An Alternative Analysis Method to the ANOVA for p k Unreplicated Fractional Factorial Experiments

Abstract

An alternative analysis method to the conventional analysis of variance is proposed for the problem of identifying the active factors in pk unreplicated fractional factorial experiments (orthogonal arrays). The sums of squares calculated are arranged in ascending order, as S(1)≤S(2)≤S(3) ≤…≤ S(n). Assuming the least sum of squares, S(1) is inactive, i.e. having zero effect, the next candidate of inactive sums of squares, S(2), is tested. The following sums of squares, S(i)’s, i = 3,…, n, are tested by the pooled inactive sums of squares, on the condition that S(2),…, S(i-1) are not significant at the preceding tests, successively. The significance level of each test, as is set the same value and the overall risk of the first kind of the whole procedure, aT, is controlled to be 1%, 5% or 10%. The critical values at each step is numerically obtained for 33 orthogonal designs, and empirically obtained for 24 orthogonal designs by the Monte Carlo method. The proposed method can be applied not only to 2k, 31` orthogonal designs but also to Plackett-Burman designs.