An exponentially weighted moving average chart based on likelihood‐ratio test for monitoring Weibull mean and variance with subgroups

• Published in: Quality and reliability engineering international 2017-12, Vol.33 (8), p.2409-2421
• Main Authors: Wang, Fu‐Kwun, Cheng, Xiao‐Bin
• Format: Article
• Language: English
• Subjects: average run length; Computer simulation; Control charts; Economic models; Error functions; exponentially weighted moving average control chart; likelihood‐ratio test; Monitoring; Quality control; Subgroups; Weibull processes
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2198

Monitoring changes in the Weibull mean and variance simultaneously is of interest in quality control. The mean and variance of a Weibull process are determined by its shape and scale parameters. Most studies are focused on monitoring the Weibull scale parameter with fixed shape parameter or the Weibull shape parameter with fixed scale parameter. In this paper, we propose an exponentially weighted moving average chart based on the likelihood‐ratio test and an inverse error function called ELR chart to monitor changes in the Weibull mean and variance simultaneously. The simulation approach is used to derive the average run length. We compare our proposed chart with other existing control charts for 3 cases, including scale parameter changes with fixed shape parameter, shape parameter changes with fixed scale parameter, and both parameters changes. The results show that the ELR chart outperforms the other control charts in terms of average run length in most cases. Two numerical examples are used to illustrate the applications of the proposed control chart.