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Design of progressively censored group sampling plans for Weibull distributions: An optimization problem

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  • Fernández, Arturo J.
  • Pérez-González, Carlos J.
  • Aslam, Muhammad
  • Jun, Chi-Hyuck

Abstract

Optimization algorithms provides efficient solutions to many statistical problems. Essentially, the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints, usually related to the quality levels required by the producer and the consumer. An optimal acceptance sampling plan is developed in this paper for the Weibull distribution with unknown scale parameter. The proposed plan combines grouping of items, sudden death testing in each group and progressive group removals, and its decision criterion is based on the uniformly most powerful life test. A mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant. The optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost. Excellent approximately optimal solutions are also provided in closed-forms. The sampling plan is considerably flexible and allows to save experimental time and cost. In general, our methodology achieves solutions that are quite robust to small variations in the Weibull shape parameter. A numerical example about a manufacturing process of gyroscopes is included for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:525-532
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    2. Wu, Chien-Wei & Aslam, Muhammad & Jun, Chi-Hyuck, 2012. "Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk," European Journal of Operational Research, Elsevier, vol. 217(3), pages 560-566.
    3. Fernández, Arturo J. & Pérez-González, Carlos J., 2012. "Optimal acceptance sampling plans for log-location–scale lifetime models using average risks," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 719-731.
    4. Ji Hwan Cha & Sophie Mercier, 2022. "Two Reliability Acceptance Sampling Plans for Items Subject to Wiener Process of Degradation," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1651-1668, September.
    5. 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.
    6. Fernández, Arturo J., 2013. "Smallest Pareto confidence regions and applications," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 11-25.
    7. Sanku Dey & Ahmed Elshahhat & Mazen Nassar, 2023. "Analysis of progressive type-II censored gamma distribution," Computational Statistics, Springer, vol. 38(1), pages 481-508, March.
    8. Maram Salem & Zeinab Amin & Moshira Ismail, 2020. "Progressively Censored Reliability Sampling Plans Based on Mean Product Lifetime," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 1-33, May.
    9. Fernández, Arturo J., 2015. "Optimum attributes component test plans for k-out-of-n:F Weibull systems using prior information," European Journal of Operational Research, Elsevier, vol. 240(3), pages 688-696.
    10. David Han, 2014. "Optimum Constant-stress and Step-stress Accelerated Life Tests under Time and Cost Constraints," Working Papers 0173mss, College of Business, University of Texas at San Antonio.
    11. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.

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