Staggered-Level Designs for Experiments With More Than One Hard-to-Change Factor

Abstract

In many industrial experiments, some of the factors are not independently set for each run. This is due to time and/or cost constraints and to the hard-to-change nature of the levels of these factors. Most of the literature restricts attention to split-plot designs in which all the hard-to-change factors are independently reset at the same points in time. This constraint is to some extent relaxed in split-split-plot designs because these allow the less hard-to-change factors to be reset more often than the most hard-to-change factors. A key feature of the split-split-plot designs, however, is that the less hard-to-change factors are reset whenever the most hard-to-change factors are reset. In this article, we relax this constraint and present a new type of design, which allows the hard-to-change factor levels to be reset at entirely different points in time. We show that the new designs are cost-efficient and that they outperform split-plot and split-split-plot designs in terms of the D- and A-optimality criteria. Because of the fact that the hard-to-change factors are independently reset alternatingly, we name the new designs staggered-level designs. Supplementary materials for this article are available online.

KEY WORDS:

• A- and D-optimality criterion
• Cost
• Gauss–Hermite quadrature
• OLS and GLS equivalence
• Split-plot design
• Split-split-plot design.

ACKNOWLEDGMENTS

The authors thank Sabine Paulussen, Sanaa Sarghini, and Dirk Vangeneugden from the Vlaamse Instelling voor Technologi- sche Ontwikkeling (VITO) for granting permission to use the anti-bacterial coating experiment as an example in this article, and the three referees, the associate editor, and the editor for their constructive suggestions.