The Behavior of and Extreme— Value Control Charts in the Case of Mixture Alternatives

Abstract

This paper evaluates the average run length properties of some control procedures for monitoring the mean and the variance of a process. In particular, a comparison is made between the and Extreme—Value charts when the underlying distribution of the control chart statistic is not normal but is a mixture of normal distributions. It is shown that the Extreme—Value chart is the most efficient of the three charts when it is desired to detect the presence of mixture alternatives. Furthermore, the power of the Extreme—Value chart is close to the power of the likelihood ratio test corresponding to the underlying test problem

Keywords:

• Control charts
• mixture alternatives
• robustness
• average run length