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

Abstract

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.

A parameter‐free exponential control chart based on Kullback‐Leibler information for time‐between‐events monitoring

“…Thus, their performance is quite similar to the Shewhart-type counterparts. Chang et al 56 and Chang and Chen 57 extended the KLI chart to memory-type control chart for mean and linear profile monitoring when samples follow normal distributions. They proposed a backward empirical sequential test (BEST) procedure to formulate the plotted statistics of the chart.…”