### Abstract

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

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 17 |

Publication status | Published - 2002 |

### Publication series

Name | Memorandum Faculty of Mathematical Sciences |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1651 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-62G15
- MSC-62P30
- IR-65837
- METIS-206704
- EWI-3471

### Cite this

*Empirical nonparametric control charts: estimation effects and corrections*. (Memorandum Faculty of Mathematical Sciences; No. 1651). Enschede: University of Twente, Department of Applied Mathematics.

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*Empirical nonparametric control charts: estimation effects and corrections*. Memorandum Faculty of Mathematical Sciences, no. 1651, University of Twente, Department of Applied Mathematics, Enschede.

**Empirical nonparametric control charts: estimation effects and corrections.** / Albers, Willem/Wim; Kallenberg, W.C.M.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Empirical nonparametric control charts: estimation effects and corrections

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

N2 - Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.

AB - Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.

KW - MSC-62G15

KW - MSC-62P30

KW - IR-65837

KW - METIS-206704

KW - EWI-3471

M3 - Report

T3 - Memorandum Faculty of Mathematical Sciences

BT - Empirical nonparametric control charts: estimation effects and corrections

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -