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A hierarchy of adaptive control charts

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  • De Magalhães, M.S.
  • Costa, A.F.B.
  • Moura Neto, F.D.

Abstract

The purpose of this article is to present a statistical design of a hierarchy of two-states adaptive parameters charts. We assume that the shift in the process mean does not occur at the beginning of the production process but at some random time in the future. The occurrence time of the shift is assumed to be an exponentially distributed random variable. This assumption allows the application of the Markov chain approach for developing performance measures. Seven adaptive charts result from the combinations of the design parameters, that is, the sample size, the sampling interval, and the factor used to define the control limits, when one, two, or all of them are allowed to vary, arranged in a hierarchy. When comparing the performance between different two-state charts one sometimes can use a chart with fewer parameters varying and yet achieve good performance, however this depends on the size of process shift. One can change the probability of the control system to be in a state of loose control; considering that, its effect on the adjusted average time to signal and on the design parameters was analyzed numerically.

Suggested Citation

  • De Magalhães, M.S. & Costa, A.F.B. & Moura Neto, F.D., 2009. "A hierarchy of adaptive control charts," International Journal of Production Economics, Elsevier, vol. 119(2), pages 271-283, June.
    • Handle: RePEc:eee:proeco:v:119:y:2009:i:2:p:271-283
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    Cited by:

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    3. Fabbri, Ricardo & Bastos, Ivan N. & Neto, Francisco D. Moura & Lopes, Francisco J.P. & Gonçalves, Wesley N. & Bruno, Odemir M., 2014. "Multi-q pattern classification of polarization curves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 332-339.
    4. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
    5. Qu, Liang & Wu, Zhang & Khoo, Michael B.C. & Castagliola, Philippe, 2013. "A CUSUM scheme for event monitoring," International Journal of Production Economics, Elsevier, vol. 145(1), pages 268-280.
    6. Ou, Yanjing & Wu, Zhang & Goh, Thong Ngee, 2011. "A new SPRT chart for monitoring process mean and variance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 303-314, August.
    7. Wu, Zhang & Yang, Mei & Khoo, Michael B.C. & Castagliola, Philippe, 2011. "What are the best sample sizes for the Xbar and CUSUM charts?," International Journal of Production Economics, Elsevier, vol. 131(2), pages 650-662, June.
    8. Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2011. "Variable parameter and double sampling charts in the presence of correlation: The Markov chain approach," International Journal of Production Economics, Elsevier, vol. 130(2), pages 224-229, April.

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