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The synthetic [Xbar] chart with estimated parameters

Author

Listed:
  • Ying Zhang
  • Philippe Castagliola
  • Zhang Wu
  • Michael Khoo

Abstract

A synthetic [Xbar] chart consists of an integration of a Shewhart [Xbar] chart and a conforming run length chart. This type of chart has been extensively used to detect a process mean shift under the assumption of known process parameters. However, in practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. The goals of this article are to (i) evaluate (using a Markov chain model) the performances of the synthetic [Xbar] chart when the process parameters are estimated; (ii) compare it with the case where the process parameters are assumed known to demonstrate that these performances are quite different when the number of samples used during Phase I is small; and (iii) suggest guidelines concerning the choice of the number of Phase I samples and to provide new optimal constants, especially dedicated to the number of samples used in practice.

Suggested Citation

  • Ying Zhang & Philippe Castagliola & Zhang Wu & Michael Khoo, 2011. "The synthetic [Xbar] chart with estimated parameters," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 676-687.
    • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:9:p:676-687
    DOI: 10.1080/0740817X.2010.549547
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    Cited by:

    1. Axel Gandy & Jan Terje Kvaløy, 2013. "Guaranteed Conditional Performance of Control Charts via Bootstrap Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 647-668, December.
    2. H.W. You & Michael B.C. Khoo & P. Castagliola & Liang Qu, 2016. "Optimal exponentially weighted moving average charts with estimated parameters based on median run length and expected median run length," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5073-5094, September.
    3. Lei Yong Lee & Michael Boon Chong Khoo & Sin Yin Teh & Ming Ha Lee, 2015. "A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-18, May.

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