Accurate ARL computation for EWMA-S² control charts
Publication date
2005-10
Document type
Forschungsartikel
Author
Organisational unit
Advanced Mask Technology Center (AMTC), Dresden
Scopus ID
Publisher
Springer
Series or journal
Statistics and Computing
ISSN
Periodical volume
15
Periodical issue
4
First page
341
Last page
352
Part of the university bibliography
Nein
Language
English
Keyword
Collocation
Control charts
Fredholm integral equations
Monitoring variance
Product Nyström method
Abstract
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.
Version
Published version
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