Minimum Aberration Split-Plot Designs When the Whole Plot and Subplot Factors Do Not Have the Same Importance

Abstract

In practical factorial experiments, we sometimes find that complete randomization of the order of the runs is infeasible because it is more difficult to change the levels of some factors than the others, especially in some engineering experiments. Then, fractional factorial split-plot (FFSP) designs represent a practical option in such situations. The difficult-to-change factors are called whole plots (WP) factors, and the other factors are called subplot (SP) factors. The WP and SP factors do not have the same importance in many experiments. Then, the popular minimum aberration criterion is not suitable any more for choosing FFSP designs. This paper proposes two criteria for selecting FFSP designs. Algorithms for constructing the optimal FFSP designs under the two criteria are proposed. Some optimal designs under the two criteria are tabulated.