ROBUST STATISTICAL METHODS FOR NON-NORMAL QUALITY ASSURANCE DATA ANALYSIS IN TRANSPORTATION PROJECTS

The American Association of Highway and Transportation Officials (AASHTO) and Federal Highway Administration (FHWA) require the use of the statistically based quality assurance (QA) specifications for construction materials. As a result, many of the state highway agencies (SHAs) have implemented the use of a QA specification for highway construction. For these statistically based QA specifications, quality characteristics of most construction materials are assumed normally distributed, however, the normality assumption can be violated in several forms. Distribution of data can be skewed, kurtosis induced, or bimodal. If the process shows evidence of a significant departure from normality, then the quality measures calculated may be erroneous. In this research study, an extended QA data analysis model is proposed which will significantly improve the Type I error and power of the F-test and t-test, and remove bias estimates of Percent within Limit (PWL) based pay factor calculation. For the F-test, three alternative tests are proposed when sampling distribution is non-normal. These are: 1) Levene’s test; 2) Brown and Forsythe’s test; and 3) O’Brien’s test. One alternative method is proposed for the t-test, which is the non-parametric Wilcoxon - Mann – Whitney Sign Rank test. For PWL based pay factor calculation when lot data suffer non-normality, three schemes were investigated, which are: 1) simple transformation methods, 2) The Clements method, and 3) Modified Box-Cox transformation using “Golden Section Search” method. The Monte Carlo simulation study revealed that both Levene’s test and Brown and Forsythe’s test are robust alternative tests of variances when underlying sample population distribution is non-normal. Between the t-test and Wilcoxon test, the t-test was found significantly robust even when sample population distribution was severely non-normal. Among the data transformation for PWL based pay factor, the modified Box-Cox transformation using the golden section search method was found to be the most effective in minimizing or removing pay bias. Field QA data was analyzed to validate the model and a Microsoft® Excel macro based software is developed, which can adjust any pay consequences due to non-normality