The performance of semi-empirical Bayesian control charts for monitoring Weibull data

Abstract

In this paper we investigate the performance of semi-empirical Bayesian control charts to monitor the percentiles and the shape parameter of a Weibull distribution. These charts have been recently introduced in literature, where it is shown how Weibull-distributed data need specifically designed control schemes and how a Bayesian approach can help in such cases. The main focus of this paper, instead, is a simulation study of the charts’ performance. To this aim, a large Monte Carlo analysis is presented, highlighting the main effects on the chart performance of single/combined changes in the Weibull parameters. Some Weibull contour plots are presented to visualize the investigated technological scenarios. An illustrative example using a reference data-set is included too.

Keywords:

• Bayesian control charts
• Weibull distribution
• Weibull contour plots
• average run length

Acknowledgements

We thank the Guest Editor and all the Referees who gave us valuable suggestions and deep comments that enabled us to improve the paper significantly.