Abstract
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.
Original language | English |
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Pages (from-to) | 230-242 |
Number of pages | 13 |
Journal | Sequential Analysis |
Volume | 32 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2013 |
Keywords
- CUSUM
- Sequential analysis
- Sequential quality control
- Shewhart
- Statistical process control