On the performance of EWMA and DEWMA control charts for censored data

Abstract

Exponentially weighted moving average (EWMA) control charts are very widely used for the detection of small shifts. Another similar charting structure is double EWMA (DEWMA) control chart for the improved detection of the shifts. Many interesting features of EWMA and DEWMA have been described in the literature. This study intends to investigate EWMA and DEWMA control charts under Type-I censoring for gamma-distributed lifetimes. The idea of conditional expected values is used to monitor the mean level. The performance evaluations are carried out using average run length as a measure in this study. The optimum sample size comparisons for the specified and unspecified parameter are also part of the study. To assess the overall performance of the control charts, we also used extra quadratic loss and it is found DEWMA is an efficient chart for the detection of shift in scale parameter. Moreover, an illustrative example for practical considerations is included in the study. It is observed that varying censoring rates affect the performance of the chart depending upon the type of chart, the method of estimation, and the amount of shift.

Keywords:

• average run length
• Bayes estimates
• control charts
• conditional expected values
• EWMA
• extra quadratic loss
• gamma processes
• MLE
• type-I censoring

Acknowledgments

The authors are thankful to the reviewers for the constructive comments that helped in improving the last version of the paper. The author Muhammad Riaz is thankful to King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing outstanding research environment and facilities.