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A note on decision making method for product acceptance based on process capability indices Cpk and Cpmk

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  • Lepore, A.
  • Palumbo, B.
  • Castagliola, P.

Abstract

In this short note, we prove that the derivation of the required sample size and critical acceptance value under the normality assumption of the quality characteristic proposed by Wu, C. W., Aslam, M., & Jun, C. H. (2012). Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk. European Journal of Operational Research, 217(3), 560–566, is inappropriate. In fact, it leads to a lower probability of acceptance than the one desired by the producer. The same issue also occurs in the case of a variables single sampling plan described in a previous paper by Pearn, W. L., & Wu, C. W. (2007). An effective decision making method for product acceptance. Omega, 35(1), 12–21. Nevertheless, a similar yet less severe inaccuracy is also noticed in Wu, C. W., & Pearn, W. L. (2008). A variables sampling plan based on Cpmk for product acceptance determination. European Journal of Operational Research, 184(2), 549–560.

Suggested Citation

  • Lepore, A. & Palumbo, B. & Castagliola, P., 2018. "A note on decision making method for product acceptance based on process capability indices Cpk and Cpmk," European Journal of Operational Research, Elsevier, vol. 267(1), pages 393-398.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:1:p:393-398
    DOI: 10.1016/j.ejor.2017.12.032
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    References listed on IDEAS

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    1. Hsu, Ya-Chen & Pearn, W.L. & Wu, Pei-Ching, 2008. "Capability adjustment for gamma processes with mean shift consideration in implementing Six Sigma program," European Journal of Operational Research, Elsevier, vol. 191(2), pages 517-529, December.
    2. Wu, Chien-Wei & Pearn, W.L., 2008. "A variables sampling plan based on Cpmk for product acceptance determination," European Journal of Operational Research, Elsevier, vol. 184(2), pages 549-560, January.
    3. Nourelfath, Mustapha & Hassan, Jawad, 2015. "Six Sigma performance for non-normal processesAuthor-Name: Aldowaisan, Tariq," European Journal of Operational Research, Elsevier, vol. 247(3), pages 968-977.
    4. 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.
    5. Pearn, W.L. & Wu, Chien-Wei, 2007. "An effective decision making method for product acceptance," Omega, Elsevier, vol. 35(1), pages 12-21, February.
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    Cited by:

    1. Kuen-Suan Chen & Tsun-Hung Huang & Ruey-Chyn Tsaur & Wen-Yang Kao, 2022. "Fuzzy Evaluation Models for Accuracy and Precision Indices," Mathematics, MDPI, vol. 10(21), pages 1-12, October.
    2. Kuen-Suan Chen & Tsang-Chuan Chang, 2022. "Fuzzy testing model for the lifetime performance of products under consideration with exponential distribution," Annals of Operations Research, Springer, vol. 312(1), pages 87-98, May.
    3. Michele Scagliarini, 2022. "A sequential test and a sequential sampling plan based on the process capability index Cpmk," Computational Statistics, Springer, vol. 37(3), pages 1523-1550, July.
    4. 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.
    5. Chun-Min Yu & Tsun-Hung Huang & Kuen-Suan Chen & Tsung-Yu Huang, 2022. "Construct Six Sigma DMAIC Improvement Model for Manufacturing Process Quality of Multi-Characteristic Products," Mathematics, MDPI, vol. 10(5), pages 1-13, March.
    6. Chien-Wei Wu & Ming-Hung Shu & Pei-An Wang & Bi-Min Hsu, 2021. "Variables skip-lot sampling plans on the basis of process capability index for products with a low fraction of defectives," Computational Statistics, Springer, vol. 36(2), pages 1391-1413, June.

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