# Using p values to design statistical process control charts

Zhonghua Li, Peihua Qiu, Snigdhansu B Chatterjee, Zhaojun Wang

Research output: Contribution to journalArticle

11 Citations (Scopus)

### 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) 523-539 17 Statistical Papers 54 2 https://doi.org/10.1007/s00362-012-0447-0 Published - Jan 1 2013

### Fingerprint

Statistical Process Control
Control Charts
p-Value
Process Monitoring
Significance level
Chart
Statistic
Cumulative Sum
Design
P value
Statistical process control
Control charts
Control Design
Univariate
Likelihood
Exceed
Demonstrate

### Keywords

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

### Cite this

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

In: Statistical Papers, Vol. 54, No. 2, 01.01.2013, p. 523-539.

Research output: Contribution to journalArticle

Li, Zhonghua ; Qiu, Peihua ; Chatterjee, Snigdhansu B ; Wang, Zhaojun. / Using p values to design statistical process control charts. In: Statistical Papers. 2013 ; Vol. 54, No. 2. pp. 523-539.
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