Control charts for the shape parameter of reflected power function distribution under classical estimators

• Published in: Quality and reliability engineering international 2021-10, Vol.37 (6), p.2458-2477
• Main Authors: Zaka, Azam, Akhter, Ahmad Saeed, Jabeen, Riffat, Sanaullah, Aamir
• Format: Article
• Language: English
• Subjects: 62P30; Control charts; Electric power distribution; EWMA control chart; HEWMA control chart; Maximum likelihood estimators; modified maximum likelihood estimator; percentile estimator; reflected power function distribution; Reliability analysis; Reliability engineering; Survival analysis
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2866

The reflected power function distribution (RPFD) has applications in the fields of reliability engineering and survival analysis. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows RPFD, we develop control charts to keep the process in control. A memory less control chart like a Shewhart control chart, and two memory‐based control charts like an exponentially weighted moving average (EWMA) control chart and a hybrid exponentially weighted moving average (HEWMA) control chart are discussed and compared with each other. Proposal of these control charts is based on two different estimators, the percentile estimator (PE) and the modified maximum likelihood estimator (MMLE). This study shows that an HEWMA control chart based on PE performs better than PE‐based Shewhart and EWMA control charts, as well as MMLE‐based Shewhart, EWMA, and HEWMA control charts.