Richard M Weed

Derivation of Equation for Cost of Premature Pavement Failure

With the continuing interest in performance-related specifications and the development of software packages to compute the appropriate level of payment associated with variable levels of quality, there is a need for a simple, easily understood method to validate the output of these computer programs. A standard validation procedure is to create realistic hypothetical cases that can be calculated readily by hand and then to compare the results with the output of the procedure under test. An equation is derived that can serve two extremely useful purposes: it can be used as a validation tool for software currently under development, or it can be used directly to establish pay schedules that award payment appropriate for the level of quality received.

A RATIONAL METHOD FOR RELATING AS-BUILT QUALITY TO PAVEMENT PERFORMANCE AND VALUE

Highway construction specifications routinely use adjusted-payment provisions to award payment in proportion to the level of quality received. Work that meets the level of quality defined as acceptable is eligible for 100 percent payment, whereas work that fails to meet the desired quality level but that is not sufficiently deficient to warrant removal and replacement typically receives some degree of pay reduction. More recently, many agencies have begun to offer monetary incentives in the form of bonus provisions for work that substantially exceeds the desired level of quality. Although the pay-adjustment approach to highway quality assurance is now widely used, there is not yet a consistency of practice regarding the magnitude of pay adjustment judged appropriate for varying levels of as-built quality. To achieve consistency and make this approach more effective and defensible, there is need for a method to relate as-built quality to expected performance, which can then be related to value by engineering-economics procedures. The extension and refinement of earlier work are described here and an example structured around one of the performance relationships in the AASHTO Guide for Design of Pavement Structures is provided. This methodology suggests that many pay schedules currently in use may not fully recoup the real costs incurred by highway agencies as a result of defective work.

Method to Model Performance Relationships and Pay Schedules

Performance-related specifications require mathematical models to link construction quality to expected life and, ultimately, to value expressed in the form of pay schedules. Although ongoing research efforts continue to advance the state of the art, the type of data needed to develop accurate and precise models may not become available for several years. In the interim, present engineering and mathematical knowledge can be used to create rational and practical models that will perform effectively until better models are available. Several examples are presented to illustrate how both analytical data and survey data can be used to develop realistic performance models and pay schedules useful for statistical construction specifications. The issue of the proper method that can be used to combine the effects of multiple deficiencies is also addressed.

Mathematical Modeling of Pavement Smoothness

The vast majority of states, as well as many local agencies, now use statistical end-result specifications to encourage high-quality construction by awarding payment in proportion to the level of quality received. Because many of the specification procedures were developed by intuition and guesswork, more recent efforts have been directed at converting the specifications to true performance-related specifications, thus providing a rational and defensible basis for price-adjustment decisions. To develop practical and effective specifications of this type, it is necessary to have at least approximate quantitative (mathematical) models of the manner in which construction quality affects performance. By using pavement smoothness as an example, a method is presented by which empirical performance data can be combined with logical assumptions about mathematical form and boundary conditions to develop quantitative models sufficiently accurate for use with statistical construction specifications.

PRACTICAL FRAMEWORK FOR PERFORMANCE-RELATED SPECIFICATIONS

As highway agencies moved away from the older prescription-type specifications and began to develop end-result and performance-related specifications, several different statistical measures of quality have been used. These include the sample mean (x); percent defective or its complement, percent within limits; and the average absolute deviation. Conformal index is yet another measure that has been proposed. What has not been undertaken during this developmental period is any sort of formal analysis to determine which, if any, of these measures accurately reflects the expected performance of the construction items to which they are applied. Specialized computer programs were developed to demonstrate potential weaknesses of current quality measures and to explore alternate approaches that may overcome these weaknesses. It was found that pay equations based on the mean and standard deviation computed from the sample can be tailored to closely match the value of the constructed product as estimated by life-cycle cost techniques. It is believed that this forms a practical starting point for the development of construction acceptance procedures more closely linked to quantified performance models.

Accuracy and precision of typical quality measures

Computer simulation studies were performed to evaluate the accuracy and precision of the estimators for three quality measures: percent within limits (PWL), average absolute deviation (AAD), and conformal index (CI). Sample sizes of 3, 5, and 10 were simulated for various levels of actual population PWL, AAD, or CI. The estimators for all three quality measures exhibited similar trends for the variabilities of their respective individual estimates. For each estimator, the variability decreased as the sample size increased. For PWL, the variabilities increased as the actual population PWL departed from either 0 or 100 PWL, peaking at 50 PWL. For AAD and CI, the variabilities increased as the actual population value, AAD or CI, departed from 0. Both PWL and AAD were unbiased estimators of their respective population parameters. However, the CI appeared to be a biased estimator, consistently underestimating the true population CI. Since the CI offers no benefits compared to AAD, and since it appears to be a ...

Mathematical Modeling Procedures for Performance-Related Specifications

Performance-related specifications (PRS) that depend on quantified relationships between various construction characteristics and performance provide one of the best means for achieving both effectiveness and fairness in the administration of highway construction contracts. But if this approach is to be used to its fullest advantage, current knowledge must be synthesized into a simple and straightforward process that can be easily understood and applied by engineers having only a basic background in statistics, mathematics, and computer science. A previous paper described how several approaches used successfully by the New Jersey Department of Transportation can form the basis for such a process. A logical continuation of this work has resulted in two important refinements. The first allows high and low failures of a two-sided requirement to be treated as separate quality measures, when appropriate, and the second provides a more general mathematical model to allow greater flexibility in developing multicharacteristic performance relationships. An extensive series of tests necessary to validate performance models derived by this procedure is described. The complete developmental process is offered as a practical alternative for agencies that want to develop their own versions of PRS.

Estimating Percent Within Limits for Skewed Populations

Computer simulation, using samples of size 3, 5, and 10, was used to evaluate the percent within limits (PWL) estimates for populations with skewness coefficients from 0.0 to ±3.0. The average bias and variability were then determined for the 10,000 PWL estimates. The analyses show that even a moderate amount of skewness in the underlying population can affect both the accuracy (bias) and the variability of individual lot PWL values. The amount of bias increased as the amount of skewness increased, and the bias also increased as the sample size increased. The results show that with two-sided specifications the bias varies not only in its magnitude but also in its sign, that is, positive or negative, depending on the split of defective material outside the lower and upper limits (the PDLLPDU split). The amount of variability also increases as a greater percentage of the defective material is on the long tail of the distribution. Increased variability means that errors in individual lot estimates will be la...

Development of composite quality measures

Statistical construction specifications based on multiple quality characteristics frequently use pay equations that include a separate term for each of the quality characteristics so that the resultant pay adjustment is a function of the combined effect of all quality measures. An alternate method that can be used to accomplish the same purpose is to base the pay equation on a single quality measure that is a composite of the individual quality measures. The latter approach, because it keys the various decision-making steps to a single performance indicator, simplifies the procedure and offers several practical advantages. It is believed that this approach makes significant strides toward the ultimate goal of developing quality assurance procedures that are at the same time technically sound, fair and effective, and easy to understand and apply. Examples of a two-variable case for hot-mix asphalt pavement and a general three-variable case are presented.

Understanding Statistics in Maintenance Quality Assurance Programs

From the 1990s to now, transportation maintenance quality assurance (MQA) programs have been developed to ensure that maintenance quality is being achieved. MQA programs must be capable of detecting insufficient maintenance efforts, poor material performance, and incorrect procedures when evaluating end-product performance. At the Maintenance Quality Assurance Peer Exchange held at Madison, Wisconsin, in October 2004, participants expressed interest in exploring how statistical tools might be more effectively applied in MQA programs. The purpose of this paper is to provide maintenance practitioners with knowledge of how to understand and use statistics in MQA programs. Literature pertaining to recent efforts in this area was reviewed and synthesized. In addition, hazardous debris data from Wisconsin and level of service data from North Carolina were analyzed to demonstrate how an agency could apply traditional statistical methods such as analysis of variance, confidence limits, means comparison, data stratification, and sample size determination to an MQA program.