Improving the ARL profile and the accuracy of its calculation for Poisson EWMA charts
Publication date
2020-01-26
Document type
Forschungsartikel
Author
Cabral Morais, Manuel
Organisational unit
Scopus ID
Publisher
Wiley
Series or journal
Quality and Reliability Engineering International
ISSN
Periodical volume
36
Periodical issue
3
First page
876
Last page
889
Part of the university bibliography
✅
Language
English
Keyword
Arl-unbiased chart
Counts of nonconformities
Markov chain approximations
Statistical process control
Abstract
The Poisson exponentially weighted moving average (PEWMA) chart was proposed in 1998 by Borror, Champ, and Rigdon to monitor the mean of counts of nonconformities. This chart regrettably fails to have an in‐control average run length (ARL) larger than any out‐of‐control ARL, ie, the PEWMA chart is ARL‐biased. Moreover, due to the discrete character of its control statistic the PEWMA chart and the resulting subtleties of its ARL calculation, it is difficult to set the control limits in such way that the in‐control ARL takes a desired value, say. In this paper, we establish an improved Markov chain technique to approximate the ARL of EWMA for count output; propose two ARL‐unbiased counterparts of the PEWMA chart; and use the R statistical software to provide illustrations of these charts with a decidedly superior ARL profile and an in‐control ARL equal to. We also compare the ARL performance of the proposed charts with the one of a few competing control charts for the mean of independent and identically distributed (i.i.d.) Poisson counts.
Version
Published version
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