On the identification of active factors in nonregular two-level designs with a small number of runs

Abstract

Nonregular two-level designs are attractive screening designs due to their good projection properties and flexible run sizes. In particular, the 12-run Plackett–Burman (PB) design has become quite popular. However, existing methods struggle with the identification of active factors when the number of active factors exceeds the projectivity of the designs. This is especially the case when interactions are present, the variance is high and the number of runs is small. In this paper, we propose a method for analysing nonregular two-level designs that particularly addresses the issues above. It exploits the projection properties of designs and is here applied on the 12-run PB design and the 16-run no-confounding (NC) designs. In the construction of the method, the use of test- and penalty-based procedures are avoided. Instead, the number of allowed terms in a model is restricted. The effectiveness of the method and comparison between designs are evaluated by simulations for different scenarios. Ways to evaluate the reliability of the screening procedure are pointed out. An example with real data is given to demonstrate how one might perform the analysis in practice.