Weighted EWMA Charts for Monitoring Type I Censored Weibull Lifetimes

• Activity Number: 324 - Leading with Statistics: Process Monitoring and Improvement
• Type: Invited
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Daniel R Jeske* and Shangjie Xu
• Companies: University of California - Riverside and University of California
• Keywords: Type I censoring; Weighted EWMA; Joint monitoring; Lifetime data; Weibull distribution; Control charts

Abstract

In this paper, we first propose a control chart for monitoring the Weibull scale parameter in the context of Type I censored data, assuming 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 previous 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 sizes and censoring times. A rust resistant example is used to illustrate the proposed WEWMA chart. We extend the WEWMA and the 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.