Control Charts for the Percentiles of an Inverse Pareto Distribution Under Complete and Middle‐Censored Data

ABSTRACT In this paper, we aim to develop the Shewhart‐type control charts for monitoring the percentiles of an inverse Pareto distribution (IPD) using the complete and middle‐censored data sets. We obtain the maximum likelihood (ML) estimators of the percentile function under both cases. Furthermore, we discuss the asymptotic properties of the ML estimators and use them to develop the Shewhart‐type control charts. A large‐scale simulation analysis is performed to investigate the in‐control (IC) performance of the proposed control chart schemes. This analysis is based on various criteria such as the average run length (ARL) for different choices of percentiles, false‐alarm rates (FARs), and sample sizes. We also study the behavior of the out‐of‐control (OOC) performance of the proposed charts for several choices of shifts in the IPD parameter. Two real data sets are analyzed to complement the utility of the proposed control chart schemes. We establish that the proposed control charts detect the OOC signals very well.