Multivariate control charts are valuable tools for multivariate statistical process control (MSPC) used to monitor industrial processes and to detect abnormal process behavior. It has been shown in the literature that Bayesian control charts are optimal tools to control the process compared with the non-Bayesian charts. To use any control chart, three control chart parameters must be specified, namely the sample size, the sampling interval and the control limit. Traditionally, control chart design is based on its statistical performance. Recently, industrial practitioners and academic researchers have increasingly recognized the cost benefits obtained by applying the economically designed control charts to quality control, equipment condition monitoring, and maintenance decision-making. The primary objective of this research is to design multivariate Bayesian control charts (MVBCH) both for quality control and conditional-based maintenance (CBM) applications. Although considerable research has been done to develop MSPC tools under the assumption that the observations are independent, little attention has been given to the development of MSPC tools for monitoring multivariate autocorrelated processes. In this research, we compare the III performance of the squared predication error (SPE) chart using a vector autoregressive moving average with exogenous variables (VARMAX) model and a partial least squares (PLS) model for a multivariate autocorrelated process. The study shows that the use of SPE control charts based on the VARMAX model allows rapid detection of process disturbances while reducing false alarms.Next, the economic and economic-statistical design of a MVBCH for quality control considering the control limit policy proved to be optimal by Makis (2007) is developed. The computational results illustrate that the MVBCH performs considerably better than the MEWMA chart, especially for smaller mean shifts. Sensitivity analyses further explore the impact of the misspecified out-of-control mean on the actual average cost. Finally, design of a MVBCH for CBM applications is considered using the same control limit policy structure and including an observable failure state. Optimization models for the economic and economic statistical design of the MVBCH for a 3 state CBM model are developed and comparison results show that the MVBCH performs better than recently developed CBM Chi-square chart.

Recently, there has been a growing interest among industrial practitioners and researchers for applying economically designed control charts in quality control, condition monitoring, and condition-based maintenance (CBM). Control charts are powerful tools for process control which are used extensively to ensure the process stability over the production run. It has been proved that traditional control charts are not optimal and the control chart parameters should be determined based on the posterior probability that the process is out of control. Design and development of Bayesian control charts in both quality control and CBM applications are the main focuses of this thesis. Traditionally, in designing of a control chart, the observations are collected periodically. However, in many real applications, high sampling cost is associated with collecting observable data, therefore, it could be beneficial to monitor the process/system less frequently when it is in a healthier state and more frequently when a sample shows some indication of a change in the process/system state. The motivation of this thesis comes from such applications when collecting observations is costly, and observations carry partial information about the process or system state. To overcome the drawback of period monitoring, this thesis proposes an optimal control problem in Bayesian framework which uses a novel sampling strategy referred to as dual sampling scheme (DSS) and dual control limits. The system/process is monitored less frequently using a longer sampling interval when the posterior probability is below the warning limit. If the posterior probability exceeds the warning limit, switching to the shorter sampling interval occurs. If the posterior probability exceeds the control limit, the system/process is stopped and full inspection is performed. The proposed model is formulated in both semi-Markov decision process and renewal theory frameworks to obtain the optimal control chart parameters as well as the minimum long-run expected average cost per unit time. For the first time in quality control literature, an explicit formula is derived for computation of average time to signal for multivariate Bayesian control chart with DSS. In addition, the closed-form expressions are derived for system residual life and reliability as functions of the posterior probability statistics.

Although there are many Bayesian statistical books that focus on biostatistics and economics, there are few that address the problems faced by engineers. Bayesian Process Monitoring, Control and Optimization resolves this need, showing you how to oversee, adjust, and optimize industrial processes. Bridging the gap between application and dev

Given their key position in the process control industry, process monitoring techniques have been extensively investigated by industrial practitioners and academic control researchers. Multivariate statistical process control (MSPC) is one of the most popular data-based methods for process monitoring and is widely used in various industrial areas. Effective routines for process monitoring can help operators run industrial processes efficiently at the same time as maintaining high product quality. Multivariate Statistical Process Control reviews the developments and improvements that have been made to MSPC over the last decade, and goes on to propose a series of new MSPC-based approaches for complex process monitoring. These new methods are demonstrated in several case studies from the chemical, biological, and semiconductor industrial areas. Control and process engineers, and academic researchers in the process monitoring, process control and fault detection and isolation (FDI) disciplines will be interested in this book. It can also be used to provide supplementary material and industrial insight for graduate and advanced undergraduate students, and graduate engineers. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

A text for students or professionals involved with multivariate quality control who are knowledgeable about univariate statistical estimation and control procedures, and certain probability functions such as the normal and chi-square distributions. The coverage is limited to the Hotelling T2 statistic as being the most benefit to practitioners. The disk contains a demonstration version of statistical software compatible with recent Windows products. Annotation copyrighted by Book News Inc., Portland, OR.

Geared toward upper-level undergraduates and graduate students, this two-part treatment deals with the foundations of multivariate analysis as well as related models and applications. Starting with a look at practical elements of matrix theory, the text proceeds to discussions of continuous multivariate distributions, the normal distribution, and Bayesian inference; multivariate large sample distributions and approximations; the Wishart and other continuous multivariate distributions; and basic multivariate statistics in the normal distribution. The second half of the text moves from defining the basics to explaining models. Topics include regression and the analysis of variance; principal components; factor analysis and latent structure analysis; canonical correlations; stable portfolio analysis; classifications and discrimination models; control in the multivariate linear model; and structuring multivariate populations, with particular focus on multidimensional scaling and clustering. In addition to its value to professional statisticians, this volume may also prove helpful to teachers and researchers in those areas of behavioral and social sciences where multivariate statistics is heavily applied. This new edition features an appendix of answers to the exercises.