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On Probabilities for Complex Switching Rules in Sampling Inspection

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Scan Statistics

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

Switching rules between different levels of sampling are widely used in quality control, as in the well-known Military Standard 105E (MIL STD 105E) and similar acceptance-sampling schemes. These switching rules are typically defined by specific patterns of inspection outcomes within a sequence of previous inspections. The probability distributions of the rules are usually hard to find, and many of them remain unknown. In this chapter, we will provide a general and simple method, the finite Markov chain imbedding technique, to obtain the distributions of switching rules. We demonstrate the utility of this method primarily by (i) deriving the generating function of a basic switching rule (k consecutive acceptances) for the practically important case of a two-state, first-order autoregressive AR(1) sequence, (ii) treating jointly the normal and tightened inspection regimes of MIL STD 105E including the overall probability of discontinuing inspection, and (iii) considering a stratified sampling scheme with three possible inspection outcomes.

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Author information

Authors and Affiliations

  1. Dalla Lana School of Public Health, University of Toronto, Toronto, Ontario, Canada

    W.Y. Wendy Lou

  2. Department of Statistics, University of Manitoba Winnipeg, Manitoba, Canada

    James C. Fu

Authors
  1. W.Y. Wendy Lou
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  2. James C. Fu
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Editor information

Editors and Affiliations

  1. Dept. Statistics, University of Connecticut, Glenbrook Rd. 215, Storrs, 06269-3120, U.S.A.

    Joseph Glaz

  2. Dept. Statistics, University of Connecticut, Glenbrook Road 215, Storrs, 06269-4120, U.S.A.

    Vladimir Pozdnyakov

  3. Center for Biomathematical Sciences, Mount Sinai School of Medicine, Gustave L Levy Place 1, New York, 10029, U.S.A.

    Sylvan Wallenstein

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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Lou, W.W., Fu, J. (2009). On Probabilities for Complex Switching Rules in Sampling Inspection. In: Glaz, J., Pozdnyakov, V., Wallenstein, S. (eds) Scan Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4749-0_10

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