Analysis of an Unreplicated Fractional-Factorial Design Using Nonparametric Tests

Abstract

ABSTRACT Construction quality management requires the prediction of optimum values of quality works characteristics such as the safety factor before the blueprint plans have been finalized. Predesign, high accuracy data from a professional CAD/CAE software package was used to feed an appropriate factorial design. A standard analysis tool such as the analysis of variance (ANOVA) was used to provide a hierarchy in factor strength dependence. All-available-factor-column engagement forces nullification of the method due to the known lack of degrees of freedom and the nonexistent error contribution due to the nature of this optimization. To circumvent this problem a novel integration of a factorial design with proven nonparametric tests is proposed to remedy this deadlock situation. Based on data from an excavation project on contract, a case study illustrates the use of a 7-factor L8(27) orthogonal array to organize the data collection phase. Factor-settings comparisons are performed to determine their efficacy on the safety factor. The method includes a combination of response tables based on median evaluations and the application of Wilcoxon's two-sample rank-sum test (Mann-Whitney's test) to investigate the statistical significance of the variation caused by each factor separately. This method succeeds in producing statistically reliable factor dependence on the safety factor when compared with posteriori pooled GLM ANOVA where the number of experiments has to be kept small and the need for considering the effect of many factors simultaneously is practically inescapable. It is a first attempt at a nongraphical method based on powerful exact statistics to resolve unreplicated and saturated designs during a screening phase. The method is very efficient, convenient and nonempirical, requiring no computational aids. It is discussed how it competes with well-accepted graphical methods.