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: | [1] Atienza O. O., Ang B. W., Tang L. C.: Statistical process control and forecasting.Internat. J. Quality Science 1 (1997), 37–51 10.1108/13598539710159077 |

Reference: | [2] Engelking R.: General Topology.PWN, Warszawa 1977 Zbl 0684.54001, MR 0500780 |

Reference: | [3] Feigenbaum A. V.: Total Quality Control.McGraw–Hill, New York 1991 |

Reference: | [4] Gitlow H., Gitlow S., Oppenheim, A., Oppenheim R.: Tools and Methods for the Improvement of Quality.Irwin, Boston 1989 Zbl 0713.62102 |

Reference: | [5] James P. T. J.: Total Quality Management: An Introductory Text.Prentice Hall, London 1996 |

Reference: | [6] Arquardt D. W.: Twin metric control - CUSUM simplified in a Shewhart framework.Internat. J. Quality & Reliability Management 3 1997), 220–233 10.1108/02656719710165464 |

Reference: | [7] Ncube M. M.: Cumulative score quality control procedures for process variability.Internat. J. Quality & Reliability Management 5 (1994), 38–45 10.1108/02656719410062894 |

Reference: | [8] Quesenberry C. P.: SPC Methods for Quality Improvement.Wiley, New York 1997 |

Reference: | [9] Roberts S. W.: A comparison of some control chart procedures.Technometrics 1 (1966), 239–250 MR 0196887 |

Reference: | [10] Srivastava M. S., Wu Y.: Economical quality control procedures based on symmetric random walk model.Statistica Sinica 6 (1996), 389–402 Zbl 0843.62100, MR 1399310 |

Reference: | [11] Taguchi G.: Quality engineering in Japan.Commentaries in Statistics, Series A 14 (1985), 2785–2801 10.1080/03610928508829076 |

. |

Files | Size | Format | View |
---|---|---|---|

Kybernetika_40-2004-4_8.pdf | 1.447Mb | application/pdf |
View/ |