Order Statistics for a Two-Level, Eight-Run Saturated-Unreplicated Fractional-Factorial Screening

Saturated-unreplicated fractional factorial designs remain popular in factor screening investigations. Among the most commonly used schemes is the classical two-level, eight-run orthogonal design. A brute force method is employed to compute a reference cumulative population frequency and cumulative distribution function by permuting directly ranked observations. The technique is simple and nongraphical. It is based on Wilcoxon-Mann-Whitney rank-sum test appropriately adapted for fractional-factorial composite inference. Contrary to most popular methods, this new approach does not rely to the effect-sparsity assumption. The method is illustrated in three unreplicated-saturated case studies. We discuss the performance of this test with other mainstream competing schemes.