A Markov Chain Model for the Adaptive CUSUM Control Chart

In practice, when the magnitude of a future mean shift is unknown, it is always desired to design a control chart to perform reasonably well over a range of shifts rather than to optimize the performance at detecting a particular level of shifts. Compared with the conventional cumulative sum (CUSUM)...

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Bibliographic Details
Published in:Journal of quality technology 2006-04, Vol.38 (2), p.135-147
Main Authors: Shu, Lianjie, Jiang, Wei
Format: Article
Language:English
Subjects:
Applied sciences
Average Run Length
Computer science
control theory
systems
Control charts
Control theory. Systems
EWMA
Exact sciences and technology
Inventory control, production control. Distribution
Markov analysis
Mathematical models
Operational research and scientific management
Operational research. Management science
Process control. Computer integrated manufacturing
Reliability theory. Replacement problems
Statistical Process Control
Studies
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Summary:In practice, when the magnitude of a future mean shift is unknown, it is always desired to design a control chart to perform reasonably well over a range of shifts rather than to optimize the performance at detecting a particular level of shifts. Compared with the conventional cumulative sum (CUSUM) control chart designed based on a prespecified mean shift, the adaptive CUSUM (ACUSUM) chart proposed by Sparks (2000) can detect a broader range of mean shifts. This paper develops a two-dimensional Markov chain model to analyze the performance of ACUSUM charts. Moreover, a more general operating model is suggested for the current ACUSUM chart to simplify its implementation.
ISSN:0022-4065
2575-6230
DOI:10.1080/00224065.2006.11918601