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Improved binomial and Poisson approximations to the Type-A operating characteristic function

Nataliya Chukhrova (Faculty of Business Administration, University of Hamburg, Hamburg, Germany)
Arne Johannssen (Faculty of Business Administration, University of Hamburg, Hamburg, Germany)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 11 February 2019

Issue publication date: 22 March 2019

Abstract

Purpose

In acceptance sampling, the hypergeometric operating characteristic (OC) function (so called type-A OC) is used to be approximated by the binomial or Poisson OC function, which actually reduce computational effort, but do not provide suffcient approximation results. The purpose of this paper is to examine binomial- and Poisson-type approximations to the hypergeometric distribution, in order to find a simple but accurate approximation that can be successfully applied in acceptance sampling.

Design/methodology/approach

The authors present a new binomial-type approximation for the type-A OC function, and derive its properties. Further, the authors compare this approximation via an extensive numerical study with other common approximations in terms of variation distance and relative efficiency under various conditions on the parameters including limiting cases.

Findings

The introduced approximation generates best numerical results over a wide range of parameter values, and ensures arithmetic simplicity of the binomial distribution and high accuracy to meet requirements regarding acceptance sampling problems. Additionally, it can considerably reduce the computational effort in relation to the type-A OC function and therefore is strongly recommended for calculating sampling plans.

Originality/value

The newly presented approximation provides a remarkably close fit to the type-A OC function, is discrete and needs no correction for continuity, and is skewed in the same direction by roughly the same amount as the exact OC. Due to less factorials, this OC in general involves lower powers than the type-A OC function. Moreover, the binomial-type approximation is easy to fit to the conventional statistical computing packages.

Keywords

Acknowledgements

The authors would like to thank both anonymous reviewers for their valuable feedback and suggestions, which were helpful to significantly improve the paper.

Citation

Chukhrova, N. and Johannssen, A. (2019), "Improved binomial and Poisson approximations to the Type-A operating characteristic function", International Journal of Quality & Reliability Management, Vol. 36 No. 4, pp. 620-652. https://doi.org/10.1108/IJQRM-10-2017-0203

Publisher

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Emerald Publishing Limited

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