Multivariate Bayesian Control Chart with Dual Sampling Scheme

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.Ph.D.2019-12-19 00:00:0