New design comparison criteria in Taguchi's robust parameter design

Abstract

Choice of an experimental design is an important concern for most researchers. Judicious selection of an experimental design is also a weighty matter in Robust Parameter Design (RPD). RPD seeks to choose the levels of fixed controllable variables that provide insensitivity (robustness) to the variability of a process induced by uncontrollable noise variables. We use the fact that in the RPD scenario interest lies primarily with the ability of a design to estimate the noise and control by noise interaction effects in the fitted model. These effects allow for effective estimation of the process variance — an understanding of which is necessary to achieve the goals of RPD.

Possible designs for use in RPD are quite numerous. Standard designs such as crossed array designs, Plackett-Burman designs, combined array factorial designs and many second order designs all vie for a place in the experimenters tool kit. New criteria are developed based on classical optimality criteria for judging various designs with respect to their performance in RPD. Many different designs are studied and compared. Several first-order and many second order designs such as the central-composite designs, Box-Behnken designs, and hybrid designs are studied and compared via our criteria. Numerous scenarios involving different models and designs are considered; results and conclusions are presented regarding which designs are preferable for use in RPD. Also, a new design rotatability entity is introduced.

Optimality conditions with respect to our criteria are studied. For designs which are rotatable by our new rotatability entity, conditions are given which lead to optimality for a number of the new design comparison criteria.

Finally, a sequential design-augmentation algorithm was developed and programmed on a computer. By cultivating a unique mechanism the algorithm implements a D_s-optimal strategy in selecting candidate points. D_s-optimality is likened to D-optimality on a subset of model parameters and is naturally suited to the RPD scenario. The algorithm can be used in either a sequential design-augmentation scenario or in a design-building scenario. Especially useful when a standard design does not exist to match the number of runs available to the researcher, the algorithm can be used to generate a design of the requisite size that should perform well in RPD.