Change Point Estimation Based Statistical Monitoring with Variable Time Between Events (TBE) Control Charts

Abstract

Statistical process control efforts are considered to ensure high-quality production and reduce costs in the competitive environment of business. The signal issued by a control chart triggers the process professionals to identify and eliminate the cause(s) of an out-of-control situation. As a potential delay may exist in generating the signal, follow-up change point procedures are proposed for statistical monitoring. Knowing the time of a disturbance also simplifies the search for a special cause. Moreover, process professionals can focus on a narrower search window and find the root cause easily with change point analysis. Recent literature has indicated effective methods for normal processes, but the research for applications in gamma processes are scarce. In this study, several change point models based on maximum likelihood estimation (MLE) are considered to monitor variable TBE data which follows a Gamma distribution. The performance under the assumption that the process is monitored with cumulative quantity control (CQC-r), exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are compared.