IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v117y2009i2p338-359.html
   My bibliography  Save this article

An overview of theory and practice on process capability indices for quality assurance

Author

Listed:
  • Wu, Chien-Wei
  • Pearn, W.L.
  • Kotz, Samuel

Abstract

Process capability indices (PCIs), Cp, Ca, Cpk, Cpm, and Cpmk have been developed in certain manufacturing industry as capability measures based on various criteria, including process consistency, process departure from a target, process yield, and process loss. It is noted in certain recent quality assurance and capability analysis works that the three indices, Cpk, Cpm, and Cpmk provide the same lower bounds on the process yield. In this paper, we investigate the behavior of the actual process yield, in terms of the number of non-conformities (in ppm), for processes with fixed index values of Cpk=Cpm=Cpmk, possessing different degrees of process centering. We also extend Johnson's [1992. The relationship of Cpm to squared error loss. Journal of Quality Technology 24, 211-215] result formulating the relationship between the expected relative squared loss and PCIs. Also a comparison analysis among PCIs is carried out based on various criteria. The result illustrates some advantages of using the index Cpmk over the indices Cpk and Cpm in measuring process capability (yield and loss), since Cpmk always provides a better protection for the customers. Additionally, several extensions and applications to real world problem are also discussed. The paper contains some material presented in the Kotz and Johnson [2002. Process capability indices--a review, 1992-2000. Journal of Quality Technology 34(1), 1-19] survey but from a different perspective. It also discusses the more recent developments during the years 2002-2006.

Suggested Citation

  • Wu, Chien-Wei & Pearn, W.L. & Kotz, Samuel, 2009. "An overview of theory and practice on process capability indices for quality assurance," International Journal of Production Economics, Elsevier, vol. 117(2), pages 338-359, February.
    • Handle: RePEc:eee:proeco:v:117:y:2009:i:2:p:338-359
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(08)00376-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Chang, Y.C. & Wu, Chien-Wei, 2008. "Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances," European Journal of Operational Research, Elsevier, vol. 190(1), pages 205-227, October.
    2. Wu, Chien-Wei, 2008. "Assessing process capability based on Bayesian approach with subsamples," European Journal of Operational Research, Elsevier, vol. 184(1), pages 207-228, January.
    3. Wang, F. K. & Du, T. C. T., 2000. "Using principal component analysis in process performance for multivariate data," Omega, Elsevier, vol. 28(2), pages 185-194, April.
    4. Arjun Gupta & S. Kotz, 1997. "A new process capability index," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 213-224, January.
    5. Wright, Peter A., 2000. "The cumulative distribution function of process capability index Cpm," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 249-251, April.
    6. K. Palmer & K.-L. Tsui, 1999. "A review and interpretations of process capability indices," Annals of Operations Research, Springer, vol. 87(0), pages 31-47, April.
    7. Samuel Kotz & Wen Lea Pearn & N. L. Johnson, 1993. "Some Process Capability Indices are More Reliable than One Might Think," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(1), pages 55-62, March.
    8. Pearn, W. L. & Wu, Chien-Wei, 2005. "A Bayesian approach for assessing process precision based on multiple samples," European Journal of Operational Research, Elsevier, vol. 165(3), pages 685-695, September.
    9. W. L. Pearn, 1998. "New generalization of process capability index Cpk," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(6), pages 801-810.
    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. Wu, Chien-Wei, 2008. "Assessing process capability based on Bayesian approach with subsamples," European Journal of Operational Research, Elsevier, vol. 184(1), pages 207-228, January.
    2. Wu, Chien-Wei, 2009. "Decision-making in testing process performance with fuzzy data," European Journal of Operational Research, Elsevier, vol. 193(2), pages 499-509, March.
    3. 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.
    4. Pearn, W.L. & Wu, Chien-Wei, 2007. "An effective decision making method for product acceptance," Omega, Elsevier, vol. 35(1), pages 12-21, February.
    5. Hsi-Tien Chen & Kuen-Suan Chen, 2016. "Assessing the assembly quality of a T-bar ceiling suspension by using an advanced multi-process performance analysis chart with asymmetric tolerance," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 10(2), pages 264-283.
    6. Chang, Y.C. & Wu, Chien-Wei, 2008. "Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances," European Journal of Operational Research, Elsevier, vol. 190(1), pages 205-227, October.
    7. Dja-Shin Wang & Tong-Yuan Koo & Chao-Yu Chou, 2009. "Yield measure for the process with multiple streams," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(4), pages 661-668, July.
    8. Noureddine Kouaissah & Sergio Ortobelli Lozza & Ikram Jebabli, 2022. "Portfolio Selection Using Multivariate Semiparametric Estimators and a Copula PCA-Based Approach," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 833-859, October.
    9. Daniel Dasig Jr, 2017. "A frontier in organizational and business process innovation in service management through lean six sigma Kaizen project implementation," Journal of Administrative and Business Studies, Professor Dr. Usman Raja, vol. 3(6), pages 263-283.
    10. A. Parchami & M. Mashinchi, 2010. "A new generation of process capability indices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 77-89.
    11. Chien-Wei Wu & Tsai-Yu Lin, 2009. "A Bayesian procedure for assessing process performance based on the third-generation capability index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1205-1223.
    12. Bo Xiong & Martin Skitmore & Bo Xia, 2015. "Exploring and validating the internal dimensions of occupational stress: evidence from construction cost estimators in China," Construction Management and Economics, Taylor & Francis Journals, vol. 33(5-6), pages 495-507, June.
    13. Daniela F. Dianda & Marta B. Quaglino & José A. Pagura, 2018. "Impact of measurement errors on the performance and distributional properties of the multivariate capability index $$\mathbf{NMC }_\mathbf{pm }$$ NMC pm," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 117-143, January.
    14. Kuen-Suan Chen & Chun-Min Yu, 2024. "Developing a novel fuzzy testing model for capability index with asymmetric tolerances," Annals of Operations Research, Springer, vol. 340(1), pages 149-162, September.
    15. V�ctor Leiva & Carolina Marchant & Helton Saulo & Muhammad Aslam & Fernando Rojas, 2014. "Capability indices for Birnbaum-Saunders processes applied to electronic and food industries," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1881-1902, September.
    16. Marta Benková & Dagmar Bednárová & Gabriela Bogdanovská, 2024. "Process Capability Evaluation Using Capability Indices as a Part of Statistical Process Control," Mathematics, MDPI, vol. 12(11), pages 1-29, May.
    17. Panagopoulos, Orestis P. & Pappu, Vijay & Xanthopoulos, Petros & Pardalos, Panos M., 2016. "Constrained subspace classifier for high dimensional datasets," Omega, Elsevier, vol. 59(PA), pages 40-46.
    18. CHEN, Piao & YE, Zhi-Sheng, 2018. "A systematic look at the gamma process capability indices," European Journal of Operational Research, Elsevier, vol. 265(2), pages 589-597.
    19. Sajid Ali & Muhammad Riaz, 2014. "On the generalized process capability under simple and mixture models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 832-852, April.
    20. Nozer Singpurwalla & G. Box & D. Cox & D. Dey & A. Fries & J. Ghosh & M. Gómez-Villegas & T. Irony & W. Kliemann & S. Kotz & D. Lindley & M. McGrath & D. Peña & N. Singpurwalla, 1998. "The stochastic control of process capability indices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 1-74, June.

    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:proeco:v:117:y:2009:i:2:p:338-359. 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/ijpe .

    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.