Abstract
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.
Highlights
Control charts are one of the most important tools for the statistical process monitoring and have been widely studied and applied in industrial applications
Keeping in mind the popularity of average run length (ARL), this study proposes a new criterion to evaluate the closeness of distance between the ARLs of different charts
The results suggested that chart based on the exponential distribution is suitable for the process deterioration monitoring while a chart based on the generalized exponential distribution is preferable for the upper and the two-sided process monitoring
Summary
Control charts are one of the most important tools for the statistical process monitoring and have been widely studied and applied in industrial applications. Their usage, are not limited to industrial application but successfully applied recently to medical and business experiments. Due to modern industrial revaluation, it is common nowadays to deal with processes and products where defect rate is very low, e.g., part per million (ppm) or part per billion (ppb). Such types of processes are known as a high-quality processes [1]. For a comprehensive overview of the TBE control charts for monitoring the high-quality processes, the readers are referred to [1]–[9], and references cited therein
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