### Abstract

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

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 10 |

Publication status | Published - 2006 |

### Publication series

Name | Applied Mathematics Memoranda |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1791 |

ISSN (Print) | 0169-2690 |

### Keywords

- IR-65596
- EWI-2690
- MSC-62G32
- MSC-62G30
- MSC-62P30
- METIS-230991

### Cite this

*Improved data driven control charts*. (Applied Mathematics Memoranda; No. 1791). Enschede: University of Twente, Department of Applied Mathematics.

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*Improved data driven control charts*. Applied Mathematics Memoranda, no. 1791, University of Twente, Department of Applied Mathematics, Enschede.

**Improved data driven control charts.** / Albers, Willem/Wim; Kallenberg, W.C.M.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Improved data driven control charts

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

PY - 2006

Y1 - 2006

N2 - Classical control charts for monitoring the mean are based on the assumption of normality. When normality fails, these control charts are no longer valid and serious errors often arise. Data driven control charts, which choose between the normal chart, a parametric one and a nonparametric chart, have recently been proposed to solve the problem. They also correct for estimation errors due to estimation of the parameters involved or, in the nonparametric chart, for estimation of the appropriate quantiles of the distribution. In many cases these data driven control charts are performing very well. However, when the data point towards the nonparametric chart no satisfactory solution is obtained unless the number of Phase I observations is very large. The problem is that accurate estimation of an extreme quantile in a nonparametric way needs a huge number of observations. Replacing the nonparametric individual chart by a nonparametric chart for grouped observations does the job. These improved data driven control charts are presented here. Ready-made formulas are given, which make implementation of the charts quite straightforward. An application on real data clearly shows the improvement: estimation of extreme quantiles is replaced by estimation of ordinary quantiles, which can be done in an accurate way for common sample sizes.

AB - Classical control charts for monitoring the mean are based on the assumption of normality. When normality fails, these control charts are no longer valid and serious errors often arise. Data driven control charts, which choose between the normal chart, a parametric one and a nonparametric chart, have recently been proposed to solve the problem. They also correct for estimation errors due to estimation of the parameters involved or, in the nonparametric chart, for estimation of the appropriate quantiles of the distribution. In many cases these data driven control charts are performing very well. However, when the data point towards the nonparametric chart no satisfactory solution is obtained unless the number of Phase I observations is very large. The problem is that accurate estimation of an extreme quantile in a nonparametric way needs a huge number of observations. Replacing the nonparametric individual chart by a nonparametric chart for grouped observations does the job. These improved data driven control charts are presented here. Ready-made formulas are given, which make implementation of the charts quite straightforward. An application on real data clearly shows the improvement: estimation of extreme quantiles is replaced by estimation of ordinary quantiles, which can be done in an accurate way for common sample sizes.

KW - IR-65596

KW - EWI-2690

KW - MSC-62G32

KW - MSC-62G30

KW - MSC-62P30

KW - METIS-230991

M3 - Report

T3 - Applied Mathematics Memoranda

BT - Improved data driven control charts

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -