Bayes estimation of Gumbel mixture models with industrial applications

The Gumbel distribution is a popular model in different disciplines such as engineering, business and the environment. In certain situations, these models are used in a mixture framework. This study deals with the Bayesian estimation of a Gumbel mixture model and suggests its application in process monitoring. The idea of mixture-charting structures looks very practical and is an attractive approach. This study proposes an individual Type II Gumbel cumulative quantity control chart (GCQC-chart) and a mixture of Type II Gumbel cumulative quantity control charts (MGCQC chart). We have developed the design structure of these charts and evaluated their performance using some run-length-based performance measures. The implementation and interpretations are provided and a numerical example is used to verify the application procedure.