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On exact and optimal single-sampling plans by variables

Author

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  • Wolf Krumbholz
  • Detlef Steuer

Abstract

We deal with sampling by variables with two-way protection in the case of a $$N\>(\mu ,\sigma ^2)$$ N ( μ , σ 2 ) distributed characteristic with unknown $$\sigma $$ σ . The LR sampling plan proposed by Lieberman and Resnikoff (JASA 50: 457 $${-}$$ - 516, 1955 ) and the BSK sampling plan proposed by Bruhn-Suhr and Krumbholz (Stat. Papers 31: 195–207, 1990 ) are based on the UMVU and the plug-in estimator, respectively. For given $$p_1$$ p 1 (AQL), $$p_2$$ p 2 (RQL) and $$\alpha ,\beta $$ α , β (type I and II errors) we present an algorithm allowing to determine the optimal LR and BSK plans having minimal sample size among all plans satisfying the corresponding two-point condition on the OC. An R (R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/ 2012 ) package, ExLiebeRes‘ (Krumbholz and Steuer ExLiebeRes: calculating exact LR- and BSK-plans, R-package version 0.9.9. http://exlieberes.r-forge.r-project.org 2012 ) implementing that algorithm is provided to the public. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Wolf Krumbholz & Detlef Steuer, 2014. "On exact and optimal single-sampling plans by variables," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(1), pages 87-101, January.
    • Handle: RePEc:spr:alstar:v:98:y:2014:i:1:p:87-101
    DOI: 10.1007/s10182-013-0217-x
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    References listed on IDEAS

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    1. Kossler, W. & Lenz, B. & Lenz, H. -J., 1994. "ExVar - exact variable inspection plans in statistical quality control," Computational Statistics & Data Analysis, Elsevier, vol. 17(1), pages 97-99, January.
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    Cited by:

    1. Wolfgang Kössler & Janine Ott, 2019. "Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 437-452, September.

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    1. Wolfgang Kössler & Janine Ott, 2019. "Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 437-452, September.

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