Abstract
Nonnormality in the form of skewness and kurtosis was examined in lot acceptance quality characteristics data from seven state highway agencies for their highway construction quality assurance programs. Lot skewness and kurtosis varied significantly. For most lot data sets, skewness values varied in the range of 0.0 +/- 1.0, whereas most kurtosis values varied in the range of 0.0 +/- 2.0. The analysis also reveals that, on average, 50% of lot test data sets were nonnormal with 15% of lot data sets having skewness greater than +/- 1.0 and kurtosis greater than +/- 2.0. This is a significant finding because most state transportation agencies' pay factor algorithms assume normally distributed lot. Further investigation showed that high skewness and kurtosis were associated with higher lot variability. This variability produced misleading results in regard to inflated Type I error and low power for the F-test. However, the t-test was found to be quite robust for distinguishing mean differences. Significant deviation was observed in lot pay factors based on percent within limits between assumed normal data and normalized data. Effects of nonnormal distribution on the lot pay factor were found to be varied on the basis of the specification limits, the distribution of defective materials on the tails in the case of two-sided limits, and the orientation of the nonnormal distribution itself.