A Designed Screening Study with Prespecified Combinations of Factor Settings

Abstract

ABSTRACT In many applications, the experimenter has limited options about what factor combinations can be chosen for a designed study. Consider a screening study for a production process involving five input factors whose levels have been previously established. The goal of the study is to understand the effect of each factor on the response, a variable that is expensive to measure and results in destruction of the part. From an inventory of available parts with known factor values, we wish to identify a best collection of factor combinations with which to estimate the factor effects. Though the observational nature of the study cannot establish a causal relationship involving the response and the factors, the study can increase understanding of the underlying process. The study can also help determine where investment should be made to control input factors during production that will maximally influence the response. Because the factor combinations are observational, the chosen model matrix will be nonorthogonal and will not allow independent estimation of factor effects. In this manuscript we borrow principles from design of experiments to suggest an “optimal” selection of factor combinations. Specifically, we consider precision of model parameter estimates, the issue of replication, and abilities to detect lack of fit and to estimate two-factor interactions. Through an example, we present strategies for selecting a subset of factor combinations that simultaneously balance multiple objectives, conduct a limited sensitivity analysis, and provide practical guidance for implementing our techniques across a variety of quality engineering disciplines.