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| This report is an archived publication and may contain dated technical, contact, and link information |
Publication Number: FHWA-HRT-04-046
Date: October 2004
|
Evaluation of Procedures for Quality Assurance Specifications
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Table of Contents | Next
Foreword
Much has been written to guide highway agencies in the development, implementation,
and use of quality assurance specifications. Unfortunately, the guidance is
scattered and piecemeal. In some cases, it is out-of-date, inconsistent, or
even contradicts statistical principles. Further, agencies' negative experiences
with quality assurance specifications have often not been recorded, and common
mistakes are repeated by other agencies.
This report is a companion to FHWA-RD-02-095, Optimal Procedures for Quality
Assurance Specifications. While FHWA-RD-02-095 is a manual intended to
provide guidance to highway agencies, this report summarizes the research
work that was performed and contains the analyses to explain and justify the
provided guidance. This report will be of interest to those materials, construction,
specifications, and research engineers who wish to gain a better understanding
of any specific procedures recommended in the manual.
Sufficient copies of this report are being distributed to provide three copies
to each FHWA Resource Center, a minimum of one copy to each FHWA Division,
and a minimum of two copies to each State highway agency. Direct distribution
is being made to the division offices. Additional copies for the public are
available from the National Technical Information Services (NTIS), 5285 Port
Royal Road, Springfield, VA 22161.
T. Paul Teng, P.E.
Director, Office of Infrastructure
Research and Development
Notice
This document is disseminated under the sponsorship of the U.S. Department
of Transportation in the interest of information exchange. The U.S. Government
assumes no liability for the use of the information contained in this document.
The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the object of the document.
Quality Assurance Statement
The Federal Highway Administration (FHWA) provides high-quality information
to serve Government, industry, and the public in a manner that promotes public
understanding. Standards and policies are used to ensure and maximize the
quality, objectivity, utility, and integrity of its information. FHWA periodically
reviews quality issues and adjusts its programs and processes to ensure continuous
quality improvement.
Technical Report Documentation Page
| 1. Report No.
FHWA-HRT-04-046 |
2. Government Accession No. |
3. Recipient's Catalog No. |
| 4. Title and Subtitle EVALUATION OF PROCEDURES FOR QUALITY ASSURANCE SPECIFICATIONS |
5. Report Date
October 2004 |
| 6. Performing Organization Code |
| 7. Author(s)
J.L. Burati, R.M. Weed, C.S. Hughes, and H.S. Hill |
8. Performing Organization Report No. |
| 9. Performing Organization Name and Address
Department of Civil Engineering
Clemson University
Clemson, SC 29634-0911 |
10. Work Unit No. (TRAIS) |
| 11. Contract or Grant No.
DTFH61-98-C-00069 |
| 12. Sponsoring Agency's Name and Address
Office of Research, Development, and Technology
Federal Highway Administration
6300 Georgetown Pike
McLean, VA 22101-2296 |
13. Type of Report and Period Covered
Final Report Sept. 1998 - Oct. 2003 |
| 14. Sponsoring Agency's Code |
| 15. Supplementary Notes
Contracting Officer's Technical Representative (COTR): Peter A. Kopac,
HRDI-11
This study was conducted under State Planning and Research Pooled
Fund Study No. 2 (199) and was administered by the Federal Highway
Administration (FHWA). |
| 16. Abstract
The objective of this project was to develop a comprehensive quality
assurance (QA) manual, supported by scientific evidence and statistical
theory, which provides step-by-step procedures and instructions for
developing effective and efficient QA specifications.
This technical report summarizes the steps taken to accomplish this
goal, along with the analyses that were conducted to support the recommendations
made in the QA manual (FHWA-RD-02-095). The analytical techniques
used depended on the decision that needed to be made. Both analytical
and computer simulation approaches were used.
Percent within limits (PWL) (or its complement, percent defective
(PD)) was selected as the best quality measure because it combines
both the sample mean and standard deviation into a single measure
of quality. An approach based on a single composite quality measure
derived from a general performance model to predict expected pavement
life was developed and is the recommended approach for determining
payment factors when multiple quality characteristics are measured.
A detailed discussion and analysis are also presented regarding the
risks involved in the various approaches to verifying the contractor's
test results. The relatively high risks that are associated with typical
agency verification testing frequencies are highlighted. |
| 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, VA 22161. |
| 19. Security Classif. (of this report)
Unclassified |
20. Security Classif. (of this page)
Unclassified |
21. No. of Pages
414 |
22. Price |
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
SI (Modern Metric) Conversion Factors
Preface
It is important to note that two documents have been prepared for this project-a
manual for use by State highway administrations (SHAs), and this technical
report, which summarizes the procedures and findings of the project. The manual
is intended to be a comprehensive guide that a SHA can use when developing
new or modifying existing acceptance plans and quality assurance (QA) specifications.
While the focus and objectives of these documents are quite different, they
are not entirely stand-alone documents. In preparing the two documents, an
attempt has been made to minimize duplication of the contents. As such, this
technical report should be read in conjunction with and as a companion to
the QA specifications manual, Optimal Procedures for Quality Assurance
Specifications (Report No. FHWA-RD-02-095), which also resulted from this
project.
The focus of the manual is on what should be done when developing
QA specifications. The reasons for the various steps and possible decisions
are explained and easy-to-follow examples are included to assist in understanding
the process that is involved. The manual does not explain what was done during
the project, nor what analytical and simulation analyses were conducted, unless
it was necessary to clarify why certain steps in the process were necessary.
This technical report contains the detailed descriptions and summaries of
the results for the analyses that were conducted to arrive at the decisions
and recommendations included in the manual.
Table of Contents
- INTRODUCTION
- LITERATURE AND SPECIFICATION REVIEW
- SPECIFICATIONS DEVELOPMENT PROCESS
- SELECTING TOPICS FOR DETAILED ANALYSES
- QUALITY MEASURES: ACCURACY AND PRECISION
- QUALITY MEASURES: NORMALITY ASSUMPTION
- VERIFICATION PROCEDURES
- QUALITY MEASURES AND PAYMENT
- EVALUATING RISKS
- THE COMPOSITE PAYMENT FACTOR
- RELATING PAYMENT TO PERFORMANCE
- BRIEF SUMMARY AND RECOMMENDATIONS
APPENDIX A: ANNOTATED BIBLIOGRAPHY OF SELECTED ITEMS FROMTHE INITIAL LITERATURE SEARCH
APPENDIX B: SUMMARY OF AGENCY HMAC SPECIFICATIONS RECEIVED
APPENDIX C: SUMMARY OF AGENCY SUPERPAVE SPECIFICATIONS RECEIVED
APPENDIX D: SUMMARY OF AGENCY PCC SPECIFICATIONS RECEIVED
APPENDIX E: MINUTES FROM THE FIRST PANEL MEETING
APPENDIX F: ILLUSTRATIONS OF POSSIBLE RANGES FOR PD OR PWL ESTIMATES
APPENDIX G: BIAS HISTOGRAMS FROM THE SIMULATION PROGRAM
APPENDIX H: DISTRIBUTION OF SAMPLE PWL ESTIMATES
REFERENCES
List of Figures
1. States that provided funding for the study
2. Flowchart for phase I-Initiation and planning
3. Flowchart for phase II-Specifications development
4. Flowchart for phase III-Implementation
5. Survey sent to panel members
6. Graphical presentation of survey results for the first ranking method
7. Graphical presentation of survey results for the second ranking method
8. Plot of how the standard deviation of PWL estimates varies with the
population PWL
9a. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 90 PWL, sample 3
9b. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 90 PWL, sample 5
9c. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 90 PWL, sample 10
10a. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 70 PWL, sample 3
10b. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 70 PWL, sample 5
10c. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 70 PWL, sample 10
11a. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 50 PWL, sample 3
11b. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 50 PWL, sample 5
11c. Histogram illustrating the distribution of estimated PWL values for
1000 simulated lots from a population with 50 PWL, sample 10
12a. Illustration 1 of accuracy and precision of PWL estimates
12b. Illustration 2 of accuracy and precision of PWL estimates
12c. Illustration 3 of accuracy and precision of PWL estimates.
13. Plot of average difference of simulated PWL values versus actual PWL
values for sample sizes = 3, 5, and 10
14a. Plots of the 95th percentile for the average estimated PWL
minus the actual PWL at 50 versus the number of lots per project
14b. Plots of the 95th percentile for the average estimated PWL
minus the actual PWL at 70 versus the number of lots per project
14c. Plots of the 95th percentile for the average estimated PWL
minus the actual PWL at 90 versus the number of lots per project
15. Plot of average difference of simulated AAD values versus actual AAD
values for sample sizes = 3, 5, and 10
16. Plot of how the standard deviation of AAD estimates varies with the
population AAD value
17. Plot of average difference of simulated CI values versus actual CI
values for sample sizes = 3, 5, and 10
18. Plot of how the standard deviation of CI estimates varies with the
population CI value
19a. Plots of bias versus actual PWL for 10,000 simulated lots with 3 tests
per lot and one-sided limits showing positive skewness
19b. Plots of bias versus actual PWL for 10,000 simulated lots with 3 tests
per lot and one-sided limits showing negative skewness
20a. Plots of bias versus actual PWL for 10,000 simulated lots with 5 tests
per lot and one-sided limits showing positive skewness
20b. Plots of bias versus actual PWL for 10,000 simulated lots with 5 tests
per lot and one-sided limits showing negative skewness
21a. Plots of bias versus actual PWL for 10,000 simulated lots with 10 tests
per lot and one-sided limits with positive skewness
21b. Plots of bias versus actual PWL for 10,000 simulated lots with 10 tests
per lot and one-sided limits with negative skewness
22a. Plot of bias versus actual PWL for 10,000 simulated lots with various
tests per lot and one-sided limits with +1 skewness
22b. Plot of bias versus actual PWL for 10,000 simulated lots with various
tests per lot and one-sided limits with +2 skewness
22c. Plot of bias versus actual PWL for 10,000 simulated lots with various
tests per lot and one-sided limits with +3 skewness
23a. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=8/0)
23b. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=7/1)
23c. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=6/2)
23d. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=5/3)
23e. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=4/4)
23f. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=3/5)
23g. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=2/6)
23h. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=1/7)
23i. Illustration of the divisions that SKEWBIAS2H uses to calculate bias
in the PWL estimate for two-sided specification limits (skewness coefficient
= +1.0, split=0/8)
24a. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 10, sample=3, and two-sided limits
24b. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 10, sample=5,and two-sided limits
24c. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 10, sample=10, and two-sided limits
25a. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 30, sample = 3, and two-sided limits
25b. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 30, sample = 5, and two-sided limits
25c. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 30, sample = 10, and two-sided limits
26a. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 50, sample = 3, and two-sided limits
26b. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 50, sample = 5, and two-sided limits
26c. Plot of bias versus PDL/PDU divisions
for 10,000 simulated lots with PD = 50, sample = 10, and two-sided limits
27a. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 10, skewness = 1, and two-sided limits
27b. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 10, skewness = 2, and two-sided limits
28a. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots
with PD = 30, skewness = 1, and two-sided limits
28b. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots
with PD = 30, skewness = 2, and two-sided limits
29a. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots
with PD = 50, skewness = 1, and two-sided limits
29b. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots
with PD = 50, skewness = 2, and two-sided limits
30. Comparison of a normal population with a population with a skewness coefficient = +1.0
31. Sample program output screen for a population with PD = 10, skewness
coefficient = 0.00, and sample size = 5
32a. Portion of program output screens for PD = 10, skewness coefficient
= 0.00, and sample sizes = 3
32b. Portion of program output screens for PD = 10, skewness coefficient
= 0.00, and sample sizes = 5
32c. Portion of program output screens for PD = 10, skewness coefficient
= 0.00, and sample sizes = 10
33. Sample program output screen for a population with PD = 30, skewness coefficient = 1.00, and sample size = 5
34a. Portion of program output screens for PD = 30, skewness coefficient
= 1.00, and sample sizes = 3
34b. Portion of program output screens for PD = 30, skewness coefficient
= 1.00, and sample sizes = 5
34c. Portion of program output screens for PD = 30, skewness coefficient
= 1.00, and sample sizes = 10
35a. Examples of shapes and actual AAD values for populations centered on
the target and skewness coefficient of 0
35b. Examples of shapes and actual AAD values for populations centered on
the target and with skewness coefficients between .5 and 1.5
35c. Examples of shapes and actual AAD values for populations centered on
the target and with skewness coefficients between 2.0 and 3.0
36a. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients
36b. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients, sample
size = 3
36c. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients, sample
size = 5
36d. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients, sample
size = 10
37. Comparison of the shapes and spread of estimated AAD values for normal populations centered on and offset from the target
38. Example 1 of populations that are very dissimilar in shape, but have
approximately the same AAD
39a. Bias of the AAD sample estimates for populations centered on the target, but with various levels of skewness
39b. Spread of the AAD sample estimates for populations centered on the target, but with various levels of skewness
40a. Bias of the AAD sample estimates for normal populations with various offsets from the target and n = 5
40b. Spread of the AAD sample estimates for normal populations with various offsets from the target and n = 5
41a. Bias of the AAD sample estimates for normal populations centered on the target, with various standard deviation values, and n = 5
41b. Spread of the AAD sample estimates for normal populations centered on the target, with various standard deviation values, and n = 5
42. Sample output screen from the simulation program for bimodal distributions
43a. Program output screens for sample size = 5 and mean offsets = 1
43b. Program output screens for sample size = 5 and mean offsets = 2
43c. Program output screens for sample size = 5 and mean offsets = 3
43d. Program output screens for sample size = 5 and mean offsets = 4
43e. Program output screens for sample size = 5 and mean offsets = 5
44a. Illustration 1 of program output screens when combining distributions with equal means for sample size = 5
44b. Illustration 2 of program output screens when combining distributions with equal means for sample size = 5
44c. Illustration 3 of program output screens when combining distributions with equal means for sample size = 5
44d. Illustration 4 of program output screens when combining distributions with equal means for sample size = 5
45. OC surface for the maximum allowable difference test method verification method (assuming the smaller s = stest)
46. OC surface for the maximum allowable difference test method verification method (assuming the smaller s = 0.5stest)
47. OC surface for the maximum allowable difference test method verification method (assuming the smaller s = 2stest)
48a. Example 1 of some of the cases considered in the average run length
analysis for the maximum allowable difference method
48b. Example 2 of some of the cases considered in the average run length
analysis for the maximum allowable difference method
48c. Example 3 of some of the cases considered in the average run length
analysis for the maximum allowable difference method
49. OC curves for a two-sided t-test (a = 0.05)
50. OC curves for a two-sided t-test (a = 0.01)
51a. OC surfaces (also called power surfaces) for the appendix G
method for 5 contractor tests compared to a single agency test
51b. OC surfaces (also called power surfaces) for the appendix G
method for 6 contractor tests compared to a single agency test
51c. OC surfaces (also called power surfaces) for the appendix G
method for 7 contractor tests compared to a single agency test
51d. OC surfaces (also called power surfaces) for the appendix G
method for 8 contractor tests compared to a single agency test
51e. OC surfaces (also called power surfaces) for the appendix G
method for 9 contractor tests compared to a single agency test
51f. OC surfaces (also called power surfaces) for the appendix G method for 10 contractor tests compared to a single agency test
52. OC curves for the two-sided F-test for level of significance
a = 0.05
53. OC curves for the two-sided F-test for level of significance
a = 0.01
54a. EP curves for PWL payment schedule with sample size = 3
54b. EP curves for PWL payment schedule with sample size = 5
54c. EP curves for PWL payment schedule with sample size = 10
55a. Distribution of individual lot PWL = 90, sample = 3, and the resulting payment factors
55b. Distribution of individual lot PWL = 50, sample = 3, and the = resulting payment factors
55c. Distribution of individual lot PWL = 90, sample = 5, and the resulting payment factors
55d. Distribution of individual lot PWL = 50, sample = 5, and the resulting payment factors
55e. Distribution of individual lot PWL = 90, sample = 10, and the resulting payment factors
55f. Distribution of individual lot PWL = 50, sample = 10, and the resulting payment factors
56. EP curve with the 90th and 10th payment percentiles for the AAD payment schedule
57. Illustration of measuring AAD in standard deviation units (ZTarg)
from the mean
58. Example illustrating the PWL specification limits and the offset in
s units between the population mean and the target
59. EP curves for matched PWL and AAD payment equations for sample size = 5
60. Standard deviations for individual payment factors for matched PWL and AAD payment equations for sample size = 5
61a. Illustration 1 of two normal variables with various values for the correlation coefficient
61b. Illustration 2 of two normal variables with various values for the correlation coefficient
61c. Illustration 3 of two normal variables with various values for the correlation coefficient
61d. Illustration 4 of two normal variables with various values for the correlation coefficient
61e. Illustration 5 of two normal variables with various values for the correlation coefficient
61f. Illustration 6 of two normal variables with various values for the correlation coefficient
61g. Illustration 7 of two normal variables with various values for the
correlation coefficient
61h. Illustration 8 of two normal variables with various values for the correlation coefficient
62. Expected combined weighted average payment factors for various weights and correlation coefficients based on PWL.
63. Standard deviations of weighted average payment factors for various weights and correlation coefficients based on PWL.
64. Expected combined weighted average payment factors for various weights and correlation coefficients based on AAD
65. Standard deviations of weighted average payment factors for various weights and correlation coefficients based on AAD
66. Expected average payment factors for two populations with various correlation coefficients based on PWL
67. Expected average payment factors for two populations with various correlation coefficients based on AAD
68. Standard deviations of individual payment factors for two populations with various correlation coefficients based on PWL
69. Standard deviations of individual payment factors for two populations with various correlation coefficients based on AAD
70. Bias for the average payment for two populations with various actual PWL values
71. Bias for the average payment for two populations with various actual AAD values
72. Standard deviation for the individual average payment values for two populations with various actual PWL values
73. Standard deviation for the individual average payment values for two populations with various actual AAD values
74. OC curve for an acceptance plan that calls for rejection if the estimated PWL is less than 60, for sample size = 4
75. OC curves for the probabilities of receiving at least some payment and at least 100-percent payment, sample size = 4
76. OC curves for the probability of receiving various payments, sample size = 4
77. EP curve for the payment relationship Pay = 55 + 0.5PWL, with
an RQL provision, sample size = 4
78a. Distribution of estimated PWL values for an AQL population
78b. Distribution of payment factors for an AQL population
79. EP curve for the payment relationship Pay = 55 + 0.5PWL, sample
size = 4
80. Distributions of sample PWL estimates for a population with 90 PWL
81a. Distributions of sample PWL estimates for a population with 50 PWL
and one-sided speculations
81b. Distributions of sample PWL estimates for a population with 50 PWL
and two-sided speculations
82a. Distribution of sample standard deviations for a sample size, n = 3,
based on 1000 simulated samples
82b. Distribution of sample standard deviations for a sample size, n = 5,
based on 1000 simulated samples
82c. Distribution of sample standard deviations for a sample size, n = 10,
based on 1000 simulated samples
83. EP contours for the values in table 53
84. EP surface for the values in table 53
85. EP curves for the values in table 53
86. OC curve for an acceptance plan that calls for rejection if the estimated
PWL is less than 60, sample sizes = 5
87a. Simulation results of expected payment for the averaging method, combining two populations with equal PWL values
87b. Simulation results of standard deviation values for the averaging method, combining two populations with equal PWL values
88a. Simulation results of expected payment for the weighted average method,
combining two populations with equal PWL values
88b. Simulation results of standard deviation values for the weighted average
method, combining two populations with equal PWL values
89a. Simulation results of expected payment for the multiplication method,
combining two populations with equal PWL values
89b. Simulation results of standard deviation values for the multiplication
method, combining two populations with equal PWL values
90a. Simulation results of expected payment for the summation method, combining two populations with equal PWL values
90b. Simulation results of standard deviation values for the summation method,
combining two populations with equal PWL values
91a. Simulation results of expected payment for the maximum method, combining two populations with equal PWL values
91b. Simulation results of standard deviation values for the maximum method,
combining two populations with equal PWL values
92a. Simulation results of expected payment for the minimum method, combining two populations with equal PWL values
92b. Simulation results of standard deviation values for the minimum method,
combining two populations with equal PWL values
93a. Comparison of simulation results for various methods for combining
individual expected payment factors for two populations with PWL = 90
93b. Comparison of simulation results for various methods for combining individual standard deviation payment factors for two populations with PWL = 90
94a. Comparison of simulation results for various methods for combining
individual expected payment factors for two populations with PWL = 70
94b. Comparison of simulation results for various methods for combining
individual standard deviation factors for two populations with PWL = 70
95a. Comparison of simulation results for various methods for combining
individual expected payment factors for two populations with PWL = 50
95b. Comparison of simulation results for various methods for combining individual standard deviation payment factors for two populations with PWL
= 50
96. Flowchart of the PRS process
97. Illustration of the net impact of rescheduling an overlay 2 years
earlier than originally planned
98. Spread of possible sample means for a normal distribution with 10
PD below the lower specification limit and sample size = 3
99. Spread of possible sample means for a normal distribution with 10
PD below the lower specification limit and sample size = 10
100. Spread of possible sample means for a normal distribution with 5 PD
outside each specification limit and sample size = 3
101. Spread of possible sample means for a normal distribution with 5 PD
outside each specification limit and sample size = 10
102. Spread of possible sample means for a normal distribution with 50 PD
below the lower specification limit and sample size = 3
103. Spread of possible sample means for a normal distribution with 50 PD
below the lower specification limit and sample size = 10
104. Spread of possible sample means for a normal distribution with 25 PD
outside each specification limit and sample size = 3
105. Spread of possible sample means for a normal distribution with 25 PD
outside each specification limit and sample size = 10
106. Spread of possible sample means for a distribution with skewness =
1.0, 10 PD below the lower specification limit, and sample size = 3
107. Spread of possible sample means for a distribution with skewness =
1.0, 10 PD below the lower specification limit, and sample size = 10
108. Spread of possible sample means for a distribution with skewness = 1.0, 5 PD outside each specification limit, and sample size = 3
109. Spread of possible sample means for a distribution with skewness = 1.0, 5 PD outside each specification limit, and sample size = 10
110. Spread of possible sample means for a distribution with skewness = 1.0, 50 PD below the lower specification limit, and sample size = 3
111. Spread of possible sample means for a distribution with skewness = 1.0, 50 PD below the lower specification limit, and sample size = 10
112. Spread of possible sample means for a distribution with skewness = 1.0, 25 PD outside each specification limit, and sample size = 3
113. Spread of possible sample means for a distribution with skewness = 1.0, 25 PD outside each specification limit, and sample size = 10
114. Sample output screen for a population with PD = 10, skewness coefficient = 0.00, and sample size = 5
115. Portions of output screens for PD = 10, skewness coefficient = 0.00, and sample sizes = 3, 5, and 10
116. Sample output screen for a population with PD = 10, skewness coefficient = 1.00, and sample size = 5
117. Portions of output screens for PD = 10, skewness coefficient = 1.00, and sample sizes = 3, 5, and 10
118. Sample output screen for a population with PD = 10, skewness coefficient = 2.00, and sample size = 5
119. Portions of output screens for PD = 10, skewness coefficient = 2.00, and sample sizes = 3, 5, and 10
120. Sample output screen for a population with PD = 30, skewness coefficient = 0.00, and sample size = 5
121. Sample output screen for a population with PD = 50, skewness coefficient = 0.00, and sample size = 5
122. Sample output screen for a population with PD = 30, skewness coefficient = 0.00, and sample size = 10
123. Sample output screen for a population with PD = 50, skewness coefficient = 0.00, and sample size = 10
124. Portions of output screens for PD = 50, sample size = 5, and skewness coefficients = 0.00, 1.00, 2.00, and 3.00
125. Sample output screen for a population with PD = 10, skewness coefficient = 3.00, and sample size = 5
126. Sample output screen for a population with PD = 30, skewness coefficient = 3.00, and sample size = 5
127. Sample output screen for a population with PD = 50, skewness coefficient = 3.00, and sample size = 5
128a. Distribution of sample means for 1000 samples from a normal population with μ = 0.00, σ =1.00
128b. Distribution of standard deviations for 1000 samples from a normal population with μ = 0.00, σ =1.00
129a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 90, one-sided specifications
129b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 90, two-sided specifications
130a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 80, one-sided specifications
130b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 80, two-sided specifications
131a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 70, one-sided specifications
131b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 70, two-sided specifications
132a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 60, one-sided specifications
132b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 60, two-sided specifications
133a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 50, one-sided specifications
133b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 50, two-sided specifications
134. Illustration of the populations for which the distributions of sample PWL values are shown in figures 129 through 133
List of Tables
1. Project team
2. Panel members
3. Agencies that provided copies of their specifications
4. Survey results for the first ranking method
5. Survey results for the second ranking method
6. Overall rankings of the survey topics
7. Quality index values for estimating PWL
8. Accuracy and precision for PWL estimates (based on the results of 10,000 simulated lots)
9. Results of simulation analyses with actual PWL = 90 (distribution of the results from 1000 simulated projects)
10. Results of simulation analyses with actual PWL = 70 (distribution
of the results from 1000 simulated projects)
11. Results of simulation analyses with actual PWL = 50 (distribution
of the results from 1000 simulated projects)
12. Distributions of sample AAD values for a population centered on the
target and for sample sizes = 1, 3, 5, and 10
13. Distributions of sample AAD values for sample size = 3 and population means offset from the target by 0.50, 1.00, 1.50, 2.00, and 2.50 standard deviations
14. Accuracy and precision for AAD estimates (based on the results of 10,000 simulated lots)
15. Accuracy and precision for CI estimates (based on the results of 10,000 simulated lots)
16. Distributions with various levels of skewness
17. Bias in estimating PWL for various skewness coefficients and one-sided limits (3 tests per lot and 10,000 simulated lots)
18. Bias in estimating PWL for various skewness coefficients and one-sided limits (5 tests per lot and 10,000 simulated lots)
19. Bias in estimating PWL for various skewness coefficients and one-sided limits (10 tests per lot and 10,000 simulated lots)
20. Bias in estimating PWL for various skewness coefficients, sample sizes, and one-sided limits (10,000 simulated lots)
21. Results of simulations with PD = 10, 10,000 simulated lots, sample sizes = 3, 5, and 10, and two-sided limits
22. Results of simulations with PD = 30, 10,000 simulated lots, sample sizes = 3, 5, and 10, and two-sided limits
23. Results of simulations with PD = 50, 10,000 simulated lots, sample sizes = 3, 5, and 10, and two-sided limits
24. Bias and spread of the AAD sample estimates for populations centered on the target, but with various levels of skewness
25. Bias and spread of the AAD sample estimates for normal populations with various offsets from the target and n = 5
26. Bias and spread of the AAD sample estimates for normal populations with various standard deviation values and n = 5
27. Bias results for combining two populations with equal s with one-sided limits
28. Bias results for combining two populations with equal s with two-sided limits equidistant from the mean
29. Shapes of combined distributions when the combined distributions have different means and standard deviations
30. Bias in estimating PD when two populations are combined (sample size = 5, 10,000 simulated lots)
31. Average run length results for the single split-sample method (5000 simulated lots)
32. Allowable intervals for the AASHTO appendix G method
33. Average run length results for the appendix G method (5000 simulated
lots)
34. F-test power values for n = 3-10 and s-ratio l
= 1-5
35. F-test power values for n = 3-10 and s-ratio l
= 0-1
36. F-test power values for n = 5-100 and s-ratio l
= 1-3
37. Average run length results for the appendix H method (5 contractor tests and 1 agency test per lot) for 1000 simulated lots
38. Simulated EP factors and correct payment factors based on AAD
39. Relationship between ZTarg, AAD, and PWL for a normal population when the PWL specification limits are set at 1.645s
40. Relationship between AAD, ZTarg, and PWL for a normal population when the PWL specification limits are set at 1.645s
41. Relationship between PWL, AAD, and ZTarg for a normal population when the PWL specification limits are set at 1.645s
42. AAD values equivalent to the corresponding PWL payment factors
43. Results of the simulation of matched PWL and AAD payment equations for sample size = 5
44. Demonstration of the simulation of three correlated normal variables with selected values for correlation coefficients
45. Demonstration of the simulation of four correlated normal variables
with selected values for correlation coefficients
46. Results of PWL simulation analyses for two correlated normal variables.
47. Results of AAD simulation analyses for two correlated normal variables.
48. Bias in EP for two populations with equal PWL values and various correlation coefficients
49. Bias in EP for two populations with equal AAD values and various correlation coefficients
50. Standard deviations of individual payment factors for two populations
with equal PWL values and various correlation coefficients
51. Standard deviations of individual payment factors for two populations
with equal AAD values and various correlation coefficients
52. EP values using Pay = 55 + 0.5PWL for two individual payment
factors and then averaging them, sample size = 5
53. EP values using Pay = 55 + 0.5PWL for two individual payment
factors and then multiplying them, sample size = 5, correlation coefficient = +0.5
54. Probabilities that populations with various quality levels would require
removal and replacement for the example in figure 86
55. Completed data matrix for the example of an exponential model
56. Examples of computed PD* values for selected individual PD values
57. Illustration of the problem with separate RQL provisions
58. Alaska weight factors
59. Alaska QC/QA tests
60. Arkansas QC/QA tests
61. Colorado pay factor equations
62. Colorado QC/QA tests
63. Idaho QC/QA tests
64. Illinois smoothness pay factors
65. Illinois QC/QA tests
66. Iowa pay factors for density
67. Iowa pay factors for thickness
68. Iowa QC/QA tests
69. Maryland profile index adjustment (normal projects)
70. Maryland profile index adjustment (incentive projects)
71. Maryland QC/QA tests
72. Michigan QC/QA tests
73. Minnesota payment schedule
74. Minnesota determination of lots for density
75. Minnesota adjusted payment schedule for maximum density (disincentive)
76. Minnesota adjusted payment schedule for maximum density (incentive)
77. Minnesota payment schedule for smoothness
78. Minnesota QC/QA tests
79. Montana price reduction factors
80. Montana QC/QA tests
81. Nebraska density of asphalt concrete (first lot)
82. Nebraska density of asphalt concrete (subsequent lots)
83. Nebraska QC/QA tests
84. Nevada pay factors for profile index
85. Nevada pay factors for gradation
86. Nevada pay factors for asphalt content
87. Nevada pay factors for in-place air voids
88. Nevada QC/QA tests
89. North Dakota QC/QA tests.
90. Ohio QC/QA tests
91. Ontario QC/QA tests
92. Oregon weighting factors
93. Oregon QC/QA tests
94. Pennsylvania adjustment of contract price relative to the specification limits
95. Pennsylvania QC/QA tests
96. South Carolina required QC tests and verifications
97. South Carolina required acceptance tests
98. Texas pay factors for flexural strength
99. Texas pay factors for thickness
100. Texas QC/QA tests
101. Virginia QC/QA tests
102. Washington QC/QA tests
103. Wisconsin sampling frequencies
104. Wisconsin percent payment for mixture
105. Wisconsin QC/QA tests
106. Wyoming QC/QA tests
107. Connecticut M.A.D. from job-mix formula for consecutive tests
108. Connecticut pay factors for joint and mat density
109. Connecticut QC/QA tests
110. Kansas pay factors for specified density
111. Kansas pay factors for air voids (lot size of four tests)
112. Kansas pay factors for air voids (lot size of three tests)
113. Kansas pay factors for air voids (lot size of five tests)
114. Kansas pay factors for air voids (lot size of six tests)
115. Kansas QC/QA tests
116. Louisiana payment adjustment schedule
117. Louisiana QC/QA tests
118. Maine QC/QA tests
119. Minnesota payment schedule
120. Minnesota determination of lots for density
121. Minnesota payment schedule for density
122. Minnesota payment schedule for smoothness
123. Minnesota QC/QA tests
124. Mississippi sampling frequency
125. Mississippi lot determination for density
126. Mississippi pay factors for mixture quality
127. Mississippi pay factors for density
128. Mississippi pay factors for smoothness
129. Mississippi QC/QA tests
130. New York QC/QA tests
131. North Carolina testing frequency
132. North Carolina payment for mix produced in warning bands
133. North Carolina pay factor
134. North Carolina QC/QA tests
135. Kansas concrete thickness and comprehensive strength pay adjustment
136. Kansas QC/QA tests
137. Illinois QC/QA tests
138. Iowa pay factors for thickness
139. Iowa pay factors for flexural strength
140. Iowa QC/QA tests
141. North Carolina pay factors for thickness
142. North Carolina pay factors for flexural strength
143. North Carolina QC/QA tests
144. Oregon pay factors for thickness
145. Oregon QC/QA tests
146. Pennsylvania QA/QC tests.
147. Texas pay factors for flexural strength.
148. Texas pay factors for thickness
149. Texas QC/QA tests
150. Wisconsin pay factors for compressive strength
151. Wisconsin pay factors for the profile index
152. Wisconsin pay factors for thickness
153. Wisconsin QC/QA tests
