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Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis

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Abstract

Assuming a beta prior distribution on the fraction defective, \(p\), failure-censored sampling plans for Weibull lifetime models using classical (or average) and Bayesian (or posterior) producer’s and consumer’s risks are designed to determine the acceptability of lots of a given product. The average risk criterion provides a certain assurance that good (bad) lots will be accepted (rejected), whereas the posterior risk criterion provides a determined confidence that an accepted (rejected) lot is indeed good (bad). The performance of classical and Bayesian risks are analyzed in developing sampling plans when the lifetime variable follows the Weibull distribution. Several figures and tables illustrate the sensitivity of the risks and optimal sample sizes for selected censoring levels and specifications according to the available prior information on \(p\). The analysis clarifies the distinction among the different risks for a given sampling plan, and the effect of the prior knowledge on the required sample size. The study shows that, under uncertainty in the prior variance of \(p\), the designs using Bayesian risks are more appropriate.

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Acknowledgments

The authors thank the editor and the anonymous reviewer for their valuable comments. This research was partially supported by the grant SolSubC200801000048 from the Canary Islands Government and the grant MTM2010-16828 from Spanish Ministerio de Ciencia e Innovación (MICINN).

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de La Laguna, 38271, Tenerife, Spain

    Carlos J. Pérez-González & Arturo J. Fernández

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  1. Carlos J. Pérez-González
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  2. Arturo J. Fernández
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Correspondence to Carlos J. Pérez-González.

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Pérez-González, C.J., Fernández, A.J. Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis. Comput Stat 28, 1333–1350 (2013). https://doi.org/10.1007/s00180-012-0360-y

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