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Shewhart control charts for dispersion adjusted for parameter estimation

Author

Listed:
  • Rob Goedhart
  • Michele M. da Silva
  • Marit Schoonhoven
  • Eugenio K. Epprecht
  • Subha Chakraborti
  • Ronald J. M. M. Does
  • Álvaro Veiga

Abstract

Several recent studies have shown that the number of Phase I samples required for a Phase II control chart with estimated parameters to perform properly may be prohibitively high. Looking for a more practical alternative, adjusting the control limits has been considered in the literature. We consider this problem for the classic Shewhart charts for process dispersion under normality and present an analytical method to determine the adjusted control limits. Furthermore, we examine the performance of the resulting chart at signaling increases in the process dispersion. The proposed adjustment ensures that a minimum in-control performance of the control chart is guaranteed with a specified probability. This performance is indicated in terms of the false alarm rate or, equivalently, the in-control average run length. We also discuss the tradeoff between the in-control and out-of-control performance. Since our adjustment is based on exact analytical derivations, the recently suggested bootstrap method is no longer necessary. A real-life example is provided in order to illustrate the proposed methodology.

Suggested Citation

  • Rob Goedhart & Michele M. da Silva & Marit Schoonhoven & Eugenio K. Epprecht & Subha Chakraborti & Ronald J. M. M. Does & Álvaro Veiga, 2017. "Shewhart control charts for dispersion adjusted for parameter estimation," IISE Transactions, Taylor & Francis Journals, vol. 49(8), pages 838-848, August.
    • Handle: RePEc:taf:uiiexx:v:49:y:2017:i:8:p:838-848
    DOI: 10.1080/24725854.2017.1299956
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    References listed on IDEAS

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    1. Subha Chakraborti, 2006. "Parameter estimation and design considerations in prospective applications of the X chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(4), pages 439-459.
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    Cited by:

    1. Song, Zhi & Mukherjee, Amitava & Liu, Yanchun & Zhang, Jiujun, 2019. "Optimizing joint location-scale monitoring – An adaptive distribution-free approach with minimal loss of information," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1019-1036.
    2. Ishaq Adeyanju Raji & Muhammad Hisyam Lee & Muhammad Riaz & Mu’azu Ramat Abujiya & Nasir Abbas, 2020. "Outliers Detection Models in Shewhart Control Charts; an Application in Photolithography: A Semiconductor Manufacturing Industry," Mathematics, MDPI, vol. 8(5), pages 1-17, May.

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