C multiplied by a quantity. The quantity consists of the sum of one infinite series from which the sum of another infinite series is subtracted. The first series consists of R raised to the twentieth power to which is added R raised to the thirtieth power to which is added R raised to the fortieth power. This continues to infinity. From this sum the sum of another infinite series is subtracted. The second series consists of R raised to the fifteenth power to which is added R raised to the twenty-fifth power to which is added R raised to the thirty-fifth power. This continues to infinity.

Equation 81: NPV equals the product of C multiplied by a quantity. The quantity consists of the sum of one infinite series from which the sum of another infinite series is subtracted. The first series consists of R raised to the D power to which is added R raised to the D plus O power to which is added R raised to the power that results from adding D to the product of 2 multiplied by O. This continues to infinity. From this sum the sum of another infinite series is subtracted. The second series consists of R raised to the E power to which is added R raised to the E plus O power to which is added R raised to the power that results from adding E to the product of 2 multiplied by O. This continues to infinity.

Equation 82: NPV equals the product of C multiplied by a quantity. The quantity consists of a product from which another product is subtracted. The first product consists of R raised to the D power multiplied by the sum that results from adding 1 plus the quantity R raised to the O power plus the quantity R raised to the power that results from multiplying 2 by O. The series of summing continues to infinity. From this product another product is subtracted. The second product consists of R raised to the E power multiplied by the sum that results from adding 1 plus the quantity R raised to the O power plus the quantity R raised to power that results from multiplying 2 by O, with this series continuing to infinity.

Equation 83: NPV equals the product of C multiplied by two quantities. The first quantity consists of the quantity R raised to the D power minus the quantity R raised to the E power. The second quantity consists of 1 plus the quantity R raised to the O power to which is added the quantity R raised to the 2 multiplied by O power, with this series continuing to infinity.

Equation 84: The sum of 1 plus the quantity R raised to the O power plus the quantity R raised to the 2 multiplied by O power, with this series continuing to infinity, equals a quotient with a numerator consisting of 1 and a denominator consisting of 1 minus the quantity R raised to the O power.

Equation I-14 85: NPV equals a quotient with the numerator consisting of C multiplied by the sum that results from subtracting the quantity R raised to the E power from the quantity R raised to the D power. The denominator consists of 1 minus the quantity R raised to the O power.

Figure 61: Diagram. Graph of Two Possible Mathematical Models for an RQL Provision. This chart plots "PD subscript VOIDS" on the horizontal axis against "PD subscript THICK" on the vertical axis. The range of the horizontal axis is from 0 to 80 and the range of the vertical axis is from 0 to 100. There are two curves shown on the plot. The first curve, labeled "Model number 1," is a downward concave curve that begins at a "PD subscript THICK" value of approximately 78 for a "PD subscript VOIDS" of 0. There are three points marked along this curve. The first is at a "PD subscript VOIDS" value of 10 for a "PD subscript THICK" value of approximately 75. This curve then passes through a point where both "PD subscript THICK" and "PD subscript VOIDS" are both 50. The third point is marked at a "PD subscript VOIDS" value of approximately 75 for a "PD subscript THICK" value of 10 and here the curve is shown to intersect with the second curve. The first curve then continues and intersects with the horizontal axis at a "PD subscript THICK" value of 0 for a "PD subscript VOIDS" value of approximately 78. The second curve, labeled "Model number 2," is concave upward beginning at a "PD subscript THICK" value of 100 when "PD subscript VOIDS" is about 7. There are three points marked along this curve. The first is at a "PD subscript VOIDS" value of 10 for a "PD subscript THICK" value of 90. This curve then passes through a point where both "PD subscript THICK" and "PD subscript VOIDS" are 40. The third point is marked at a "PD subscript VOIDS" value of approximately 75 for a "PD subscript THICK" value of 10 and here the curve is shown to intersect with the first curve. The second curve then continues and intersects with the horizontal axis at a "PD subscript THICK" value of 0 for a "PD subscript VOIDS" of about 92.

Equation 86: The product of C subscript 1 multiplied by PD subscript VOIDS, plus the product that results from multiplying C subscript 2 by PD subscript THICK, plus the product that results from multiplying C subscript 3 by PD subscript VOIDS by PD subscript THICK is greater than or equal to 100.

Equation 87:The product of 75 multiplied by C subscript 1, plus the product of 10 multiplied by C subscript 2, plus the product that results from multiplying 750 by C subscript 3 is equal to 100.

Equation 88: The product of 10 multiplied by C subscript 1, plus the product of 75 multiplied by C subscript 2, plus the product of 750 multiplied by C subscript 3 is equal to 100.

Equation 89: The product of 50 multiplied by C subscript 1, plus the product of 50 multiplied by C subscript 2, plus the product of 2500 multiplied by C subscript 3 is equal to 100.

Equation 90: The product of 1.273 multiplied by PD subscript VOIDS, plus the product of 1.273 multiplied by PD subscript THICK, minus the product that results from multiplying 0.0109 by PD subscript VOIDS by PD subscript THICK is greater than or equal to 100.

Equation 91: The product of 1.076 multiplied by PD subscript VOIDS, plus the product of 0.847 multiplied by PD subscript THICK, plus the product that results from multiplying 0.0144 by PD subscript VOIDS by PD subscript THICK is greater than or equal to 100.

Figure 62: Diagram. Average Results Obtained with Survey Questionnaire for

HMAC Pavement Performance. This is a diagram that is labeled "HMA Pavement Performance Survey." The instructions shown state: "Please fill in the estimate of expected life (years) in the seven empty boxes using the assumptions listed at the bottom of the page."

Next there is a two-by-two matrix that is labeled "Case 1: Good Initial Smoothness." The columns are titled "Thickness" and there are two ratings, "Good" or "Thick." The rows are titled "In–Place Air Voids" and there are two ratings, "Good" or "Poor." There are four entries in the matrix. When "In Place Air Voids" is Good and "Thickness" is Good, the life is 20 years. When "In–Place Air Voids" is Poor and "Thickness" is Good, the life is 11.6 years. When "In–Place Air Voids" is Good and "Thickness" is Poor, the life is 15 years. When "In–Place Air Voids" is Poor and "Thickness" is Poor, the life is 8.7 years.

Next there is another matrix that is labeled "Case 2: Poor Initial Smoothness." The columns are titled "Thickness" and there are two ratings, "Good" or "Thick." The rows are titled "In–Place Air Voids" and there are two ratings, "Good" or "Poor." There are four entries in the matrix. When "In–Place Air Voids" is Good and "Thickness" is Good, the life is 16.1 years. When "In–Place Air Voids" is Poor and "Thickness" is Good, the life is 9.3 years. When "In–Place Air Voids" is Good and "Thickness" is Poor, the life is 11.9 years. When "In–Place Air Voids" is Poor and "Thickness" is Poor, the life is 6.8 years.

Below the matrices, the following "Assumptions" are listed:

Good quality in all three categories, (air voids, thickness, smoothness), corresponds to an expected service life (time after which resurfacing is required), of 20 years.

For in-place air voids: Good equals average value around 5 to 6 percent. Poor equals average value around 10 to 11 percent.

For thickness: Good equals average value somewhat greater than design HMA layer thickness of 6 inches. Poor equals average thickness one-half to three-quarters of an inch less than the design value.

For smoothness (qualitative): Good equals result that agency regards as clearly acceptable. Poor equals result that agency would accept only with substantial pay reduction.

Equation 92: EXPLIF equals C subscript 0, plus the product of C subscript 1 multiplied by PD subscript VOIDS, plus the product of C subscript 2 multiplied by PD subscript THICK, plus the product of that results from multiplying C subscript 3 by PD subscript VOIDS by PD subscript THICK.

Equation 93: EXPLIF equals 22.9 minus the product of 0.163 multiplied by PD subscript VOIDS, minus the product of 0.135 multiplied by PD subscript THICK, plus the product that results from multiplying 0.000961 by PD subscript VOIDS by PD subscript THICK.

Equation 94: The product of 1.264 multiplied by PD subscript VOIDS, plus the product of 1.047 multiplied by PD subscript THICK, minus the product that results from multiplying 0.00745 by PD subscript VOIDS by PD subscript THICK is greater than or equal to 100.

Figure 63: Diagram. Graph of Expected Life, in Years, Generated by Equation 93. This is a plot with "PD subscript VOIDS" ranging from 0 to 100 on the horizontal axis and "PD subscript THICK" ranging from 0 to 100 on the vertical axis. On the plot are 20 curves, each corresponding to an expected pavement life of 3, 4, 5, and so no up to 22 years. Each curve is slightly concave downward with the concavity facing towards the origin of 0 "PD subscript THICK" and 0 "PD subscript VOIDS." The curve for a 22-year life is in the lower left corner and extends from a "PD subscript THICK" value of about 6 for a "PD subscript VOIDS" value of 0 down to a "PD subscript THICK" value of 0 at a "PD subscript VOIDS" value of approximately 6. The curve for a 3-year life is in the upper right corner and extends from a "PD subscript THICK" value of 100 at a "PD subscript VOIDS" value of about 95 down to a "PD subscript THICK" value of about 92 for a "PD subscript VOIDS" value of 100. The other curves are distributed between these two curves, with intervals increasing slightly as the plot moves from the 22-year life curve to the 3-year life curve.

Equation 95: The product of 1.273 multiplied by PD subscript VOIDS, plus the product of 1.273 multiplied by PD subscript THICK, minus the product that results from multiplying 0.0109 by PD subscript VOIDS by PD subscript THICK is greater than or equal to 100.

Figure 64: Diagram. Graph of RQL Provision Given by Equation 95. This chart plots "PD subscript VOIDS" on the horizontal axis against "PD subscript THICK" on the vertical axis. The scales of both the horizontal and vertical axes are from 0 to 100. There is a curve shown on the plot. A concave downward curve is plotted that intersects the vertical axis at a "PD subscript THICK" value of approximately 78 for a "PD subscript VOIDS" of 0. The curve passes through a point where both "PD subscript THICK" and "PD subscript VOIDS" are both 50, and intersects the horizontal axis at a "PD subscript THICK" value of 0 for a "PD subscript VOIDS" of approximately 78.

Equation 96: EXPLIF equals C subscript 0, plus the product of C subscript 1 multiplied by PD subscript VOIDS, plus the product of C subscript 2 multiplied by PD subscript THICK, plus the product that results from multiplying C subscript 3 by PD subscript VOIDS by PD subscript THICK.

Equation 97: C subscript 0 plus the product of 10 multiplied by C subscript 1, plus the product of 10 multiplied by C subscript 2, plus the product of 100 multiplied by C subscript 3 is equal to 20.

Equation 98: C subscript 0 plus the product of 75 multiplied by C subscript 1, plus the product of 10 multiplied by C subscript 2, plus the product of 750 multiplied by C subscript 3 is equal to 10.

Equation 99: C subscript 0 plus the product of 10 multiplied by C subscript 1, plus the product of 90 multiplied by C subscript 2, plus the product of 900 multiplied by C subscript 3 is equal to 10.

Equation 100: C subscript 0 plus the product of 75 multiplied by C subscript 1, plus the product of 90 multiplied by C subscript 2, plus the product of 6750 multiplied by C subscript 3 is equal to 5.

Equation 101: EXPLIF equals 22.9 minus the product of 0.163 multiplied by PD subscript VOIDS, minus the product of 0.135 multiplied by PD subscript THICK, plus the product that results from multiplying 0.000961 by PD subscript VOIDS by PD subscript THICK.

Figure 65: Diagram. Graph of Expected Life in Years Generated by Equation 101. This is a plot with "PD subscript VOIDS" ranging from 0 to 100 on the horizontal axis and "PD subscript THICK" ranging from 0 to 100 on the vertical axis. On the plot are 20 curves, each corresponding to an expected pavement life of 3, 4, 5, and so forth up to 22 years. Each curve is slightly concave downward with the concavity facing towards the origin of 0 "PD subscript THICK" and 0 "PD subscript VOIDS." The curve for a 22-year life is in the lower left corner and extends from a "PD subscript THICK" value of about 6 for a "PD subscript VOIDS" value of 0 to a "PD subscript THICK" value of 0 at a "PD subscript VOIDS" value of approximately 6. The curve for a 3-year life is in the upper right corner and extends from a "PD subscript THICK" value of 100 for a "PD subscript VOIDS" value of about 95 to a "PD subscript THICK" value of about 92 for a "PD subscript VOIDS" value of 100. The other curves are distributed between these two curves, with intervals increasing slightly as the plot moves from the 22-year life curve to the 3-year life curve.

Equation K-5 102: PD star equals the product of 0.807 multiplied by PD subscript VOIDS, plus the product of 0.669 multiplied by PD subscript THICK, minus the product that results from multiplying 0.00476 by PD subscript VOIDS by PD subscript THICK.

Figure 66: Diagram. Graph of Composite Quality Measure (PD star) Given by Equation 102. This is a plot with "PD subscript VOIDS" ranging from 0 to 100 on the horizontal axis and "PD subscript THICK" ranging from 0 to 100 on the vertical axis. On the plot are 9 curves, each corresponding to a PD star value of 10, 20, 30, 40, 50, 60, 70, 80, and 90. Each curve is slightly concave downward with the concavity facing towards the origin of 0 "PD subscript THICK" and 0 "PD subscript VOIDS." The curve for a PD star of 10 is in the lower left corner and runs from a "PD subscript THICK" value of about 15 for a "PD subscript VOIDS" value of 0 to a "PD subscript THICK" value of 0 for a "PD subscript VOIDS" value of approximately 12. The curve for a PD star of 90 is in the upper right corner and runs from a "PD subscript THICK" value of 100 for a "PD subscript VOIDS" value of about 70 to a "PD subscript THICK" value of about 48 at a "PD subscript VOIDS" value of 100. The other curves are distributed between these two curves, with intervals increasing as the plot moves from the 10-year life curve to the 90-year life curve. The plot is also labeled to indicate that a PD star value of 100 corresponds to a "PD subscript THICK" value of 100 and a "PD subscript VOIDS."

Equation 103. PAYADJ equals 14,000 minus the product of 1,000 multiplied by PD star.

104: If PD star is less than 39, then PAYADJ equals 5,000 minus the product of 357 multiplied by PD star.

Equation 105: If PD star is greater than or equal to 39, then PAYADJ equals 55,154 minus the product of 1,643 multiplied by PD star.

Figure 67: Diagram. Compound Payment Schedule Given by Equations 104 and 105. This chart plots "PD star" on the horizontal axis against "PAYADJ" on the vertical axis. The scale of the horizontal axis ranges from 0 to 100 and the scale of the vertical axis ranges from ranging from a negative 110,000 to a positive 10,000. On the plot chart are two straight-line segments that are contiguous. The first line begins at a "PAYADJ" value of a positive 5,000 for a "PD star" value of 0 and slopes downward to a point with a "PAYADJ" value of a negative 8923 (NOT SURE HOW THEY KNOW THIS) To get this, from the plot you would have to approximate the value. You can get the exact number by simultaneously solving equations 104 and 105 for where they intersect.) and a "PD star" value of 39. At this point, the RETEST value is indicated for a "PD star" value of 39, but there is no corresponding "PAYADJ" value noted. The second line begins at this the point that the first line ends and slopes downward at a greater slope to a point with a "PAYADJ" value of a negative 109,146 (to get this value, r from the plot you would have to approximate the value. You can get the exact number substituting PD* of 100 into equation 105. and a "PD star" value of 100. On the plot the AQL value is indicated as a "PD star" value of 14 with a corresponding "PAYADJ" value of 0. The RQL value is indicated as a "PD star" value of 64 with a corresponding "PAYADJ" value of negative 50,000.

Figure 68: Diagram. Conceptual Steps to Develop a Performance Model for Pavement Smoothness. There are four plots, each labeled as step 1, step 2, step 3, or step 4. Each plot has "Mechanical Output" on the horizontal axis and has an untitled vertical axis that ranges from values of 0 to 5. Each horizontal axis begins at 0 and increases to the right, but no scale is shown. The step 1 plot shows a curve that begins at a point, labeled "A," with a value of 5 on the vertical axis and a corresponding "Mechanical Output" value of 0. The curve, which is concave downward, passes through a point, labeled "B," with a value of approximately 5 on the vertical axis and a corresponding small positive value for "Mechanical Output." The step 2 plot has the same curve that is in step 1, but also has an additional curve. This curve begins at a point, labeled "D," with a value of 0 on the vertical axis and a corresponding large value for "Mechanical Output." The curve, which is concave upward, passes through a point, labeled "C," with a value of 0 on the vertical axis and a corresponding slightly smaller large positive value for "Mechanical Output." The step 3 plot shows the same two curves that are in step 2, but also has an additional curve represented by a dashed line that connects the two curve segments from step 2. The dashed curve connects to the two previous curves to form a continuous curve that is in the shape of a reversed and elongated "S." Two points labeled "E" and "F" are shown on the dashed section of the curve, with the "E" point located towards the "B" point and the "F" point located towards the "C" point. The step 4 plot shows the completed curve from step 3, which is now plotted as a solid line. The curve is labeled with the equation Y equals the product of 5 multiplied by the quantity E that has been raised to a power that is the product of X raised to the C power multiplied by a negative B.

Equation 106: Y equals the product of A multiplied by E that has been raised to a power represented by the quantity minus B multiplied by the quantity X to the power of C.

Equation 107: Y equals the product of A multiplied by the quantity E raised to a power represented by taking the negative of the following: the product that results from multiplying the quantity B subscript 1 by the quantity X subscript 1 that has been raised to the C subscript 1 power, plus the product that results from multiplying B subscript 2 by the quantity X subscript 2 that has been raised to the C subscript 2 power, continuing until the final term is B subscript K multiplied by the quantity X subscript K that has been raised to the C subscript K power.

Equation 108:EXPLIF equals the product of A multiplied by the quantity E raised to a power represented by taking the negative of the following: the product of quantity B subscript 1 multiplied by the quantity PD subscript 1, plus the product that results from multiplying B subscript 2 by the quantity PD subscript 2, continuing until the final term is B subscript K multiplied by the quantity PD subscript K.

Equation 109: The natural logarithm of EXPLIF equals the natural logarithm of A, minus the product that results from multiplying quantity B subscript 1 by the quantity PD subscript 1, minus the product that results from multiplying B subscript 2 by the quantity PD subscript 2, continuing until the final term is minus B subscript K multiplied times the quantity PD subscript K

Equation 110: A equals the quantity E that has been raised to the B subscript zero power.

Equation 111: 2.302585 equals B subscript zero, minus the product of 10 multiplied by B subscript 1, minus the product of 10 multiplied by B subscript 2, minus the product of 10 multiplied by B subscript 3.

Equation 112: 1.609440 equals B subscript zero, minus the product of 65 multiplied by B subscript 1, minus the product of 10 multiplied by B subscript 2, minus the product of 10 times B subscript 3.

Equation 113: 1.609440 equals B subscript zero, minus the product of 10 multiplied by B subscript 1, minus the product of 75 multiplied by B subscript 2, minus the product of 10 multiplied by B subscript 3.

Equation 114: 1.609440 equals B subscript zero, minus the product of 10 multiplied by B subscript 1, minus the product of 10 multiplied by B subscript 2, minus the product of 85 multiplied by B subscript 3.

Equation 115: EXPLIF equals the product of 13.8 multiplied by the quantity E that has been raised to a power represented by taking the negative of the following: the product that results from multiplying the quantity 0.0126 multiplied by the quantity PD subscript VOIDS, plus the product that results from multiplying the quantity 0.0107 by the quantity PD subscript THICK, plus the product that results from multiplying 0.00924 by the quantity PD subscript SMOOTH.

Equation 116: PAYADJ equals a quotient with the numerator consisting of C multiplied by the sum that results from subtracting the quantity R raised to the E power from R raised to the D power. The denominator consists of subtracting the quantity R raised to the O power from 1.

Figure 69: Diagram. Payment Schedule Developed from Table 59. This is a plot with "Expected Life in Years" ranging from 0 to 15 on the horizontal axis and "Pay Adjustment in 1,000 Dollars per Lane Kilometer" ranging from a negative 90 to a positive 30 on the vertical axis. Below the vertical axis label is a note that indicates 1,000 dollars per lane kilometer multiplied by 1.61 is equal to 1,000 dollar per lane mile. On the plot is indicated that the pay adjustment is 0 at the design life of 10 years. On the plot is a straight line, labeled "Table 8 Relationship," (however, note that this was an error that was not caught before this publication went to press. It should read Table 59 relationship. JLB that starts at a point corresponding to a "Pay Adjustment" value of negative 80,202 and an "Expected Life" value of 0.7 years, and then increases to a point corresponding to a "Pay Adjustment" value of 25,484 and an "Expected Life" value of 13.8 years (NOT SURE HOW THEY KNOW THESE VALUES) These values can be read from Table 59. The last row of the table gives the 0.7 years and –80,202, while the first line of the table gives the 13.8 and +25,484. JLB This line goes through the point with 0 payment adjustment at the design life of 10 years. Also on the plot is another line, labeled "Pay Schedule," that is made up of two contiguous lines with different slopes. The first line segment begins at an point of ???. "Expected Life" of 5 years and "Pay Adjustment" of negative 13,000- JLB and and increases to a point corresponding to a "Pay Adjustment" value of 9,880 and an "Expected Life" value of 13.8 years. (NOT SURE IF THESE VALUES ARE re correct. JLB This line is labeled "PAYADJ equals 2600 EXPLIF minus 26,000." This line also goes through the point with 0 payment adjustment at the design life of 10 years. The second line segment begins at a point corresponding to a "Pay Adjustment" value of negative 90,000 and an "Expected Life" value of 0. This segment is labeled "PAYADJ equals 15,400 EXPLIF minus 90,000." The line extends upwards until it intersects with the first line segmen at a point corresponding to a "Pay Adjustment" value of negative 13,000 and an "Expected Life" value of 5 years. at this point and increases.

Equation 117: PAYADJ equals the product of 2,600 multiplied by EXPLIF. From this product, 26,000 is then subtracted.

Equation 118: PAYADJ equals the product of 15,400 multiplied by EXPLIF. From this product, 90,000 is then subtracted.

Figure M-1: Diagram. Conventional OC Curve for Pass/Fail Acceptance Procedure. There is a chart with "Probability of Acceptance" ranging from 0 to 100 percent on the vertical axis. The horizontal axis is labeled "Level of Quality," with the range of the scale increasing from the right edge towards the left. An elongated reversed S-curve is plotted that decreases from 100 percent probability of acceptance at the left edge of the horizontal axis, indicating a higher level of quality, to 0 probability of acceptance near the right edge of the horizontal axis, indicating a lower level of quality. On the horizontal axis the RQL is noted with a vertical line that extends up to meet the curve. At the point of intersection, there is a horizontal line that extends to meet the vertical axis at a probability of acceptance value of approximately 10 percent. This probability of acceptance is labeled "Agency's risk." On the horizontal axis the AQL is also noted with a vertical line that extends up to meet the curve. At the point of intersection, there is a horizontal line that extends to meet the vertical axis at a probability of acceptance value of approximately 90 percent. The difference between this probability of acceptance and 100 percent is labeled "Contractor's Risk."

Figure M-2: Diagram. Typical EP Curve for Acceptance Procedure with Adjusted Payment Schedule. There is a chart with "Expected Payment" ranging from 50 to 110 percent on the vertical axis. The horizontal axis is labeled "Level of Quality," with the range of the scale increasing from the right edge towards the left. An elongated reversed S-curve is plotted that decreases from a maximum payment factor of 102 percent at the left edge of the horizontal axis, indicating the highest level of quality to an expected payment of 0 percent at the right edge of the horizontal axis, indicating the lowest level of quality. On the horizontal axis the RQL is noted with a vertical line that extends up to the curve. At this point of intersection, there is a horizontal line that extends to meet the vertical axis at an expected payment value of 70 percent. On the horizontal axis the AQL is also noted with a vertical line that extends up to the curve. At this point of intersection, there is a horizontal line that extends to meet the vertical axis at an expected payment value of 100 percent. The highest left edge of the curve is labeled "Maximum Payment Factor equals 102 percent."

Figure M-3: Diagram. Selections Available in Program OCPLOT. This diagram represents the options that may be selected in the OCPLOT program. The first option listed is the type of "Acceptance Method." The two choices are "Pass or Fail" and "pay Adjustment." If "Pass or Fail" is chosen, then the "Type of Plan" must also be selected as either "Attributes" or "Variables." it is correct. – JLB]Next, the "Quality Measure" is selected as "Percent Defective, PD" or "Percent Within Limits, PWL." Then the "Limit Type" option is selected as either "Single-Sided" or "Double-Sided." Then, "Pay Equation Type" is selected as either "Linear" or "Nonlinear," and the values for the equation are entered. Next, whether or not to use a "Maximum Pay Factor" is selected as either "Yes," in which case the value is entered, or as "no," in which case no value is entered. Next, the "Acceptable Quality Level, AQL" and "Rejectable Quality Level, RQL" values are entered. Then, whether or not to use an "RQL provision" is selected as either "Yes," in which case the "RQL Payment Factor" is entered, or as "no," in which case no value is entered. Then, whether or not to use a "Retest Provision" is selected as either "Yes," in which case whether the "Initial Tests" should be "Combined" or "discarded" is selected, or as "No," in which case no options are selected. Finally, the "Sample Size" value or values are entered.

Figure M-4: Diagram. First and Second Menus for Program OCPLOT. The "First Menu" is titled "Enter the Following Information" and below this is the following summary of selections made in the first menu:

Acceptance Method is Pay Adjustment.

Quality Measure is Percent Defective.

Limit Type is Double-Sided.

The Pay Equation is PF equals 102 minus the product of 0.2 multiplied by PD.

Maximum Pay Factor is 102.0.

Acceptable Quality Level is PD equals 10.

Rejectable Quality Level is PD equals 50.

RQL Pay Factor is 70.

Retest Provision is None.

Sample Size is 10.

Below the selections, there is a prompt labeled "Press any key to continue." In the lower left hand corner of the table is an option labeled "ESC equals Back," and in the lower right hand corner is the option labeled "END equals Exit."

The Second Menu asks the user to "Select Level of Precision" as one of the following:

1.     Low, which provides "Faster Execution."

2.     Intermediate.

3.     High, which provides "Slower Execution."

Below the precision levels, there is a prompt labeled "selection." In the lower left hand corner of the table is an option labeled "ESC equals Back" and in the lower right hand corner is the option labeled "END equals Exit."

Figure 74: Diagram. Typical Display at AQL at Intermediate Precision by Program OCPLOT. This shows two histograms; at the top one for the distribution of "PD Estimates" and, below it, one for the distribution of "Pay Factors." The top histogram has a label stating, "Performance at AQL." To the left of the histogram, there is a bell-shaped curve representing a normal distribution that is shaded to indicate that the AQL value is equal to 10 PD. To the right of the histogram, there is a legend that lists performance as either "acceptable," "marginal," or rejectable." These rankings correspond to shadings of black, dark gray and light gray, respectively. The histogram has a horizontal axis that represents samples and ranges from 0 to 100. The vertical axis, which shows no scale, represents the relative number of "PD Estimates" for each value on the horizontal scale.The highest bar in the histogram is at a horizontal scale value of 1 and a PD estimate of acceptable. Between 2 and 10 on the horizontal scale, the heights of the bars are relatively constant and have acceptable PD estimates. Between approximately 11 and 34 on the horizontal scale, the bars are shaded as marginal and their heights steadily decrease. At 35 on the horizontal bar, there is no vertical bar. At 36,there is a small bar shaded as marginal. At 37 on the horizontal bar, there is no vertical bar. And, at 38, there is a small bar shaded as marginal. There are no additional bars after this point.

The second histogram has a horizontal axis that represents samples and ranges from 0 to 100. The vertical axis, which shows no scale, represents the relative number of "Pay Factors" for each value on the horizontal scale. There is a label below this histogram that states average pay factor is equal to 100. The first bar appears at a very low height and corresponds to a horizontal axis value of 94. Between horizontal axis values of 94 and 99, the bars are each shaded marginal and the height of each bar is increasing. At a horizontal axis value of 100, the height of the bar continues to increase until it peaks at a value of 101. Both of these bars are shaded acceptable. There is one additional bar shown at a horizontal axis value of approximately 102, which is very low in height and shaded as acceptable.

Figure 75. Typical Display at RQL at Intermediate Precision by Program OCPLOT. This shows two histograms, one for the distribution of "PD Estimates" and, below it, one for the distribution of "Pay Factors." The top histogram has a label stating "Performance at RQL." To the right of the histogram, there is a legend that lists performance as either "acceptable," "marginal," or rejectable." These rankings correspond to shadings of black, dark gray and light gray, respectively. To the left of the histogram is a small bell shaped curve with the area around the peak shaded in black and the two tails shaded in light gray. Below the curve is noted that the PWL, then in parentheses, RQL, is equal to 50. The horizontal axis of the histogram has a scale that ranges from 0 to 100. There is no vertical axis as such but there is label to the left of the histogram that states "PWL Estimates." On the histogram are bars whose heights represent the relative frequency of PWL Estimates for each sample represented on the horizontal scale. The distribution and frequency of the bars appear to be bell-shaped with the peak at around 53. The left and right tails of the curve extend to horizontal axis values of approximately 13 and 79. The bars are shaded to indicate that between horizontal axis values of approximately 13 and 49, performance is marginal and that between horizontal axis values of approximately 50 and 79, performance is rejectable.

The second histogram displays a different distribution and frequency to the first histogram. The scale of the second histogram's horizontal axis ranges from 0 to 100. Below the horizontal axis is a note that indicates that the average pay factor is equal to 80.4. There is no vertical axis as such but there is a label to the left of the histogram that states "Pay Factors." There is a group of bars between the horizontal axis values of approximately 93 and 99, with the heights of the bars decreasing as the horizontal axis scale increases. There is also a very high solitary bar represented at a horizontal axis value of 70. There is a prompt at the bottom of the figure that states, "Press any key to continue."

Figure M-7: Diagram. Points on EP Curve Plotted by Program OCPLOT. There is chart is a plots with "Expected Pay Factor" ranging from on the vertical axis against "Percent Defective on the horizontal axis. The scale of the vertical axis ranges from 0 to 120 and the scale of the horizontal axis ranges "Percent from 0 to 100. There is a title above the chart that reads 'High Precision." A series of points are plotted on the chart that forms a slightly concave downward curve. The series starts at an "Expected Pay Factor" value of a approximately 100 for a "Percent Defective" value of approximately 5 and decreases to an "Expected Pay Factor" value of approximately 70 for a "Percent Defective" value of approximately 65. Between these two points are plotted 11 points at roughly equal "Percent Defective" Intervals of 5. A horizontal line on the chart indicates that the minimum pay factor is approximately 70.

Figure 77: Diagram. Display of EP Curve Plotted by Program OCPLOT with AQL and RQL Performance Highlighted. This chart plots "Expected Pay Factor" on the vertical axis against "Percent Defective" on the horizontal axis. The scale of the vertical axis ranges from 0 to 120 and the scale of the horizontal axis ranges from 0 to 100. A line that is slightly concave downward is plotted on the axes. The line begins at an "Expected Pay Factor" value of approximately 102 for a "Percent Defective" value of 0 and decreases to an "Expected Pay Factor" value of approximately 70 for a "Percent Defective" value of approximately 65. At the AQL of 10 percent defective, a vertical line is drawn that extends up to meet the curve. At this point of intersection, there is a horizontal line that extends to meet the vertical axis at an "Expected Pay Factor" value of 100. At the RQL of 50 percent defective, a vertical line is drawn that extends up to meet the curve. At this point of intersection, there is a horizontal line that extends to meet the vertical axis at an "Expected Pay Factor" value of approximately 80. There is a title above the chart that reads 'High Precision."

Figure 78: Diagram. Third Menu for Program OCPLOT. The third menu screen that appears in the OCPLOT program is represented. The menu requires the user to "Select Desired Option" from among the following:

1.     Display operating characteristic table.

2.     Select precision level and run again.

3.     Change some values and run again.

4.     Run again with new input data.

5.     Exit program.

Beneath the fifth option is the prompt, "selection." In the lower left hand corner of the menu is an option labeled "ESC equals Back" and in the lower right hand corner is the option labeled "END equals Exit."

Figure 79: Diagram. Display of Numerical Values of Points on EP Curve Computed at High Precision by Program OCPLOT. A table that appears on the program computer screen is represented. There are two columns, the first represents "Percent Defective" and the second represents the corresponding "Expected Pay Factor." The following values are included in the figure for "Percent Defective," which is here represented as PD, and for "Expected Pay Factor," which is here represented as PF:

For PD 0.0, the PF is 102.0.

For PD of 5.0, PF is 101.0.

For PD of 10.0, which is the AQL, PF is 100.0.

For PD of 15.0, PF is 99.1.

For PD of 20.0, PF is 98.0.

For PD of 25.0, PF is 96.9.

For PD of 30.0, PF is 95.5.

For PD of 35.0, PF is 93.4.

For PD of 40.0, PF is 90.0.

For PD of 45.0, PF is 85.5.

For PD of 50.0, which is the RQL, PF is 81.2.

For PD of 55.0, PF is 76.6.

For PD of 60.0, PF is 73.4.

For PD of 65.0, PF is 71.30.

Figure 80: Diagram. Completed Menu for Analysis of Pass/Fail Attributes Acceptance Plan with N equals 10 and C equals 2. The menu shows a summary of the input data for an example. Beneath the prompt, "Enter the Following Information, is the following list indicating the selections made in the menu:

Acceptance Method is Pass or Fail.

Type of Procedure is Attributes.

Quality Measure is Percent Defective.

Limit Type is Single-Sided.

Acceptable Quality Level is PD equals 10.

Rejectable Quality Level is PD equals 50.

Retest Provision is None.

Sample Size is 10.

Acceptance Number is 2.

Below the final selection there is the prompt, "Press any key to continue." In the lower left hand corner of the table is an option labeled "ESC equals Back" and in the lower right hand corner is the option labeled "END equals Exit."

 

Figure 81: Diagram. Numerical Values of Points on EP Curve for Pass/Fail Attributes Acceptance Plan with N equals 10 and C equals 2. A table that appears on the program computer screen is represented. There are two columns, the first represents "Percent Defective" and the second represents the corresponding "Acceptance Probability." The following values are included in the figure for "Percent Defective," which is represented here as PD, and for "Acceptance Probability," which is represented here as AP:

For PD 0.0, the AP is 1.000.

For PD of 5.0, AP is 0.991.

For PD of 10.0, which is the AQL, AP is 0.927.

For PD of 15.0, AP is 0.813.

For PD of 20.0, AP is 0.681.

For PD of 25.0, AP is 0.525.

For PD of 30.0, AP is 0.380.

For PD of 35.0, AP is 0.260.

For PD of 40.0, AP is 0.167.

For PD of 45.0, AP is 0.101.

For PD of 50.0, which is the RQL, AP is 0.052.

For PD of 55.0, AP is 0.030.

For PD of 60.0, AP is 0.013.

 

Figure M - 13: Diagram. Completed Menu for Pass/Fail Variables Acceptance Plan Example.

The menu shows a summary of the input data for an example. Beneath the prompt, "Enter the Following Information, is the following list that indicates the selections made in the menu:

Acceptance Method is Pass or Fail.

Type of Procedure is Variables.

Quality Measure is Percent Defective.

Limit Type is Single-Sided.

Acceptable Quality Level is PD equals 10.

Rejectable Quality Level is PD equals 50.

Retest Provision is None.

Sample Size is 8.

Acceptance Limit is PD equals 26.

Below the final selection there is the prompt, "Press any key to continue." In the lower left hand corner of the table is an option labeled "ESC equals Back" and in the lower right hand corner is the option labeled "END equals Exit."

Equation M-1: PR equals PWL subscript SPEC, minus PWL subscript COMP.

Equation M-2. PF equals 10 plus PWL subscript COMP.

Figure M-14: Diagram. Completed Menu for Analysis of Payment Equation. The menu shows a summary of the input data for an example. Beneath the prompt, "Enter the Following Information," is the following list that indicates the selections made in the menu:

Acceptance Method is Pay Adjustment.

Quality Measure is Percent Within Limits.

Limit Type is Single-Sided.

The Pay Equation is PF equals 10 plus the product of 1 multiplied by PWL.

Maximum Pay Factor is 100.

Acceptable Quality Level is PWL equals 90.

Rejectable Quality Level is PWL equals 50.

RQL Provision is None.

Retest Provision is None.

Sample Size is 5.

Below the final selection there is the prompt, "Press any key to continue." In the lower left hand corner of the table is an option labeled "ESC equals Back" and in the lower right hand corner is the option labeled "END equals Exit."

 

Figure M-15: Diagram. Performance of Payment Equation at AQL. This shows two histograms, one for the distribution of "PWL Estimates," and below it, one for the distribution of "Pay Factors." The top histogram has a label stating "Performance at AQL." To the left of the histogram is noted that the PWL, then in parentheses, AQL, is equal to 90. The horizontal axis of the histogram has a scale that ranges from 0 to 100. There is no vertical axis as such but there is label to the left of the histogram that states "PWL Estimates." On the histogram are bars whose heights represent the relative frequency of PWL Estimates for each sample represented on the horizontal scale. The lowest estimated PWL corresponds to a horizontal axis value of approximately 47. Between the approximate values of 47 and 61 on the horizontal axis, are five bars of a similar low PWL estimate. These bars are spread out unevenly at values of approximately 48, 53, 55, 56, and 58. From a horizontal axis value of 61 to value of approximately 68, these bars are of the same low height. Between a horizontal axis value of approximately 69 and 99, the bars are of a slightly higher and fluctuating height. There is a very tall bar at the horizontal axis value of 100.

The second histogram displays a similar distribution and frequency as the first histogram. The scale of the second histogram's horizontal axis ranges from 0 to 100. Below the horizontal axis is a note that indicates that the average pay factor is equal to 95.1. There is no vertical axis as such but there is a label to the left of the histogram that states "Pay Factors." At horizontal axis values of approximately 57, 58, 63, 65, 66, 68, and between 70 and 86, the bars are all of similar low heights. Between horizontal axis values of approximately 87 and 99, the bars have slightly higher and fluctuating heights. There is a very tall bar that corresponds to a horizontal axis value of 105.

 

Figure M-16: Diagram. EP Curve for Analysis of Payment Equation. There is a plot with "Expected Pay Factor" ranging from 0 to 120 on the vertical axis. The horizontal axis is "Percent Within Limits" and ranges from 100 on the far left to 0 on the far right of the axis. On the plot, an approximate straight line representing a linear relationship extends from an "Expected Pay Factor" value of 100 for a "Percent Within Limits" value of 100 to an "Expected Pay Factor" value of about 15 for a "Percent Within Limits" value of 5. At a "Percent Within Limits" value of 50, the RQL is noted with a vertical line that goes extends up to meet the line. At this point of intersection, at which point a horizontal line goes extends to meet the vertical axis to at an "Expected Pay Factor" value of approximately 60. At a "Percent Within Limits" value of 90, the AQL is noted with a vertical line that goes extends upwards to meet the line. At this point of intersection, at which point a horizontal line goes extends to meet the vertical axis at an "Expected Pay Factor" value of about 95.

Figure M-17: Diagram.Numerical Values for Points on EP Curve for Analysis of Payment Equation. A table that appears on the program computer screen is represented. There are two columns, the first represents "Percent Within Limits" and the second represents the corresponding "Expected Pay Factor." The following values are included in the figure for "Percent Within Limits," which is represented here as PWL, and for "Expected Pay Factor," which is represented here as PF:

For PWL of 100.0, the PF is 100.0.

For PWL of 95.0, PF is 98.3.

For PWL of 90.0, which is the AQL, PF is 95.1.

For PWL of 85.0, PF is 91.8.

For PWL of 80.0, PF is 87.0.

For PWL of 75.0, PF is 83.6.

For PWL of 70.0, PF is 79.2.

For PWL of 65.0, PF is 74.0.

For PWL of 60.0, PF is 68.8.

For PWL of 55.0, PF is 65.0.

For PWL of 50.0, which is the RQL, PF is 59.7.

For PWL of 45.0, PF is 55.1.

For PWL of 40.0, PF is 50.1.

For PWL of 35.0, PF is 44.3.

For PWL of 30.0, PF is 40.3.

For PWL of 25.0, PF is 35.1.

For PWL of 20.0, PF is 30.2.

For PWL of 15.0, PF is 24.6.

For PWL of 10.0, PF is 19.7.

For PWL of 5.0, PF is 14.7.

 

Figure M-18: Diagram. Completed Menu for Analysis of Acceptance Procedure with Incentive Payment Provision. The menu shows a summary of the input data for an example. Beneath the prompt, "Enter the Following Information," is the following list that indicates the selections made in the menu:

Acceptance Method is Pay Adjustment.

Quality Measure is Percent Within Limits.

Limit Type is Single-Sided.

The Pay Equation is PF equals 10 plus the product of 1 multiplied by PWL.

Maximum Pay Factor is 110.

Acceptable Quality Level is PWL equals 90.

Rejectable Quality Level is PWL equals 50.

RQL Provision is None.

Retest Provision is None.

Sample Size is 5.

Below the final selection there is the prompt, "Press any key to continue." In the lower left hand corner of the table is an option labeled "ESC equals Back" and in the lower right hand corner is the option labeled "END equals Exit."

 

Figure M-19: Diagram. Performance at AQL of Acceptance Procedure with Inventive Payment Provision. This shows two histograms, one for the distribution for "PWL Estimates," and below it, one for the distribution of "Pay Factors." The top histogram has a label stating, "Performance at AQL. To the left of the histogram is noted that the PWL, then in parentheses AQL, is equal to 90. The horizontal axis of the histogram has a scale that ranges from 0 to 100. There is no vertical axis as such but there is a label to the left of the histogram that states "PWL Estimates." On the histogram are bars whose heights represent the relative frequency of PWL Estimates for each value on the horizontal scale. The lowest estimated PWL corresponds to a horizontal axis value of about 31. Between the values of 31 and 58 on the horizontal axis are seven bars of a similar low PWL Estimate. These bars are spread out unevenly at values of approximately 39, 45, 47, 48, 51, 54, and 56. From a horizontal axis value of 58 to a value of 81, the bars are of roughly the same height. From a horizontal axis value of 81 to a value of 99, the bars are of slightly higher and roughly equal heights. There is a very tall bar at the horizontal axis value of 100.

The second histogram has a horizontal axis with a scale that ranges from 0 to 110. There is no vertical axis as such but there is a label to the left of the histogram that states "Pay Factors." Below the horizontal axis there is a note that indicates the average pay factor is equal to 100.0. The distribution and frequencies of the second histogram are very similar to the top histogram, with the lowest pay factor at a horizontal value of 40 and the very tall bar occurring at a horizontal value of 110.

Equation M-3: PF equals 55 plus the product of 0.5 multiplied by PWL.

Figure M-20: Diagram. Completed Menu for Using OCPLOT to Determine the Probability of Receiving Greater than or Equal to 100 Percent Payment for Example M–5. The menu shows a summary of the input data for an example. Below prompt, "Enter The Following Information" is the following list that indicates the selections made in the menu:

Acceptance Method is Pass or Fail.

Type of Procedure is Variables.

Quality Measure is Percent Within Limits.

Limit Type is Single-Sided.

Acceptable Quality Level is PWL equals 90.

Rejectable Quality Level is PWL equals 50.

Retest Provision is None.

Sample Size is 5.

Acceptance Limit is PD equals 90.

Below the final selection there is the prompt, "Press any key to continue." In the lower left hand corner of the table is an option labeled "ESC equals Back" and in the lower right hand corner is the option labeled "END equals Exit."

Figure M-21: Diagram. OC Curve for the Probability of Receiving Greater than or Equal to 100 Percent Payment for Example M-5. There is a plot with "Acceptance Probability" ranging from 0 to 1.0 on the vertical axis. The horizontal axis is "Percent Within Limits" and ranges from 100 on the far left to 0 on the far right of the axis. On the plot, a curve that is concave upward decreases from an "Acceptance Probability" value of 1.0 for a "Percent Within Limits" value of 100 to an "Acceptance Probability" value of about 0 for a "Percent Within Limits" value of 45.

Figure M-22: Diagram. Family of OC Curves Showing the Performance of the Acceptance Plan Using a Sample of Size N equals 5 and Payment Equation M-21. There is a plot with "Probability of Receiving greater than or equal to PF" ranging from 0 percent to 100 percent on the vertical axis. The horizontal axis is "Level of Quality, PWL" and ranges from 100 on the far left to 0 on the far right of the axis. On the plot there are six reversed elongated S-curves that each decrease from a "Probability of Receiving greater than or equal to PF" value of 100 for a "Level of Quality" value of 100 PWL to a "Probability of Receiving greater than or equal to PF" value of 0 as they meet the right portion of the horizontal axis. From highest to lowest these curves are labeled "70 percent," "80 percent," "90 percent," "95 percent," "100 percent," and "104 percent," respectively. The "70 percent" curve reaches the horizontal axis at a "Level of Quality" value of approximately 1 PWL. The "80 percent" curve reaches the horizontal axis at a "Level of Quality" value of approximately 12 PWL. The "90 percent" curve reaches the horizontal axis at a "Level of Quality" value of approximately 26 PWL. The "95 percent" curve reaches the horizontal axis at a "Level of Quality" value of approximately 30 PWL. The "100 percent" curve reaches the horizontal axis at a "Level of Quality" value of approximately 40 PWL. The "104 percent" curve reaches the horizontal axis at a "Level of Quality" value of approximately 49 PWL.

 

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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