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Publication Number: FHWA-RD-02-095

Optimal Acceptance Standards for Statistical Construction Specifications

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Technical Report Documentation Page

1. Report No.

FHWA-RD-02-095

2. Government Accession No. 3 Recipient's Catalog No.
4. Title and Subtitle

Optimal Procedures for Quality Assurance Specifications

5. Report Date

 

6. Performing Organization Code
7. Author(s)

J. L. Burati, R. M. Weed, C. S. Hughes, H. S. Hill

8. Performing Organization Report No.

 

9. Performing Organization Name and Address

Clemson University
Civil Engineering Department
Clemson, SC 29634-0911

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-98-C-00069

12. Sponsoring Agency Name and Address

Office of Research, Development, and Technology
Federal Highway Administration (FHWA)
6300 Georgetown Pike
McLean, VA 22101-2296

13. Type of Report and Period Covered

Final Report

14. Sponsoring Agency Code

 

15. Supplementary Notes

This study was conducted under State Planning and Research Pooled-Fund Study number 2(199) and was administered by FHWA. FHWA Contracting Officer's Technical Representative (COTR): Peter A. Kopac, HRDI-12.

16. Abstract

This manual is a comprehensive guide that a highway agency can use when developing new, or modifying existing, acceptance plans and quality assurance specifications. It provides necessary instruction and illustrative examples to lead the agency through the entire process of acceptance plan development, including:

  • Setting up the initial data collection/experimentation to determine typical parameters of current construction.
  • Establishing the desired level of quality to be specified.
  • Designing the actual acceptance plan itself, including selecting quality characteristics, statistical quality measure, buyer's and seller's risks, lot size, number of samples (sample size), specification and/or acceptance limits, and payment-adjustment provisions.
  • Monitoring how the acceptance plan is performing.
  • Making necessary adjustments.
17. Key Words

Quality Assurance, Quality Control, Specifications, Statistical Specifications, QA, QC, Payment Adjustments

18. Distribution Statement

No restrictions. This document is available to the public through the National Technical Information Service, Springfield, Virginia 22161

19. Security Classification
(of this report)

Unclassified

20. Security Classification
(of this page)

Unclassified

21. No. of Pages

347

22. Price
Form DOT F 1700.7 Reproduction of completed page authorized

SI* (MODERN METRIC) CONVERSION FACTORS


OPTIMAL PROCEDURES FOR QUALITY ASSURANCE SPECIFICATIONS

PREFACE

This manual is intended as a comprehensive guide that a highway agency can use when developing new, or modifying existing, acceptance plans and quality assurance (QA) specifications. It is intended to provide necessary instruction and illustrative examples to lead the agency through the entire process of acceptance plan development, including:

The acceptance plans described in this manual are based on QA principles intended to provide the "...confidence that a product or facility will perform satisfactorily in service." (2) To achieve this end, the acceptance plans must be realistic, must be fair to both the contractor and agency, and must be statistically accurate. The purpose of this manual is to explain how this can be done, through discussion and with examples where appropriate.

The information in this manual is based on a pooled-fund study that was administered by the Federal Highway Administration (FHWA). The material presented herein is based on review of the literature, the input of a panel comprised of a representative from each of the States in the pooled fund, numerous statistical analyses conducted for the project, and the past experiences of the authors. Additional information and more detailed discussion, as well as a thorough summary of all supporting analyses, can be found in the technical report for the project. (17)



TABLE OF CONTENTS

Chapter

  1. INTRODUCTION
  2. INITIATION AND PLANNING
  3. SPECIFICATION DEVELOPMENT
  4. QUALITY CONTROL

  5. ACCEPTANCE PROCEDURES

  6. ACCEPTANCE AND PAYMENT PROVISIONS
  7. EVALUATING RISKS

  8. IMPLEMENTATION
  9. CASE STUDIES

LIST OF FIGURES

Figure

  1. Flowchart for Phase I - Initiation and Planning
  2. Flowchart for Phase II - Specification Development
  3. Flowchart for Phase III - Implementation
  4. Flowchart for Phase I - Initiation and Planning
  5. Flowchart for Initial Portion of Phase II
  6. Flowchart for QC Portion of Phase II
  7. Flowchart for Acceptance Procedures Portion of Phase II
  8. Components of Variance for Independent Samples
  9. Components of Variance for Split Samples
  10. Simple Example of an OC Curve for a Statistical Test Procedure
  11. Flowchart for Acceptance and Payment Portion of Phase II
  12. Illustration of the Calculation of the Z-statistic
  13. Illustration of the Positive Quality Index Values
  14. Illustration of the Negative Quality Index Value
  15. Relationship between PWL and PD
  16. Illustration of the Moving Average
  17. AQL Material
  18. RQL Material
  19. AQL Material
  20. RQL Material
  21. AQL Population for the Screening Test Example
  22. RQL Population for the Screening Test Example
  23. Example of Stepped and Continuous Payment Schedules
  24. Examples of Random and Stratified Random Sampling
  25. Flowchart for Risk Analysis Portion of Phase II
  26. Typical OC Curve for an Accept/Reject Acceptance Plan
  27. Typical OC Curves for an Acceptance Plan with Payment Adjustments
  28. Typical Expected Payment (EP) Curve
  29. AQL Population for Simplifieda and bRisks Example
  30. RQL Populations for Simplifieda and bRisks Example
  31. Illustration of the a Risk for Simplified Example
  32. Illustration of the b Risk for Simplified Example
  33. OC Curve for Simplifieda and bRisks Example
  34. Histogram of PWL Estimates for Simplified PWL Example
  35. OC Curve from OCPLOT for the Accept/Reject Acceptance Plan Example
  36. EP Curve from OCPLOT for the Payment Adjustment Acceptance Plan Example
  37. Histogram for an AQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 4
  38. Histogram for an RQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 4
  39. Histogram for an AQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 20
  40. Histogram for an RQL Population Showing Variability of Individual PWL and Payment Factor Estimates for a Sample Size of 20
  41. OC Curves for a Sample of Size 4 Using the Payment Relationship in Equation 28
  42. Flowchart for Phase III-Implementation
  43. Graph of Composite RQL Provision Given in Equation 33
  44. Outline of NJDOT Superpave Acceptance Procedure
  45. Proposed Smoothness Acceptance Procedure Based on IRI
  46. Proposed Smoothness Acceptance Procedure Based on IRI
  47. Flowchart of 23 CFR 637B
  48. Excel Results for Data from Example Problem 1
  49. Excel Results for Data from Example Problem 2
  50. OC Surface for the D2S Test Method Verification Method
    (Assuming the smaller s = stest)
  51. OC Curves for a Two-Sided t-Test (a = 0.05)
  52. OC Curves for a Two-Sided t-Test (a = 0.01)
  53. OC Curves for the Two-Sided F-Test for Level of Significance a = 0.05
  54. OC Curves for the Two-Sided F-Test for Level of Significance a = 0.01
  55. OC Curves for the Single Agency Test Method
  56. Example Frequency Histogram
  57. Example of a Skewed Frequency Histogram
  58. Normal Probability Paper
  59. Normal Probability Plot for Grouped Data Example
  60. Normal Probability Plot for Ungrouped Data Example
  61. Graph of Two Possible Mathematical Models for an RQL Provision
  62. Average Results Obtained with Survey Questionnaire for HMA Pavement Performance
  63. Graph of Expected Life, in Years, Generated by Equation 93
  64. Graph of RQL Provision Given by Equation 95
  65. Graph of Expected Life in Years Generated by Equation 101
  66. Graph of Composite Quality Measure (PD*) Given by Equation 102
  67. Compound Payment Schedule Given by Equations 104 and 105
  68. Conceptual Steps to Develop a Performance Model for Pavement Smoothness
  69. Payment Schedule Developed from Table 59
  70. Conventional OC Curve for Pass/Fail Acceptance Procedure
  71. Typical EP Curve for Acceptance Procedure with Adjusted Payment Schedule
  72. Selections Available in Program OCPLOT
  73. First and Second Menus for Program OCPLOT
  74. Typical Display at AQL at Intermediate Precision by Program OCPLOT
  75. Typical Display at RQL at Intermediate Precision by Program OCPLOT
  76. Points on EP Curve Plotted by Program OCPLOT
  77. Display of EP Curve Plotted by Program OCPLOT with AQL and RQL Performance Highlighted
  78. Third Menu for Program OCPLOT
  79. Display of Numerical Values of Points on EP Curve Computed at High Precision by Program OCPLOT
  80. Completed Menu for Analysis of Pass/Fail Attributes Acceptance Plan with N = 10 and C = 2
  81. Numerical Values of Points on EP Curve for Pass/Fail Attributes Acceptance Plan with N = 10 and C = 2
  82. Completed Menu for Pass/Fail Variables Acceptance Plan Example
  83. Completed Menu for Analysis of Payment Equation
  84. Performance of Payment Equation at AQL
  85. EP Curve for Analysis of Payment Equation
  86. Numerical Values for Points on EP Curve for Analysis of Payment Equation
  87. Completed Menu for Analysis of Acceptance Procedure with Incentive Payment Provision
  88. Performance at AQL of Acceptance Procedure with Inventive Payment Provision
  89. Completed Menu for Using OCPLOT to Determine the Probability of Receiving Greater than or Equal to 100 Percent Payment for Example M-5
  90. OC Curve for the Probability of Receiving Greater than or Equal to 100 Percent Payment for Example M-5
  91. Family of OC Curves Showing the Performance of the Acceptance Plan Using a Sample of Size N = 5 and Payment Equation 121

LIST OF TABLES

Table

  1. Asphalt Content Data for Paired t-test Example
  2. Allowable Intervals for the Single Agency Test Comparison Method
  3. Example Summary of Test Results for a Project
  4. Example Project Variability Results
  5. Quality Index Values for Estimating PWL
  6. A PWL Estimation Table for Sample Size n = 5
  7. Another PWL Estimation Table for Sample Size n = 5
  8. Areas Under the Standard Normal Distribution
  9. Example of Lots with Similar AAD Values but Different Within-Lot Means and Standard Deviations
  10. Example of Lots with Similar CI Values but Different Within-Lot Means and Standard Deviations
  11. m ± Zs Regions for Selected Areas Under the Normal Distribution
  12. Typical Stepped Payment Schedule Based on PWL
  13. Calculation of PAYADJ for Selected Levels of Expected Life
  14. Typical Matrix of Expected Pavement Lives Used to Develop Polynomial Performance Model
  15. Values Calculated for Expected Pavement Life
  16. Data Matrix to Develop Exponential Performance Model
  17. Completed Data Matrix for Example of Exponential Model
  18. Examples of Methods for Combining Individual Payment Factors Into a Composite Payment Factor
  19. Examples of Computed PD* Values for Selected Individual PD Values
  20. Illustration of Problem with Separate RQL Provisions
  21. Risk Levels Suggested in AASHTO R-9(22)
  22. OC Table from OCPLOT for the Example Problem
  23. Requirements for NJDOT Statistical Engineer Series
  24. Classes of Concrete for NJDOT Specification
  25. Intuitive Model for Air Voids, Thickness, and Smoothness of HMAC Pavement
  26. Pavement Performance Survey Results
  27. Matrix of Expected Pavement Lives Used to Develop Polynomial Performance Model
  28. Inconsistency in RQL Provision in Prototype Specification
  29. Performance of New Specification without Thickness and Smoothness Payment Schedules
  30. Performance of New Specification When All Payment Schedules Apply
  31. Performance Matrix for Smoothness Specification Based on IRI
  32. PD Related to EXPLIF and PAYADJ
  33. Asphalt Content Tests
  34. Air Void Tests
  35. Critical Values, Fcrit, for the F-test for a Level of Significance, = 0.01
  36. Critical Values, tcrit, for the t-test
  37. F-test Power Values for n = 3 to 10 and s-ratio, l = 1 to 5
  38. F-test Power Values for n = 3 to 10 and s-ratio, l = 0.0 to 1.0
  39. F-test Power Values for n = 5 to 100 and s-ratio, l = 1 to 3
  40. Derivation of the Single Agency Test Method Allowable Intervals
  41. Example Cumulative Frequency Table for Grouped Data
  42. Example Cumulative Frequency Table for Ungrouped Data
  43. Payment Adjustment as a Function of Expected Life
  44. An Inconsistent RQL Provision
  45. Example of Data Used to Develop Joint RQL Provision for Two Quality Measures
  46. Data Set Used to Develop Alternate RQL Provision Given by Equation 91
  47. Preliminary Performance Matrix of Expected Life Values for HMAC Pavement Under NJDOT Conditions
  48. Comparison of Three Methods for Combining Effects of Multiple Deficiencies
  49. Final Matrix of Expected Life Values Used to Develop HMAC Pavement Performance Model
  50. Example of an Inconsistent Rejection Provision
  51. Performance Values for Expected Life Used to Develop Equation 101
  52. Data to Develop Multiple-Characteristic Performance Model
  53. AQL and RQL Values Selected for the Example
  54. Preliminary Performance Matrix for the Example
  55. Final Performance Matrix for the Example
  56. Check of the Derivation of Equation 115
  57. Test of Equation 115 at Extreme Values
  58. Additional Tests of Equation 115
  59. Range of Values Computed with Equations 115 and 116
  60. Program OCPLOT Precision Levels
  61. Performance of Attributes Acceptance Plans
  62. Comparison of Operating Characteristics of Attributes and Variables Acceptance Plans

LIST OF EQUATIONS

Equation

  1. t-statistic for the t-test for paired measurements
  2. t-statistic for the differences in table 1
  3. Pooled estimate for the within-lot process variance
  4. Estimated combined process center and within-process variance
  5. Estimated combined standard deviation
  6. Example: actual combined process center and within-process variance
  7. Example: actual combined standard deviation
  8. Example: actual combined process center and within-process variance
  9. Example: actual combined standard deviation
  10. The Z-statistic to be used with a standard normal table
  11. Quality index for the lower specification limit
  12. Quality index for the upper specification limit
  13. Percent within the upper and lower specification limits
  14. Example: quality index value
  15. Average absolute deviation
  16. Conformal index
  17. Example: Z values
  18. Payment factor as a percent of contract price
  19. Appropriate payment adjustment for new pavement or overlay
  20. Polynomial performance model for expected pavement life, in years
  21. Values for selected combinations of air voids percent defective and thickness percent defective, using polynomial performance model for expected life, in years
  22. Exponential model for expected pavement life, in years
  23. Log of the exponential performance equation of expected pavement life, in years
  24. Performance model for expected pavement life
  25. Weighting system 1 for composite payment factor
  26. Weighting system 2 for composite payment factor
  27. Composite quality measure in units of percent defective
  28. Example: payment factor for the lot, as percent of contract price
  29. Payment adjustment (percent) if lot percent defective is less than 50
  30. Payment adjustment (percent) if lot percent defective is greater than or equal to 50
  31. NJDOT polynomial performance model for expected pavement life, in years
  32. NJDOT expected pavement life performance model
  33. NJDOT composite quality measure
  34. Percent payment adjustment developed by NJDOT, when the composite quality measure is less than 40
  35. Percent payment adjustment developed by NJDOT, when the composite quality measure is greater than or equal to 40
  36. Pay adjustments for smoothness, when smoothness percent defective is less than 2.0
  37. Pay adjustments for smoothness, when smoothness percent defective is greater than or equal to 2.0
  38. Expected pavement life as a function of various levels of quality received
  39. Solution of the performance model provided in equation 38
  40. Appropriate payment adjustment for new pavement or overlay
  41. Payment equation with maximum bonus of $12,500 per lane mile
  42. Payment equation with maximum bonus of $5,000 per lane mile
  43. Payment equation with maximum bonus of $3,000 per lane mile
  44. Asphalt content tests variance, contractor tests
  45. Asphalt content tests variance, agency tests
  46. Comparison of variances between contractor and agency asphalt content tests
  47. Air void tests variance, contractor tests
  48. Air void tests variance, agency tests
  49. Comparison of variances between contractor and agency air void tests
  50. Asphalt content tests sample mean, contractor tests
  51. Asphalt content tests sample mean, agency tests
  52. Pooled variance for contractor and agency asphalt content tests
  53. t-statistic for contractor and agency asphalt content tests
  54. Air void tests sample mean, contractor tests
  55. Air void tests sample mean, agency tests
  56. t-statistic for contractor and agency air void tests
  57. Critical t-value for the effective degrees of freedom, f'
  58. Standardized difference for a t-test for paired measurements
  59. F-test for variances with equal sample sizes
  60. t-test for means
  61. Standardized difference for figure 51 or 52
  62. Basic equation for d*
  63. Computation of d* for example 5
  64. Computation of d* for example 6
  65. Confidence interval for the population mean
  66. Population skewness coefficient
  67. Sample skewness coefficient
  68. Equation for sample skewness used in Microsoft® Excel
  69. Population kurtosis coefficient
  70. Sample kurtosis coefficient
  71. Equation for sample kurtosis used in Microsoft Excel
  72. Equation to be derived: appropriate payment adjustment of new pavement or overlay
  73. Life-cycle cost
  74. Derivation of life-cycle cost equation
  75. Net debit resulting from the rescheduling of any particular future overlay
  76. Net credit resulting from the rescheduling of any particular future overlay
  77. Net debit of a 20-year design pavement failing after 15 years
  78. Net debit of a 30-year design pavement failing after 25 years
  79. Net debit of a 40-year design pavement failing after 35 years
  80. Total value in net-present-value terms using values from equations 77-79
  81. Total net-present-value in general terms
  82. Total net-present value equation factored
  83. Total net-present value rearranged
  84. Geometric progression term in equation 83 as a finite sum
  85. Complete derivation of equation 72, appropriate payment adjustment of new pavement or overlay
  86. Rejectable quality level provision
  87. First of 3 equations with 3 unknowns
  88. Second of 3 equations with 3 unknowns
  89. Third of 3 equations with 3 unknowns
  90. Possible mathematical model for a rejectable quality level provision, plotted as model #1 in figure 61
  91. Possible mathematical model for a rejectable quality level provision, plotted as model #2 in figure 61
  92. Practical model for a performance equation based on two quality characteristics
  93. Performance model using values for expected life from table 49
  94. Possible mathematical model for a rejectable quality level provision, with 10-year lifeline
  95. Equation for RQL provision
  96. EXPLIF general performance model
  97. First of 4 equations in 4 unknowns
  98. Second of 4 equations in 4 unknowns
  99. Third of 4 equations in 4 unknowns
  100. Fourth of 4 equations in 4 unknowns
  101. Solution to equations 97-100
  102. Equation 101 converted from EXPLIF to PD*
  103. Composite payment schedule equation
  104. Compound composite payment schedule equation, part 1
  105. Compound composite payment schedule equation, part 2
  106. Performance relationship model
  107. Multiple-parameter model form-step 1
  108. Multiple-parameter model form-step 2
  109. Multiple-parameter model form-step 3
  110. Multiple-parameter model form-step 4
  111. First simultaneous equation formed from table 55 and equation 109
  112. Second simultaneous equation formed from table 55 and equation 109
  113. Third simultaneous equation formed from table 55 and equation109
  114. Fourth simultaneous equation formed from table 55 and equation 109
  115. Complete performance model
  116. Appropriate payment adjustment for new pavement or overlay
  117. Equation for upper part of figure 69 payment schedule
  118. Equation for lower part of figure 69 payment schedule
  119. Payment schedule proposed for use by an owner
  120. Equation 119 transformed for use with OCPLOT
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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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