### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 15 |

Publication status | Published - Sep 2007 |

### Publication series

Name | |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | LNCS4549/1851 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- METIS-241941
- MSC-62G30
- MSC-62P30
- MSC-62L10
- EWI-11131
- Order statistics
- Statistical Process Control
- Phase II control limits
- CUSUM-chart
- IR-64373

### Cite this

*MINDCUMIN charts*. Enschede: University of Twente, Department of Applied Mathematics.

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*MINDCUMIN charts*. University of Twente, Department of Applied Mathematics, Enschede.

**MINDCUMIN charts.** / Albers, Willem/Wim; Kallenberg, W.C.M.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - MINDCUMIN charts

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

N1 - eemcs-eprint-11131

PY - 2007/9

Y1 - 2007/9

N2 - A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used, to avoid recurrence of the problem of the need for unrealistically large Phase I samples.

AB - A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used, to avoid recurrence of the problem of the need for unrealistically large Phase I samples.

KW - METIS-241941

KW - MSC-62G30

KW - MSC-62P30

KW - MSC-62L10

KW - EWI-11131

KW - Order statistics

KW - Statistical Process Control

KW - Phase II control limits

KW - CUSUM-chart

KW - IR-64373

M3 - Report

BT - MINDCUMIN charts

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -