Contributions to statistical process control and robust parameter design.

Abstract

The thesis consists of two parts. Part I deals with methods for on-line detection and diagnosis of variation shifts in multidimensional data. The problem is motivated by applications to fixture failure diagnostics in automotive body assembly. We study various methods for detecting and diagnosing shifts in variation in one or more known directions and compare the performance of the methods with those for the general unknown direction case. Shewhart, CUSUM, and Shiryaev-Roberts type Bayesian monitoring schemes are developed for various hypotheses of interest. Their properties are studied through both asymptotic analysis and simulation. Part II deals with modeling and analysis of location and dispersion effects from robust parameter design experiments. There has been considerable interest recently in the joint estimation of location and dispersion effects from industrial experiments, stimulated by the work of Taguchi on robust parameter design. In Chapter 3, we develop Bayesian methods for analyzing data from such experiments. We consider several situations of interest for the noise array: independent replications and two different split-plot designs that arise in practice. We discuss both formal and informal methods for model selection. The implementation of the Gibbs sampler uses an auxiliary variable technique proposed by Damien, Wakefield, and Walker (1998) to improve the efficiency over the usual rejection-type algorithms. The methods are illustrated through several data sets. The efficiency and usefulness of blocking compared to completely randomized schemes are well known in situations with constant variance. In Chapter 4, we consider the case with variance heterogeneity and study the relative efficiency of estimators of location and dispersion effects. It is shown that the ordinary least squares (OLS) estimators of location effects can actually be less efficient under blocking than under a completely randomized scheme. Sharp bounds are obtained for the relative efficiency for estimators of location effects under a one-way ANOVA model and under a two-level factorial design structure. Analogous results on the relative efficiency of dispersion effects are also discussed together with implications of these results for robust parameter design experiments.