Parabolic cusum control charts

In this paper some modifications to the traditional "V-mask" CUSUM control chart, here denoted V-CUSUM, are discussed. In particular, substitution of the linear decision boundary of the V-CUSUM by a parabolic shaped decision boundary is studied. The performance, in terms of average run len...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 1997-01, Vol.26 (1), p.107-123
Main Author: Johan Wiklund, Stig
Format: Article
Language:English
Subjects:
average run length
CUSUM envelope
modified CUSUM charts
shift detection
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Summary:In this paper some modifications to the traditional "V-mask" CUSUM control chart, here denoted V-CUSUM, are discussed. In particular, substitution of the linear decision boundary of the V-CUSUM by a parabolic shaped decision boundary is studied. The performance, in terms of average run length, ARL, of the thus defined parabolic CUSUM control chart, P-CUSUM, is explored in a simulation study. The results for the P-CUSUM are compared with some other versions of CUSUM charts and with the Shewhart -chart. The results show that the P-CUSUM provides good detection for a wider range of shift sizes than the other charts under study. Another advantage of the P-CUSUM is its relative simplicity compared to other CUSUM charts, in the respect that the control limits are given by one parameter only. The P-CUSUM has the disadvantage that it cannot be handled recurrently and requires the storage of previous observations. It is argued that the P-CUSUM is better suited to provide estimates of the current process mean. and may so be preferred to other CUSUM charts in applications where deviations fiom target are counteracted by adjustments to the process.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610919708813370