Author:

Keywords:

A- and D-optimality criterion, Cost, Gauss-Hermite quadrature, OLS and GLS equivalence, Split-plot design, Split-split-plot design, Science & Technology, Physical Sciences, Statistics & Probability, Mathematics, ALGORITHM, 0104 Statistics, 4905 Statistics

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. © 2012 American Statistical Association and the American Society for Quality.