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Title: The optimal control chart procedure (English)
Author: Skřivánek, Jaroslav
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 40
Issue: 4
Year: 2004
Pages: [501]-510
Summary lang: English
Category: math
Summary: The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span $k$ is specified by a partition of the space ${\mathbb{R}} ^k$ into three disjoint parts. We call this partition as the control chart frame of span $k.$ A shift in the process parameter is signalled at time $t$ by having the vector of the last $k$ sample characteristics fall out of the central part of this frame. The optimal frame of span $k$ is selected in order to maximize the average run length (ARL) if shift in the relevant process parameter is on an acceptable level and to minimize it on a rejectable level. We have proved in this article that the set of all frames of span $k$ with an appropriate metric is a compact space and that the ARL for continuously distributed sample characteristics is continuous as a function of the frame. Consequently, there exists the optimal frame among systems of span $k.$ General attitude to control chart systems is the common platform for universal control charts with the particular point for each sample and variable control limits plotted one step ahead. (English)
Keyword: control chart
Keyword: frame of span $k$
Keyword: average run length
Keyword: probability distribution
Keyword: compact metric space
MSC: 49J30
MSC: 62F15
MSC: 62N05
MSC: 62P30
MSC: 93E20
idZBL: Zbl 1249.93178
idMR: MR2102368
Date available: 2009-09-24T20:03:14Z
Last updated: 2015-03-23
Stable URL:
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