Weighted EWMA charts for monitoring type I censored Weibull lifetimes

ABSTRACT

In this article, we first propose a control chart for monitoring the Weibull scale parameter in the context of Type I censored data, assuming that the shape parameter is fixed. The proposed chart is a Shewhart-type chart based on a likelihood ratio test (LRT) that utilizes an exponentially weighted moving average of the log-likelihood. In the literature, this type of chart is called a weighted exponentially weighted moving average (WEWMA) chart. The WEWMA chart is compared with a more standard EWMA chart and a CUSUM chart, which were recently studied as alternative solutions to the monitoring problem. Numerical results show that the WEWMA chart often performs better than these two alternatives. Sensitivity studies show that the WEWMA chart is more robust to variations in batch size and censoring time. A rust-resistant example is used to illustrate the proposed WEWMA chart. We extend the WEWMA and CUSUM charts to the context where the shape parameter also needs to be monitored. Joint charts that simultaneously look for change in either parameter are proposed.

KEYWORDS:

• joint monitoring
• statistical process control
• Weibull distribution
• WEWMA chart

About the authors

Ms. Xu is a PhD candidate in the Department of Statistics at the University of California, Riverside. Her email address is [email protected].

Dr. Jeske is a Professor in the Department of Statistics at the University of California, Riverside. His email address is [email protected].

Acknowledgments

We thank the reviewers for useful comments that led to an improved version of the article.