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 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.

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 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.

Many real-world systems experience deterioration with usage and age, which often leads to low product quality, high production cost, and low system availability. Most previous maintenance and reliability models in the literature do not incorporate condition monitoring information for decision making, which often results in poor failure prediction for partially observable deteriorating systems. For that reason, the development of fault prediction and control scheme using condition-based maintenance techniques has received considerable attention in recent years. This research presents a new framework for predicting failures of a partially observable deteriorating system using Bayesian control techniques. A time series model is fitted to a vector observation process representing partial information about the system state. Residuals are then calculated using the fitted model, which are indicative of system deterioration. The deterioration process is modeled as a 3-state continuous-time homogeneous Markov process. States 0 and 1 are not observable, representing healthy (good) and unhealthy (warning) system operational conditions, respectively. Only the failure state 2 is assumed to be observable. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The form of the optimal control policy that maximizes the long-run expected average availability per unit time has been investigated. It has been proved that a control limit policy is optimal for decision making. The model parameters have been estimated using the Expectation Maximization (EM) algorithm. The optimal Bayesian fault prediction and control scheme, considering long-run average availability maximization along with a practical statistical constraint, has been proposed and compared with the age-based replacement policy. The optimal control limit and sampling interval are calculated in the semi-Markov decision process (SMDP) framework. Another Bayesian fault prediction and control scheme has been developed based on the average run length (ARL) criterion. Comparisons with traditional control charts are provided. Formulae for the mean residual life and the distribution function of system residual life have been derived in explicit forms as functions of a posterior probability statistic. The advantage of the Bayesian model over the well-known 2-parameter Weibull model in system residual life prediction is shown. The methodologies are illustrated using simulated data, real data obtained from the spectrometric analysis of oil samples collected from transmission units of heavy hauler trucks in the mining industry, and vibration data from a planetary gearbox machinery application.

Many real-world systems experience deterioration with usage and age, which often leads to low product quality, high production cost, and low system availability. Most previous maintenance and reliability models in the literature do not incorporate condition monitoring information for decision making, which often results in poor failure prediction for partially observable deteriorating systems. For that reason, the development of fault prediction and control scheme using condition-based maintenance techniques has received considerable attention in recent years. This research presents a new framework for predicting failures of a partially observable deteriorating system using Bayesian control techniques. A time series model is fitted to a vector observation process representing partial information about the system state. Residuals are then calculated using the fitted model, which are indicative of system deterioration. The deterioration process is modeled as a 3-state continuous-time homogeneous Markov process. States 0 and 1 are not observable, representing healthy (good) and unhealthy (warning) system operational conditions, respectively. Only the failure state 2 is assumed to be observable. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The form of the optimal control policy that maximizes the long-run expected average availability per unit time has been investigated. It has been proved that a control limit policy is optimal for decision making. The model parameters have been estimated using the Expectation Maximization (EM) algorithm. The optimal Bayesian fault prediction and control scheme, considering long-run average availability maximization along with a practical statistical constraint, has been proposed and compared with the age-based replacement policy. The optimal control limit and sampling interval are calculated in the semi-Markov decision process (SMDP) framework. Another Bayesian fault prediction and control scheme has been developed based on the average run length (ARL) criterion. Comparisons with traditional control charts are provided. Formulae for the mean residual life and the distribution function of system residual life have been derived in explicit forms as functions of a posterior probability statistic. The advantage of the Bayesian model over the well-known 2-parameter Weibull model in system residual life prediction is shown. The methodologies are illustrated using simulated data, real data obtained from the spectrometric analysis of oil samples collected from transmission units of heavy hauler trucks in the mining industry, and vibration data from a planetary gearbox machinery application.