Monitoring Process Mean and Process Variance Using Collani's Statistic

In this paper the use of Collani's statistic for monitoring simultaneously process mean and process variance is investigated by a comparison with the more popular chart and chart, respectively. The comparison is performed by means of an economic design of the charts assuming two different situations with respect to the occurrence of assignable cause. The criteria used for the comparison are the average total cost (ATC) and the average run lengths (ARLs), where the latter make sense only for equal sample sizes. Various cases with respect to the economic parameters and the distribution parameters are considered omitting the case of constant process variance, because in such a case a simple -chart is in any case superior. It turns out that a chart based on Collani's statistic is by far superior than the two popular charts. In order to have the superiority documented the numerical results are displayed in numerous tables.