Monitoring time and magnitude based on the renewal reward process with a random failure threshold.

Control charts are effective tools to distinguish between special and natural variations and have applications in medical and business industries besides manufacturing industry. Due to the advancement of modern technology, we often deal with the high-quality products, where the traditional process monitoring techniques have certain drawbacks. This article presents a control chart for jointly monitoring time and magnitude based on the renewal reward process. In particular, the focus of this study is to model magnitudes by threshold exceedance. More specifically, assuming a random failure threshold, two cases for magnitude are considered: (i) magnitude is cumulative over time and, (ii) magnitude is non-cumulative or independent over time. A comparative study to show the effectiveness of the proposal is also a part of this study.