Economic Control Chart Policies for Monitoring Variables When There Are Two Components of Variance

Abstract

When controlling a process mean one can achieve optimal performance in terms of the criterion of average run length (ARL) by using a CUSUM control chart rather than a Shewhart control chart, although for very large shifts the Shewhart control chart is equivalent to a CUSUM chart. Using cost as a criterion, several authors have shown that the ARL dominance of the CUSUM chart does not translate to a cost dominance unless the fixed cost of sampling is very small and some other configurations of the input parameters are met. Additionally, because of the simplicity of the Shewart chart in terms of user training, ease of design and ease of use it may be preferable to a CUSUM chart in these situations. Here, using a large experiment, we investigate the cost advantages of the CUSUM chart versus a common Shewhart control chart, the $\overline{X}$ chart, in the situation when one is monitoring a process mean and there are two components of variance. Our results are similar to the single component of variance results in that there are predictable regions where there is a large cost advantage to using CUSUM charts and there are also predictable regions where one can use an $\overline{X}$ without incurring any large increase in cost.