The Optimality Theory Of The Whole-plot Factor Is More Important

Suppose there are n factors in an experiment, each at two levels. Among them. there are n1 factors whose levels are very difficult or expensivc to be changed. The levels of the remaining n2(=n-n1) factors are easy to be changed. The hard-to-change factors are called whole plot (WP) factors and the relatively easy-to-change factors are called subplot(SP) factors. Obviously, the factors no longer have the same status. In this case, fractional factorial split-plot, (FFSP) designs are widely used.A two-phase randomization is needed when carrying out an FFSP experiment. This results in two sources of errors in analysis of variance, the WP error term and SP error term.A lot of experiments have shown that the former is larger than the latter. This implies that the power to detect significant effects in data analysis is not the same for the two kinds of factors. The WP factors are more important than the SP factors.Minimum aberration (MA) is one of the commonly used criteria to select. the optimal designs. In the MA criterion for the FFSP designs in the literature, the WP factors and SPfactors are assumed to have the same status. Under the assumption that the WP factors aremore important than the SP factors in an experiment, the paper proposes a new optimal criterion for selecting FFSP designs, that is, the minimum aberration of type WP (WP-MA)criterion. Then, it investigates the properties of FFSP designs under the WP-MA criterion,and gives the construction methods of the optimal FFSP 2(n1+n2)-(k1+k2) designs with small k1 and k2 under the WP-MA criterion.