Shewhart Revisited

The Shewhart control chart was first to monitor an ongoing process and raise an alarm when it appears that the level has changed. We show that the Shewhart chart is optimal for the criterion of maximizing the probability of detecting a change upon its occurrence subject to an average run length to f...

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Bibliographic Details
Published in:Sequential analysis 2013-04, Vol.32 (2), p.230-242
Main Authors: Pollak, Moshe, Krieger, Abba M.
Format: Article
Language:English
Subjects:
Alarm systems
Control charts
Criteria
CUSUM
False alarms
Monitors
Multivariate analysis
Optimization
Probability distribution
Sequential analysis
Sequential quality control
Shewhart
Statistical process control
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Summary:The Shewhart control chart was first to monitor an ongoing process and raise an alarm when it appears that the level has changed. We show that the Shewhart chart is optimal for the criterion of maximizing the probability of detecting a change upon its occurrence subject to an average run length to false alarm. It is remarkable, particularly when the change is of moderate size, that Shewhart's procedure is better than cumulative sum (CUSUM). In the multivariate setting, applying the Shewhart procedure to each process separately is suboptimal. We create a generalized Shewhart procedure that is optimal for the aforementioned criterion. The results are illustrated in common settings.
ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2013.774621