Construction of Two-Level Split-Lot Fractional Factorial Designs for Multistage Processes

Abstract

Split-lot designs, also known as multiway split-unit designs, are useful in factorial experiments where there are multiple processing stages. Such experiments occur, for example, in the fabrication of integrated circuits in the semiconductor industry and in product assembly. The designs have a split-plot structure at each stage so that settings of the factors are applied to sublots of experimental runs rather than to individual runs. This allows experimental runs to be processed at much less expense than if the runs were completely randomized. In this article, split-lot designs are constructed for two, three, and four processing stages. The designs have minimum aberration under the split-lot structure and minimize in various senses the confounding of main effects and two-factor interactions with the sublots at each stage.