Skip to main content
SpringerLink
Log in

Estimating process capability indices of multivariate nonnormal processes

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

The capability analysis of production processes where there are more than one correlated quality variables is a complicated task. The problem becomes even more difficult when these variables exhibit nonnormal characteristics. In this paper, a new methodology is proposed to estimate process capability indices (PCIs) of multivariate nonnormal processes. In the proposed methodology, the skewness of the marginal probability distributions of the variables is first diminished by a root transformation technique. Then, a Monte Carlo simulation method is employed to estimate the process proportion of nonconformities (PNC). Next, the relationship between PNC and PCI is found, and finally, PCI is estimated using PNC. Several multivariate nonnormal distributions such as Beta, Weibull, and Gamma are taken into account in simulation experiments. A real-world problem is also given to demonstrate the application of the proposed procedure. The results obtained from both the simulation studies and the real-world problem show that the proposed method performs well and is able to estimate PCI properly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abbasi B (2009) A neural network applied to estimate process capability of non-normal processes. Expert Systems Appl 36:3093–3100

    Article  Google Scholar 

  2. Bai DS, Choi SS (1997) Process capability indices for skewed populations. Master Thesis, Department of Industrial Engineering, Advanced Institute of Science and Technology, Taejon, South Korea

  3. Box G, Cox DR (1964) An analysis of transformation. J R Stat Soc, Ser B 26:211–243

    MATH  MathSciNet  Google Scholar 

  4. Boyles RA (1994) Process capability with asymmetric tolerances. Commun Stat, Simul Comput 23:615–643

    Article  MATH  MathSciNet  Google Scholar 

  5. Castagliola P (1996) Evaluation of non-normal process capability indices using Burr’s distributions. Qual Eng 8:587–593

    Article  Google Scholar 

  6. Castagliola P, Castellanos JVG (2005) Capability indices dedicated to the two quality characteristic cases. Qual Tech Quantitative Management 2:201–220

    Google Scholar 

  7. Chen H (1994) A multivariate process capability index over a rectangular solid tolerance zone. Stat Sin 4:749–758

    MATH  Google Scholar 

  8. Chen KS, Hsu CH, Wu CC (2006) Process capability analysis for a multi-process product. Int J Adv Manuf Technol 27:1235–1241

    Article  Google Scholar 

  9. Choi IS, Bai DS (1996) Process capability indices for skewed populations. In: Proceedings of 20th International Conference on Computers and Industrial Engineering, 1211–1214

  10. Clements JA (1989) Process capability calculations for non-normal distributions. Qual Prog 22:95–100

    Google Scholar 

  11. Hosseinifard SZ, Abbasi B, Ahmad S, Abdollahian M (2009) A transformation technique to estimate the process capability index for non-normal processes. Int J Adv Manuf Technol 40:512–517

    Article  Google Scholar 

  12. Huang ML, Chen KS, Hung YH (2002) Integrated process capability analysis with an application in backlight module. Microelectron Reliab 42:2009–2014

    Article  Google Scholar 

  13. Hubele N, Shahriari H, Cheng C (1991) A bivariate capability vector. In: Keats JB, Montgomery DC (eds) Statistics and design in process control: keeping pace with automated manufacturing. Marcel Dekker, New York, pp 299–310

    Google Scholar 

  14. Johnson NL (1949) System of frequency curves generated by methods of translation. Biometrika 36:149–176

    MATH  MathSciNet  Google Scholar 

  15. Kane VE (1986) Process capability indices. J Qual Technol 18:41–52

    Google Scholar 

  16. Liao SJ, Chen KS, Li RK (2002) Capability evaluation for process of the larger-the-better type for non-normal populations. Adv Appl Stat 2:189–198

    MATH  MathSciNet  Google Scholar 

  17. Liu PH, Chen FL (2006) Process capability analysis of non-normal process data using the Burr XII distribution. Int J Adv Manuf Technol 27:975–984

    Article  Google Scholar 

  18. Mousa MA, Jaheen ZF (2002) Statistical inference for the Burr model based on progressively censored data. Comput Math Appl 43:1441–1449

    Article  MATH  MathSciNet  Google Scholar 

  19. Niaki STA, Abbasi B (2007) Skewness reduction approach in multi-attribute process monitoring. Commun Stat, Theory Methods 36:2313–2325

    Article  MATH  MathSciNet  Google Scholar 

  20. Pal S (2005) Evaluation of non normal process capability indices using generalized lambda distribution. Qual Eng 17:77–85

    Article  Google Scholar 

  21. Pearn WL, Kotz S (1994) Application of Clements’ method for calculating second and third generation process capability indices for non-normal Pearsonian populations. Qual Eng 7:139–145

    Article  Google Scholar 

  22. Pearn WL, Chen KS, Lin GH (1999) A generalization of Clements’ method for non-normal Pearsonian processes with asymmetric tolerances. Int J Qual Reliab Manag 16:507–521

    Article  Google Scholar 

  23. Quesenberry CP (1995) Geometric Q-charts for high quality processes. J Qual Technol 27:304–315

    Google Scholar 

  24. Ryan TP (1989) Statistical methods for quality improvement. Wiley, New York

    Google Scholar 

  25. Somerville S, Montgomery D (1996) Process capability indices and non-normal distributions. Qual Eng 19:305–316

    Article  Google Scholar 

  26. Taam W, Subbaiah P, Liddym JW (1993) A note on multivariate capability indices. J Appl Stat 20:339–351

    Article  Google Scholar 

  27. Tang LC, Than SE (1999) Computing process capability indices for non-normal data: a review and comparative study. Qual Reliab Eng Int 15:339–353

    Article  Google Scholar 

  28. Wang FK (2006) Quality evaluation of a manufactured product with multiple characteristics. Qual Reliab Eng Int 22:225–236

    Article  MATH  Google Scholar 

  29. Wang FK, Du TC (2000) Using principal component analysis in process performance for multivariate data. Omega 28:185–194

    Article  Google Scholar 

  30. Wang FK, Hubele NF (1999) Quality evaluation using geometric distance approach. Int J Reliab Qual Saf Eng 6:139–153

    Article  Google Scholar 

  31. Wang FK, Hubele NF, Lawrence FP, Miskulin JD, Shahriari H (2000) Comparison of three multivariate process capability indices. J Qual Technol 32:263–275

    Google Scholar 

  32. Wang KJB, Zimmer WJ (1996) The maximum likelihood estimation of the Burr XII parameters with censored and uncensored data. Microelectron Reliab 36:359–362

    Article  Google Scholar 

  33. Wright PA (1995) A process capability index sensitive to skewness. Stat Comput Simul 52:195–302

    Article  Google Scholar 

  34. Wu HH, Wang JS, Liu TL (1998) Discussions of the Clements-based process capability indices. In: Proceedings of the 1998 CIIE National Conference, pp 561–566

  35. Xie M, Goh TN, Tang Y (2000) Data transformation for geometrically distributed quality characteristics. Qual Reliab Eng Int 16:9–15

    Article  Google Scholar 

  36. Yeh A, Chen H (2001) A nonparametric multivariate process capability index. Int J Model Simul 21:218–223

    Google Scholar 

  37. Zimmer WJ, Keats JB, Wang FK (1998) The Burr XII distribution in reliability analysis. J Qual Tech 30:2–9

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Sharif University of Technology, P.O. Box 11155-9414, Azadi Ave., Tehran, 1458889694, Iran

    Babak Abbasi & Seyed Taghi Akhavan Niaki

Authors
  1. Babak Abbasi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seyed Taghi Akhavan Niaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seyed Taghi Akhavan Niaki.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abbasi, B., Akhavan Niaki, S.T. Estimating process capability indices of multivariate nonnormal processes. Int J Adv Manuf Technol 50, 823–830 (2010). https://doi.org/10.1007/s00170-010-2557-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-010-2557-y

Keywords

Search

Navigation