Joint Monitoring Using Information Theoretic Control Charts

Abstract

Statistical process control consists of sophisticated and well-organized methods which contribute to monitor and improve the quality of a product. Control charts are now routinely used in many applied areas to enhance the quality of products. In this study, a general framework is presented to construct univariate control charts for joint monitoring using the information theoretic approach. To this end, we monitor a process by maximizing the entropy and by minimizing the cross entropy. Information control charts are free from strict distributional assumptions, as information charts are based on information discrepancy between the initial moment μ0 and the data moments rt . These charts can jointly monitor mean and variance and thus provide a unified approach that is helpful in reducing the labor for designing separate charts. Besides real data applications, in this study, Monte Carlo simulations are used to assess the performance of the information charts using the average run length as a performance criterion assuming different distributions including normal, gamma, exponential, lognormal,Weibull and beta. Furthermore, a comparison with the traditional charts is also given for each distribution.

Keywords

• shewhart chart
• information theoretic charts
• kullback-leibler
• weibull distribution
• lognormal distribution