Accurate ARL computation for EWMA-S-2 control charts
Originally, the exponentially weighted moving average (EWMA) control chart was developed for detecting changes in the process mean. The average run length (ARL) became the most popular performance measure for schemes with this objective. When monitoring the mean of independent and normally distributed observations the ARL can be determined with high precision. Nowadays, EWMA control charts are also used for monitoring the variance. Charts based on the sample variance S-2 are an appropriate choice. The usage of ARL evaluation techniques known from mean monitoring charts, however, is difficult. The most accurate method - solving a Fredholm integral equation with the Nystrom method - fails due to an improper kernel in the case of chi-squared distributions. Here, we exploit the collocation method and the product Nystrom method. These methods are compared to Markov chain based approaches. We see that collocation leads to higher accuracy than currently established methods.
control charts fredholm integral equations collocation product nystrom method monitoring variance