Integral equations: theory and numerical treatment
Integral equations: theory and numerical treatment
Computation of the ARL for CUSUM-S2 schemes
Computational Statistics & Data Analysis
Evaluation of the run-length distribution for a combined Shewhart-EWMA control chart
Statistics and Computing
Computers and Industrial Engineering
Evaluation of exponentially weighted moving variance control chart subject to linear drifts
Computational Statistics & Data Analysis
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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 S2 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 Nyström method--fails due to an improper kernel in the case of chi-squared distributions. Here, we exploit the collocation method and the product Nyström method. These methods are compared to Markov chain based approaches. We see that collocation leads to higher accuracy than currently established methods.