Identification and Quantification in Multivariate Quality Control Problems

Abstract

Many quality control problems are multivariate in character since the quality of a given product or object consists simultaneously of more than one variable. A good multivariate quality control procedure should possess three important properties, namely, the control of the overall error rate, the easy identification of errant variables, and the easy quantification of any changes in the variable means. In this paper a procedure is suggested based on the construction of exact simultaneous confidence intervals for each of the variable means that meets each of these three goals. Both parametric and nonparametric procedures are considered, and critical point evaluation through tables, numerical integration, and simulation is discussed. Various examples of the implementation of the procedure are given.