Computation of the ARL for CUSUM-S2S2 schemes

Contrary to CUSUM schemes for monitoring the mean of normally distributed random variables, there is a lack of accurate computation of the average run length (ARL) for CUSUM schemes based on the sample variance S2S2, which are of importance for variance monitoring. Some very accurate methods will be suggested. Evaluating CUSUM charts based on S2S2 for normal data leads to, naturally, the chi-squared distribution. Then, in the case of even degrees of freedom exact results for Erlang distributed data are employed. For odd degrees piecewise collocation methods are applied for solving the ARL integral equation. Thus, with these methods the ARL for CUSUM-S2S2 schemes can be determined with high precision.