Modelling of unexpected shift in SPC

Michael Zeifman and Dov Ingman

Journal of Applied Statistics, 2005, vol. 32, issue 4, 375-386

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.

Keywords: Control charts; Markov chain; mixture distribution; information distance (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1080/02664760500079175

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