| 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:
|
http://hdl.handle.net/10338.dmlcz/135611 |
| . |
| Reference:
|
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| Reference:
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|
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| . |
