### Abstract

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

Article number | 10.1080/02331880500310181 |

Pages (from-to) | 429-443 |

Number of pages | 15 |

Journal | Statistics |

Volume | 39 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2005 |

### Keywords

- EWI-12819
- MSC-62G15
- MSC-62P30
- Exceedance probability
- Statistical Process Control
- Phase II control limits
- IR-64795
- Empirical quantiles

### Cite this

*Statistics*,

*39*(5), 429-443. [10.1080/02331880500310181]. https://doi.org/10.1080/02331880500310181

}

*Statistics*, vol. 39, no. 5, 10.1080/02331880500310181, pp. 429-443. https://doi.org/10.1080/02331880500310181

**Exceedance probabilities for parametric control charts.** / Albers, Willem/Wim; Kallenberg, W.C.M.; Sri Nurdiati, S.N.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Exceedance probabilities for parametric control charts

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

AU - Sri Nurdiati, S.N.

PY - 2005

Y1 - 2005

N2 - Common control charts assume normality and known parameters. Quite often these assumptions are not valid and large relative errors result in the usual performance characteristics, such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than are usually available. Sufficiently large parametric families then provide realistic intermediate models. In this paper the performance of charts based on such families is considered. Exceedance probabilities of the resulting stochastic performance characteristics during in-control are studied. Corrections are derived to ensure that such probabilities stay within prescribed bounds. Attention is also devoted to the impact of the corrections for an out-of-control process. Simulations are presented both for illustration and to demonstrate that the approximations obtained are sufficiently accurate for use in practice.

AB - Common control charts assume normality and known parameters. Quite often these assumptions are not valid and large relative errors result in the usual performance characteristics, such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than are usually available. Sufficiently large parametric families then provide realistic intermediate models. In this paper the performance of charts based on such families is considered. Exceedance probabilities of the resulting stochastic performance characteristics during in-control are studied. Corrections are derived to ensure that such probabilities stay within prescribed bounds. Attention is also devoted to the impact of the corrections for an out-of-control process. Simulations are presented both for illustration and to demonstrate that the approximations obtained are sufficiently accurate for use in practice.

KW - EWI-12819

KW - MSC-62G15

KW - MSC-62P30

KW - Exceedance probability

KW - Statistical Process Control

KW - Phase II control limits

KW - IR-64795

KW - Empirical quantiles

U2 - 10.1080/02331880500310181

DO - 10.1080/02331880500310181

M3 - Article

VL - 39

SP - 429

EP - 443

JO - Statistics

JF - Statistics

SN - 0233-1888

IS - 5

M1 - 10.1080/02331880500310181

ER -