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Shewhart-type control charts for variation in phase I data analysis

Author

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  • Human, S.W.
  • Chakraborti, S.
  • Smit, C.F.

Abstract

Control charts for variation play a key role in the overall statistical process control (SPC) regime. We study the popular Shewhart-type S2, S and R control charts when the mean and the variance of a normally distributed process are both unknown and are estimated from m independent samples (subgroups) each of size n. This is the Phase I setting. Current uses of these charts do not recognize that in this setting the signalling events are statistically dependent and that m comparisons are made with the same control limits simultaneously. These are important issues because they affect the design and the performance of the control charts. The proposed methodology addresses these issues (which leads to working with the joint distribution of a set of dependent random variables) by calculating the correct control limits, so that the false alarm probability (FAP), defined as the probability of at least one false alarm, is at most equal to some given nominal value FAP0. To aid practical implementation, tables are provided for the charting constants for each Phase I chart, for an FAP0 of 0.01 and 0.05, respectively. An illustrative example is given.

Suggested Citation

  • Human, S.W. & Chakraborti, S. & Smit, C.F., 2010. "Shewhart-type control charts for variation in phase I data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 863-874, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:863-874
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    References listed on IDEAS

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    1. Chakraborti, S. & Eryilmaz, S. & Human, S.W., 2009. "A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1054-1065, February.
    2. Maravelakis, Petros E. & Castagliola, Philippe, 2009. "An EWMA chart for monitoring the process standard deviation when parameters are estimated," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2653-2664, May.
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    2. Bui, Anh Tuan & Apley, Daniel W., 2019. "An exploratory analysis approach for understanding variation in stochastic textured surfaces," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 33-50.

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