### 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) |
---|---|

Pages (from-to) | 523-539 |

Number of pages | 17 |

Journal | Statistical Papers |

Volume | 54 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2013 |

### Fingerprint

### Keywords

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

### Cite this

*Statistical Papers*,

*54*(2), 523-539. https://doi.org/10.1007/s00362-012-0447-0

**Using p values to design statistical process control charts.** / Li, Zhonghua; Qiu, Peihua; Chatterjee, Snigdhansu B; Wang, Zhaojun.

Research output: Contribution to journal › Article

*Statistical Papers*, vol. 54, no. 2, pp. 523-539. https://doi.org/10.1007/s00362-012-0447-0

}

TY - JOUR

T1 - Using p values to design statistical process control charts

AU - Li, Zhonghua

AU - Qiu, Peihua

AU - Chatterjee, Snigdhansu B

AU - Wang, Zhaojun

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

KW - Bootstrap

KW - Cumulative sum control charts

KW - Process monitoring

KW - Self-starting

KW - Variable sampling

UR - http://www.scopus.com/inward/record.url?scp=84876095803&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876095803&partnerID=8YFLogxK

U2 - 10.1007/s00362-012-0447-0

DO - 10.1007/s00362-012-0447-0

M3 - Article

AN - SCOPUS:84876095803

VL - 54

SP - 523

EP - 539

JO - Statistical Papers

JF - Statistical Papers

SN - 0932-5026

IS - 2

ER -