Time‐between‐events monitoring using nonhomogeneous Poisson process with power law intensity

Abstract

AbstractThe traditional process monitoring techniques used to study high‐quality processes have several demerits, that is, high‐false alarm rate and poor detection, etc. A recent and promising idea to monitor such processes is the use of time‐between‐events (TBE) control charts. However, the available TBE control charts have been developed in a nonadaptive fashion assuming the Poisson process. There are many situations where we need adaptive monitoring, for example, health, flood, food, system, or terrorist surveillance. Therefore, the existing control charts are not useful, especially in sequential monitoring. This article introduces new adaptive TBE control charts for high‐quality processes based on the nonhomogeneous Poisson process by assuming the power law intensity. In particular, probability control limits are used to develop control charts. The proposed methodology allows us to get control limits that are dynamic and suitable for online process monitoring with an additional advantage to monitor a process where we believe the underlying failure rate may be changing over time. The average run length and coefficient of variation of the run length distribution are used to assess the performance of the proposed control charts. Besides simulation studies, we also discuss three examples to highlight the application of the proposed charts.