EWMA and DEWMA Control Charts for Poisson-Exponential Distribution: Conditional Median Approach for Censored Data

Exponentially weighted moving average (EWMA) control charts are consistently used for the detection of small shifts contrary to Shewhart charts, which are commonly used for the detection of large shifts in the process. There are many interesting features of EWMA charts that have been studied for complete data in the literature. The aim of present study is to introduce and compare the double exponentially weighted moving average (DEWMA) and EWMA control charts under type‐I censoring for Poisson‐exponential distribution. The monitoring of mean level shifts using censored data is of a great interest in many applied problems. Moreover, a new idea of conditional median is introduced and further compared with the existing conditional expected values approach for monitoring the small mean level shifts. The performance of the DEWMA and EWMA charts is evaluated using the average run length, expected quadratic loss, and performance comparison index measures. The optimum sample size comparisons for the specified and unspecified parameters are also part of this study. Two applications for practical considerations are also discussed. It is observed that different censoring rates and the size of shifts significantly affect the performance of the EWMA and DEWMA charts.