Monitoring exponentially distributed time between events data: self-starting perspective

Abstract

Time between events (TBE) control charts have been widely used to monitor high yield processes. Traditionally, an estimated in-control occurrence rate from a Phase I dataset is used to calculate the control limits when the rate is unknown. However, when Phase I analysis is time consuming or costly, the traditional Phase I/Phase II approach is not feasible. A self-starting method that sequentially updates the occurrence rate can be integrated to overcome this difficulty and leverages the use of TBE chart for cases of lack of in-control data. The motivation behind this study is to compare different self-starting TBE charts to investigate the contribution of such a sequential parameter update method. Our results indicate the potential of these schemes as they provide satisfactory performance when moderate and large sizes of base period before the shift observed. Additionally, time weighted schemes provided promising performance for relatively small sample sizes in the base period. However, our results also show a significant adverse effect in performance when the base periods are contaminated with out-of-control data.