A Bayesian approach to multivariate quality control

During the last decade, several multivariate process control procedures have been developed for the detection of small to medium, persistent shifts in processes. Although, Joseph and Bowen (1991) used a Bayesian approach to design a univariate process control procedure, a multivariate Bayesian process control procedure had not been presented. This dissertation addresses this gap by proposing a set of multivariate Bayesian process control procedures.;Using Bayesian decision theory, one can formally incorporate prior knowledge about the processes in the solution of quality management problems. The approach used in this dissertation combines the prior information about the process mean vector with the sample information to estimate the posterior mean vector and decide if the process is in control.;Several multivariate Bayesian procedures have been proposed. The first procedure, called the Initial Multivariate Bayesian Procedure (IMBP), was developed and evaluated using simulation and performed better than existing efficient multivariate procedures in terms of both in-control and out-of-control average run lengths. The IMBP was revised (now called RMBP) so that it could be designed without resorting to simulation. The RMBP also performed better than some competing procedures for detecting shifts in the mean vector with a non-centrality parameter value of at least 1.;The dissertation also looks at the problem of inertia inherent in many process control methods, including the MBPs, and suggests two ways of partially alleviating it. With respect to their robustness properties, RMBPs based on the k latest observations were found to be quite robust to departures from the assumption of a multivariate normal sampling distribution.;The univariate Bayesian procedure, a special case of the MBP, was found to perform better than existing optimal univariate procedures when it was designed based on the k latest observations.;Finally, the RMBP was applied to data from a manufacturing operation to illustrate its implementation.