A Comparison of Shewhart-Type Time-Between-Events Control Charts Based on the Renewal Process

To study the high quality processes, time-between-events (TBE) control charts have several advantages over the ordinary control charts. However, the existing TBE charts are based on the exponential distribution, which limit the application of these charts to monitor rare events. Therefore, to generalize existing exponential TBE charts, recently two new TBE charts assuming Weibull and generalized exponential distributions for the inter-arrival times of the renewal process, have been proposed in the literature. The main aim of this study is to present a detailed comparison of these charts. We use the expected quadratic loss (EQL), relative average run length (RARL), continuous rank probability score (CRPS) and closeness measure to assess the performance of the Weibull and the generalized exponential charts. We also discuss four real data examples in this article.