Control charts for monitoring a Poisson hidden Markov process
Publication date
2020-09-01
Document type
Forschungsartikel
Author
Organisational unit
Scopus ID
Publisher
Wiley
Series or journal
Quality and Reliability Engineering International
ISSN
Periodical volume
37
Periodical issue
2
First page
484
Last page
501
Part of the university bibliography
✅
Language
English
Keyword
Count time series
CUSUM charts
Hidden Markov model
Log-likelihood ratio charts
Run length performance
Statistical process control
Abstract
Monitoring stochastic processes with control charts is the main field of application in statistical process control. For a Poisson hidden Markov model (HMM) as the underlying process, we investigate a Shewhart individuals chart, an ordinary Cumulative Sum (CUSUM) chart, and two different types of log‐likelihood ratio (log‐LR) CUSUM charts. We evaluate and compare the charts' performance by their average run length, computed either by utilizing the Markov chain approach or by simulations. Our performance evaluation includes various out‐of‐control scenarios as well as different levels of dependence within the HMM. It turns out that the ordinary CUSUM chart shows the best overall performance, whereas the other charts' performance strongly depend on the particular out‐of‐control scenario and autocorrelation level, respectively. For illustration, we apply the HMM and the considered charts to a data set about weekly sales counts.
Description
This is an open access article under the terms of the Creative Commons Attribution License CC BY 4.0 ( https://creativecommons.org/licenses/by/4.0/).
Version
Published version
Access right on openHSU
Metadata only access