## Abstract

Conventional Phase II statistical process control (SPC) charts are designed using control limits; a chart gives a signal of process distributional shift when its charting statistic exceeds a properly chosen control limit. To do so, we only know whether a chart is out-of-control at a given time. It is therefore not informative enough about the likelihood of a potential distributional shift. In this paper, we suggest designing the SPC charts using p values. By this approach, at each time point of Phase II process monitoring, the p value of the observed charting statistic is computed, under the assumption that the process is in-control. If the p value is less than a pre-specified significance level, then a signal of distributional shift is delivered. This p value approach has several benefits, compared to the conventional design using control limits. First, after a signal of distributional shift is delivered, we could know how strong the signal is. Second, even when the p value at a given time point is larger than the significance level, it still provides us useful information about how stable the process performs at that time point. The second benefit is especially useful when we adopt a variable sampling scheme, by which the sampling time can be longer when we have more evidence that the process runs stably, supported by a larger p value. To demonstrate the p value approach, we consider univariate process monitoring by cumulative sum control charts in various cases.

Original language | English (US) |
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Pages (from-to) | 523-539 |

Number of pages | 17 |

Journal | Statistical Papers |

Volume | 54 |

Issue number | 2 |

DOIs | |

State | Published - May 2013 |

### Bibliographical note

Funding Information:Acknowledgments The authors are grateful to the editor and two anonymous referees for their valuable comments that have greatly improved the paper. This research is finished during Li’s visit to School of Statistics at The University of Minnesota, whose hospitality is appreciated. The research is supported in part by the NSF grants DMS-0706082 and SES-0851705, the Natural Sciences Foundation of China grants 11071128 and 11131002, the RFDP of China Grant 20110031110002, the Fundamental Research Funds for the Central Universities 65012231, and the Office of International Programs at University of Minnesota.

## Keywords

- Bootstrap
- Cumulative sum control charts
- Process monitoring
- Self-starting
- Variable sampling