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Using p values to design statistical process control charts

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  • Zhonghua Li
  • Peihua Qiu
  • Snigdhansu Chatterjee
  • Zhaojun Wang

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. Copyright Springer-Verlag 2013

Suggested Citation

  • Zhonghua Li & Peihua Qiu & Snigdhansu Chatterjee & Zhaojun Wang, 2013. "Using p values to design statistical process control charts," Statistical Papers, Springer, vol. 54(2), pages 523-539, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:523-539
    DOI: 10.1007/s00362-012-0447-0
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    References listed on IDEAS

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    1. Luo, Yunzhao & Li, Zhonghua & Wang, Zhaojun, 2009. "Adaptive CUSUM control chart with variable sampling intervals," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2693-2701, May.
    2. Chunguang Zhou & Changliang Zou & Yujuan Zhang & Zhaojun Wang, 2009. "Nonparametric control chart based on change-point model," Statistical Papers, Springer, vol. 50(1), pages 13-28, January.
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