### Abstract

This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.

Original language | English (US) |
---|---|

Pages (from-to) | 349-369 |

Number of pages | 21 |

Journal | Annals of Applied Statistics |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2009 |

### Fingerprint

### Keywords

- Cumulative sum control charts
- Distribution-free procedures
- Nonparametric model
- Resampling
- Robustness
- Statistical process control

### Cite this

**Distribution-free cumulative sum control charts using bootstrap-based control limits.** / Chatterjee, Singdhansu B; Qiu, Peihua.

Research output: Contribution to journal › Article

*Annals of Applied Statistics*, vol. 3, no. 1, pp. 349-369. https://doi.org/10.1214/08-AOAS197

}

TY - JOUR

T1 - Distribution-free cumulative sum control charts using bootstrap-based control limits

AU - Chatterjee, Singdhansu B

AU - Qiu, Peihua

PY - 2009/3/1

Y1 - 2009/3/1

N2 - This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.

AB - This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.

KW - Cumulative sum control charts

KW - Distribution-free procedures

KW - Nonparametric model

KW - Resampling

KW - Robustness

KW - Statistical process control

UR - http://www.scopus.com/inward/record.url?scp=80052933187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052933187&partnerID=8YFLogxK

U2 - 10.1214/08-AOAS197

DO - 10.1214/08-AOAS197

M3 - Article

AN - SCOPUS:80052933187

VL - 3

SP - 349

EP - 369

JO - Annals of Applied Statistics

JF - Annals of Applied Statistics

SN - 1932-6157

IS - 1

ER -