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Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis

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  • Carlos Pérez-González
  • Arturo Fernández

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. Copyright Springer-Verlag 2013

Suggested Citation

  • Carlos Pérez-González & Arturo Fernández, 2013. "Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis," Computational Statistics, Springer, vol. 28(3), pages 1333-1350, June.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:3:p:1333-1350
    DOI: 10.1007/s00180-012-0360-y
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    References listed on IDEAS

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    1. Néli Maria Costa Mattos & Hélio Santos Migon, 2001. "A Bayesian Analysis of Reliability in Accelerated Life Tests Using Gibbs Sampler," Computational Statistics, Springer, vol. 16(2), pages 299-312, July.
    2. Lu, Wanbo & Tsai, Tzong-Ru, 2009. "Interval censored sampling plans for the gamma lifetime model," European Journal of Operational Research, Elsevier, vol. 192(1), pages 116-124, January.
    3. George Tagaras & Hau L. Lee, 1987. "Optimal Bayesian single‐sampling attribute plans with modified beta prior distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 789-801, December.
    4. Arizono, Ikuo & Kawamura, Yuuki & Takemoto, Yasuhiko, 2008. "Reliability tests for Weibull distribution with variational shape parameter based on sudden death lifetime data," European Journal of Operational Research, Elsevier, vol. 189(2), pages 570-574, September.
    5. Huang, Wen-Tao & Lin, Yu-Pin, 2004. "Bayesian sampling plans for exponential distribution based on uniform random censored data," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 669-691, January.
    6. Rao G. Srinivasa, 2009. "A Group Acceptance Sampling Plans for Lifetimes Following a Generalized Exponential Distribution," Stochastics and Quality Control, De Gruyter, vol. 24(1), pages 75-85, January.
    7. Hau L. Lee & George Tagaras, 1989. "On the robustness of the modified beta distribution for acceptance sampling in statistical quality control," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 447-461, August.
    8. Fernández, Arturo J. & Pérez-González, Carlos J. & Aslam, Muhammad & Jun, Chi-Hyuck, 2011. "Design of progressively censored group sampling plans for Weibull distributions: An optimization problem," European Journal of Operational Research, Elsevier, vol. 211(3), pages 525-532, June.
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