American Society of Civil Engineers

Effects of Nonnormal Distributions on Highway Construction Acceptance Pay Factor Calculation

by Moin Uddin, (corresponding author), (Doctoral Candidate, Dept. of Civil Engineering, Univ. of Kentucky, Lexington, KY 40506-0281 E-mail:, Kamyar C. Mahboub, (Professor, Dept. of Civil Engineering, 263 Raymond Bldg., Univ. of Kentucky, Lexington, KY 40506-0281. E-mail:, and Paul M. Goodrum, (Associate Professor, Dept. of Civil Engineering, Univ. of Kentucky, 151C Raymond Bldg., Lexington, KY 40506-0281. E-mail:

Journal of Construction Engineering and Management, Vol. 137, No. 2, February 2011, pp. 108-118, (doi:

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Document type: Journal Paper
Section Heading: Construction Materials and Methods
Abstract: Percent within limits (PWL) is a commonly used quality control/quality assurance measure of highway pavement materials and construction, and it is a popular index for adjusting pay factors. However, PWL is based on the assumption of normal distribution of quality characteristics (e.g., concrete compressive strength and asphalt air voids). Skewness and kurtosis, which are common forms of statistical nonnormal distributions, can potentially bias the acceptance pay factor calculations. To examine this potential pay bias, simulations were performed to investigate the magnitude and the direction (overestimation or underestimation) of pay factor calculations. The study revealed that for both one-sided and two-sided specification limits, bias in pay factors not only did vary in magnitude but also reversed in direction over various ranges of PWL. These analyses showed that for a one-sided upper specification limit, on average, a positive skewness and kurtosis can underestimate the pay factor of an acceptable quality level population by 0.90%, and overestimates a rejectable quality level population by 3.8%. This leads to falsely penalizing acceptable products and rewarding bad products. The same was true for two-sided limits, which again varied based upon the percent of defective materials at the tails of the distribution. This is a very important issue because these biases in pay factors can easily upset the relative profit margins of the contractor. Furthermore, this may not be easily detectable without a detailed and sophisticated analysis as outlined in this paper. For multiple quality characteristics based pay factors, analyses showed that the combined magnitude of these biases was not linearly cumulative. Findings of the study indicate that bias in pay was higher for lots with fewer sublots and higher skewness and kurtosis.

ASCE Subject Headings:
Quality control
Highways and roads
Construction management

Author Keywords:
Percent within limits
Quality control