Multiple doubling: a simple effective construction technique for optimal two-level experimental designs

Abstract

Design of experiment is an efficient statistical methodology of establishing which input variables are important (have significant effects) in an experiment (process) and the conditions under which these inputs should work to optimize the outputs of that process. Two-level designs are widely used in high-tech industries and manufacturing for productivity and quality improvement experiments. The construction of (nearly) optimal two-level designs for real-life experiments with large number of input variables can be quite challenging. The practice demonstrated that the existing techniques are complex, highly time-consuming, produce limited types of designs, and likely to fail in large experiments (i.e., optimal results are not expected). To overcome these significant problems, this article gives a simple and effective technique for constructing large two-level designs with good statistical properties. To meet practical needs in different fields, the statistical properties of the generated designs by the new technique are investigated from four basic perspectives: minimizing the similarity among the experimental runs, minimizing the aliasing among the input variables, maximizing the resolution, and filling the experimental domain as uniformly as possible. New recommended saturated orthogonal main effect plans and uniform orthogonal arrays of strength three with thousands or even millions of runs and factors are generated via the new technique without recourse to optimization software.