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

Abstract

This paper proposes a Kullback-Leibler information (KLI) control chart for monitoring the occurrence rate of a process that follows an exponential distribution. The chart is designed for detecting a decrease, an increase, or both in the occurrence rate. Due to the skewness of the plotted statistic, the performance of the chart is investigated separately when the occurrence rate is estimated by the maximum likelihood estimator, the uniformly minimum variance unbiased estimator, and the minimum mean squared error estimator. The KLI chart is effective for a wide range of shifts of the occurrence rate. Its performance is slightly behind cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts around sizes of shift where these two charts are optimized. It outperforms these two charts elsewhere. The relative mean index (RMI) values show that the KLI chart has better overall performance. A backward empirical sequential test is used for the plotted statistic of the chart. It is shown equivalent to the cumulative sum scheme and the change point method for the generalized likelihood ratio chart in terms of run length. The use of KLI chart does not require any design parameter other than the control limit.