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Modelling of unexpected shift in SPC

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  • Michael Zeifman
  • Dov Ingman

Abstract

Optimal statistical process control (SPC) requires models of both in-control and out-of-control process states. Whereas a normal distribution is the generally accepted model for the in-control state, there is a doubt as to the existence of reliable models for out-of-control cases. Various process models, available in the literature, for discrete manufacturing systems (parts industry) can be treated as bounded discrete-space Markov chains, completely characterized by the original in-control state and a transition matrix for shifts to an out-of-control state. The present work extends these models by using a continuous-state Markov chain, incorporating non-random corrective actions. These actions are to be realized according to the SPC technique and should substantially affect the model. The developed stochastic model yields a Laplace distribution of a process mean. An alternative approach, based on the Information theory, also results in a Laplace distribution. Real-data tests confirm the applicability of a Laplace distribution for the parts industry and show that the distribution parameter is mainly controlled by the SPC sample size.

Suggested Citation

  • Michael Zeifman & Dov Ingman, 2005. "Modelling of unexpected shift in SPC," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(4), pages 375-386.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:4:p:375-386
    DOI: 10.1080/02664760500079175
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    1. Michael I. Zeifman & Dov Ingman, 2003. "Continuous Markovian Model for Unexpected Shift in SPC," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 455-466, December.
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