IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v286y2020i2p576-587.html
   My bibliography  Save this article

Balancing producer and consumer risks in optimal attribute testing: A unified Bayesian/Frequentist design

Author

Listed:
  • Fernández, Arturo J.
  • Correa-Álvarez, Cristian D.
  • Pericchi, Luis R.

Abstract

Unified Bayesian/frequentist approaches for the design of attributes sampling plans are introduced by minimizing and limiting a weighted-average of the classical or expected producer and consumer risks adopted by the decision maker. This change of paradigm in the construction of test plans for lot acceptance provides optimal inspection schemes from both frequentist and Bayesian perspectives. Classes of admissible test plans minimizing the weighted-average risks are first defined. Constrained optimization problems are then solved in order to determine sample sizes with smallest classical or expected weighted-average risks, as well as acceptance test plans with minimal inspection effort and controlled risks. The proposed methodology to determine optimal sample sizes and decision criteria for lot sentencing constitutes a plausible consensus between Frequentists and Bayesians. Moreover, the use of prior information on the fraction defective allows the practitioners to appreciably reduce the required sample size for lot screening. Optimal lot inspection schemes can also be easily updated using past performance of the sampling plans. Besides the advantages the suggested approach has for hypothesis testing, namely large sample consistency and reproducible results, it permits to make a trade-off between the opposite goals of customers and manufacturers. Some applications in reliability demonstration testing and industrial quality control are presented for illustrative purposes.

Suggested Citation

  • Fernández, Arturo J. & Correa-Álvarez, Cristian D. & Pericchi, Luis R., 2020. "Balancing producer and consumer risks in optimal attribute testing: A unified Bayesian/Frequentist design," European Journal of Operational Research, Elsevier, vol. 286(2), pages 576-587.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:2:p:576-587
    DOI: 10.1016/j.ejor.2020.03.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221720302150
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2020.03.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John P A Ioannidis, 2005. "Why Most Published Research Findings Are False," PLOS Medicine, Public Library of Science, vol. 2(8), pages 1-1, August.
    2. Chen, Jianwei & Choy, S. T. B. & Li, Kim-Hung, 2004. "Optimal Bayesian sampling acceptance plan with random censoring," European Journal of Operational Research, Elsevier, vol. 155(3), pages 683-694, June.
    3. 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.
    4. Feyzioglu, Orhan & Altinel, I. Kuban & Ozekici, Suleyman, 2008. "Optimum component test plans for phased-mission systems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 255-265, February.
    5. Qin, Ruwen & Cudney, Elizabeth A. & Hamzic, Zlatan, 2015. "An optimal plan of zero-defect single-sampling by attributes for incoming inspections in assembly lines," European Journal of Operational Research, Elsevier, vol. 246(3), pages 907-915.
    6. 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.
    7. Ivair R. Silva, 2018. "On the correspondence between frequentist and Bayesian tests," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(14), pages 3477-3487, July.
    8. Balamurali, S. & Jun, Chi-Hyuck, 2007. "Multiple dependent state sampling plans for lot acceptance based on measurement data," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1221-1230, August.
    9. Ayman Baklizi & Abed El Qader El Masri, 2004. "Acceptance Sampling Based on Truncated Life Tests in the Birnbaum Saunders Model," Risk Analysis, John Wiley & Sons, vol. 24(6), pages 1453-1457, December.
    10. Chen, Jianwei & Li, Kim-Hung & Lam, Yeh, 2007. "Bayesian single and double variable sampling plans for the Weibull distribution with censoring," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1062-1073, March.
    11. 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.
    12. Li, Der-Chiang & Lin, Liang-Sian, 2013. "A new approach to assess product lifetime performance for small data sets," European Journal of Operational Research, Elsevier, vol. 230(2), pages 290-298.
    13. Seo, J.H. & Jung, M. & Kim, C.M., 2009. "Design of accelerated life test sampling plans with a nonconstant shape parameter," European Journal of Operational Research, Elsevier, vol. 197(2), pages 659-666, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Fernández, Arturo J., 2017. "Economic lot sampling inspection from defect counts with minimum conditional value-at-risk," European Journal of Operational Research, Elsevier, vol. 258(2), pages 573-580.
    3. 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.
    4. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.
    5. Chien-Wei Wu & Zih-Huei Wang, 2017. "Developing a variables multiple dependent state sampling plan with simultaneous consideration of process yield and quality loss," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2351-2364, April.
    6. 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.
    7. 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.
    8. Wu, Chien-Wei, 2012. "An efficient inspection scheme for variables based on Taguchi capability index," European Journal of Operational Research, Elsevier, vol. 223(1), pages 116-122.
    9. Cheng, Yao & Liao, Haitao & Huang, Zhiyi, 2021. "Optimal degradation-based hybrid double-stage acceptance sampling plan for a heterogeneous product," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    10. 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.
    11. Amy H. I. Lee & Chien-Wei Wu & Yen-Wen Chen, 2016. "A modified variables repetitive group sampling plan with the consideration of preceding lots information," Annals of Operations Research, Springer, vol. 238(1), pages 355-373, March.
    12. Lee‐Shen Chen & Ming‐Chung Yang & TaChen Liang, 2015. "Bayesian sampling plans for exponential distributions with interval censored samples," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 604-616, October.
    13. Kiran Prajapat & Arnab Koley & Sharmishtha Mitra & Debasis Kundu, 2023. "An Optimal Bayesian Sampling Plan for Two-Parameter Exponential Distribution Under Type-I Hybrid Censoring," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 512-539, February.
    14. 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.
    15. Pérez-González, Carlos J. & Fernández, Arturo J. & Kohansal, Akram, 2020. "Efficient truncated repetitive lot inspection using Poisson defect counts and prior information," European Journal of Operational Research, Elsevier, vol. 287(3), pages 964-974.
    16. Amy Lee & Chien-Wei Wu & Yen-Wen Chen, 2016. "A modified variables repetitive group sampling plan with the consideration of preceding lots information," Annals of Operations Research, Springer, vol. 238(1), pages 355-373, March.
    17. Shih-Wen Liu & Chien-Wei Wu, 2016. "A quick switching sampling system by variables for controlling lot fraction nonconforming," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1839-1849, March.
    18. Jyotirmoy Sarkar, 2018. "Will P†Value Triumph over Abuses and Attacks?," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(4), pages 66-71, July.
    19. Kevin J. Boyle & Mark Morrison & Darla Hatton MacDonald & Roderick Duncan & John Rose, 2016. "Investigating Internet and Mail Implementation of Stated-Preference Surveys While Controlling for Differences in Sample Frames," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 64(3), pages 401-419, July.
    20. Jelte M Wicherts & Marjan Bakker & Dylan Molenaar, 2011. "Willingness to Share Research Data Is Related to the Strength of the Evidence and the Quality of Reporting of Statistical Results," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:286:y:2020:i:2:p:576-587. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.