### Abstract

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 CUMINchart: a signal occurs as soon asmconsecutive 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. The nice performance of the proposed MINDCUMIN chart and its straightforward implementation make it very useful for application in practice.

Original language | Undefined |
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Article number | 10.1080/10485250802439533 |

Pages (from-to) | 769-790 |

Number of pages | 22 |

Journal | Journal of nonparametric statistics |

Volume | 20 |

Issue number | 8 |

DOIs | |

Publication status | Published - Nov 2008 |

### Keywords

- MSC-62P30
- MSC-62G30
- MSC-62L10
- EWI-14129
- Order statistics
- Phase II control limits
- Statistical Process Control
- IR-62549
- CUSUM-chart
- METIS-255956

## Cite this

Albers, WW., & Kallenberg, W. C. M. (2008). MINDCUMIN charts.

*Journal of nonparametric statistics*,*20*(8), 769-790. [10.1080/10485250802439533]. https://doi.org/10.1080/10485250802439533