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Publication Number: FHWA-HRT-04-046
Date: October 2004

Evaluation of Procedures for Quality Assurance Specifications

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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 In some cases, it is out-of-date, inconsistent, or even contradicts statistical principles.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

  1. INTRODUCTION
  2. LITERATURE AND SPECIFICATION REVIEW
  3. SPECIFICATIONS DEVELOPMENT PROCESS
  4. SELECTING TOPICS FOR DETAILED ANALYSES
  5. QUALITY MEASURES: ACCURACY AND PRECISION
  6. QUALITY MEASURES: NORMALITY ASSUMPTION
  7. VERIFICATION PROCEDURES
  8. QUALITY MEASURES AND PAYMENT
  9. EVALUATING RISKS
  10. THE COMPOSITE PAYMENT FACTOR
  11. RELATING PAYMENT TO PERFORMANCE
  12. 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

 

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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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