Order statistics for the two-level eight-run saturated-unreplicated fractional-factorial screening: corrections for asymmetry in the three- and four-factor multi-contrasting

摘要

The eight-run, two-level, seven-factor saturated-unreplicated orthogonal array has been analysed previously by pure distribution-free multi-comparison tests. It has been found in this work that there is asymmetry for two particular reference cumulative distribution functions relating to three- and four-factor contrasting. Both of these groups are separated into two distribution families, one containing 28 members and the other seven members. However, it is stressed that the corrections proposed in this work does not essentially alter the statistical behaviour of previous results when considering the cut-off points in terms of composite rank-sums for the typical statistical significance levels of 0.1 and 0.05, respectively.