Memory-type time-between-events charts using nonhomogeneous Poisson process

Abstract

The traditional time-between-events (TBE) control charts are developed in non-adaptive fashion assuming the Poisson process, where the TBE follows the exponential distribution. However, in many situations we need an adaptive strategy, especially for healthcare or system monitoring. The focus of this study is to introduce new exponentially weighted moving average and cumulative sum adaptive TBE control charts for high-quality processes based on nonhomogeneous Poisson process by assuming the power law intensity. Charts assuming the nonhomogeneous Poisson process are dynamic and can be used where the underlying failure rate may be changing over time. The performance of the proposed control charts is evaluated using the average run length and coefficient of variation of the run length distribution. Three real data examples which correspond to different shape parameters of the power law process are also discussed in the article.