Solution to Nonnormality in Quality Assurance and Acceptance Quality Characteristics Data

Previous studies have identified high nonnormality in the form of skewness and kurtosis in highway construction data (hot-mix asphalt, portland cement concrete pavement, and aggregate materials) on the basis of analysis of field quality assurance data. [The authors use “nonnormality,” rather than “abnormality,” and define it as a term used in any discipline that involves statistical data analysis. —Ed.] The presence of high nonnormality in lot data is a significant finding because such nonnormality violates most state transportation agencies' normality assumption for quality assurance data analysis (e.g., F-test and t-test) and quality measure calculation (e.g., percent within limits). High nonnormality can have several adverse effects, such as increased variability in lot data and decreased efficiency of statistical verification tests in finding differences between contractor's and agency's data sets. Most important, however, nonnormal lot data tend to misdirect contractor payment; such misdirection can manifest in incorrectly penalizing contractors that deliver acceptable construction and rewarding contractors that deliver poor construction. A modified Box–Cox transformation using the golden section search algorithm is proposed: it can substantially reduce pay biases due to nonnormality even when lot sample size is small. The method is efficient and ensures fair and equitable payment to state agencies and contractors.