Designing a parameter‐free Kullback‐Leibler information control chart for monitoring process mean shift

• Published in: Quality and reliability engineering international Vol. 37; no. 3; pp. 1017 - 1034
• Main Authors: Chang, Yu‐Ching, Li, Ting‐Wei, Mastrangelo, Christina
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.04.2021
• Subjects: average run length; average time to signal; Control charts; Control limits; CUSUM charts; Design parameters; GLR control chart; Information control; Kullback‐Leibler information; Likelihood ratio; Mean; Monitoring; Standard deviation; statistical process control; Statistical tests
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2779

This paper proposes a parameter‐free Kullback‐Leibler information control chart for monitoring sustained shifts in the process mean of a normally distributed process in phase II. Two plotted statistics are provided. One is based on our backward empirical sequential test, the other is based on the maximum log‐likelihood ratio change point method. These two achieve similar performances for the control chart. The performance of the proposed chart is compared with those of the cumulative sum chart, the exponentially weighted moving average chart, and the generalized likelihood ratio (GLR) chart. The results show that our proposed chart and the GLR chart have similar performances. Both can detect a wide range of shifts in the process mean, and neither requires design parameters other than the control limits. The proposed chart outperforms GLR when the size of the shift is below 1.24 standard deviations, while GLR outperforms the proposed chart when the size of the shift is above 1.24 standard deviations.