The steady-state behavior of multivariate exponentially weighted moving average control charts
Publication date
2019-03-29
Document type
Forschungsartikel
Author
Organisational unit
Scopus ID
Publisher
Taylor & Francis
Series or journal
Sequential Analysis
ISSN
Periodical volume
37
Periodical issue
4
First page
511
Last page
529
Part of the university bibliography
✅
Language
English
Keyword
62L10
62P30
65R20
Fredholm integral equation of the second kind
Markov chain approximation
multivariate statistical process control
non-central Chi-square distribution
Nyström method
Abstract
Multivariate exponentially weighted moving average (MEWMA) charts are popular, handy, and effective procedures to detect distributional changes in a stream of multivariate data. For doing appropriate performance analysis, dealing with the steady-state behavior of the MEWMA statistic is essential. Going beyond early papers, we derive quite accurate approximations of the respective steady-state densities of the MEWMA statistic. It turns out that these densities could be rewritten as the product of two functions depending on one argument only that allows feasible calculation. For proving the related statements, the presentation of the noncentral chi-square density deploying the confluent hypergeometric limit function is applied. Using the new methods it was found that for large dimensions, the steady-state behavior becomes different from what one might expect from the univariate monitoring field. Based on the integral equation driven methods, steady-state and worst-case average run lengths are calculated with higher accuracy than before. Eventually, optimal MEWMA smoothing constants are derived for all considered measures.
Version
Published version
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