Skip to main content
SpringerLink
Log in

Modified multivariate process capability index using principal component analysis

  • Published:
Chinese Journal of Mechanical Engineering Submit manuscript

Abstract

The existing research of process capability indices of multiple quality characteristics mainly focuses on nonconforming of process output, the concept development of univariate process capability indices, quality loss function and various comprehensive evaluation methods. The multivariate complexity increases the computation difficulty of multivariate process capability indices(MPCI), which makes them hard to be used in practice. In this paper, a new PCA-based MPCI approach is proposed to assess the production capability of the processes that involve multiple product quality characteristics. This approach first transforms the original quality variables into standardized normal variables. MPCI measures are then provided based on the Taam index. Moreover, the statistical properties of these MPCIs, such as confidence intervals and lower confidence bound, are given to let the practitioners understand the capability indices as random variables instead of deterministic variables. A real manufacturing data set and a synthetic data set are used to demonstrate the effectiveness of the proposed method. An implementation procedure is also provided for quality engineers to apply our MPCI approach in their manufacturing processes. The case studies demonstrate the effectiveness and feasibility of this new kind of MPCI, which is easier to be used in production practice. The proposed research provides a novel approach of MPCI calculation.

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. JURAN E D. Juran’s quality control handbook[M]. New York: McGraw-Hill, 1974.

    Google Scholar 

  2. KOTZ S, JOHNSON N L. Process capability indices[M]. London: Chapman & Hall, 1993.

    Google Scholar 

  3. WU C W, PEARN W L, KOTZ S. An overview of theory and practice on process capability indices for quality assurance[J]. International Journal of Production Economics, 2009, 117(2): 338–359.

    Article  Google Scholar 

  4. YUM B J, KIM K W. A bibliography of the literature on process capability indices: 2000–2009[J]. Quality and Reliability Engineering International, 2011, 27(3): 251–268.

    Article  Google Scholar 

  5. WANG Meng, SUN Shudong. Optimized kernel space based algorithm for quality data analysis[J]. Journal of Mechanical Engineering, 2012, 48(22): 182–188. (in Chinese)

    Article  MATH  Google Scholar 

  6. Lü Shengping, QIAO Lihong, LIU Wei. Formalized and semantic modeling of manufacturing process data[J]. Journal of Mechanical Engineering, 2012, 48(10): 184–191. (in Chinese)

    Article  Google Scholar 

  7. FOSTER E J, BARTON R R, GAUTAM N, et al. The process-oriented multivariate capability index[J]. International Journal of Production Research, 2005, 43(10): 2135–2148.

    Article  Google Scholar 

  8. ABBASI B, NIAKI S. Estimating process capability indices of multivariate nonnormal processes[J]. International Journal of Advanced Manufacturing Technology, 2010, 50(8): 823–830.

    Article  Google Scholar 

  9. GONZALEZ I, SANCHEZ I. Capability indices and nonconforming proportion in univariate and multivariate processes[J]. International Journal of Advanced Manufacturing Technology, 2009, 44(9): 1036–1050.

    Article  Google Scholar 

  10. YEN C H, PEARN W L. Select better suppliers based on manufacturing precision for processes with multivariate data[J]. International Journal of Production Research, 2009, 47(11): 2961–2974.

    Article  MATH  Google Scholar 

  11. RANJAN C, Maiti J. An approach to build process-oriented basis for causation-based multivariate SPC and process capability analysis[J]. Quality and Reliability Engineering International, 2012, Online available, DOI: 10.1002/qre.1475.

    Google Scholar 

  12. SINGH R. Process capability of ultrasonic machining for titanium alloys[J]. International Journal of Materials Engineering Innovation, 2011, 2(4): 310–324.

    Article  Google Scholar 

  13. DENG Yuhao, ZHU Haiping, ZHANG Guojun, et al. Optimal tool replacement decision method based on cost and process capability[J]. Mechanical Engineering and Technology Advances in Intelligent and Soft Computing, 2012, 125(1): 9–14.

    Article  Google Scholar 

  14. AHMAD S, ABODOOAHIAN M, ZEEPHONGSEKUL P, et al. Multivariate nonnormal process capability analysis[J]. International Journal of Advanced Manufacturing Technology, 2009, 44(8): 757–765.

    Article  Google Scholar 

  15. WANG F K. Quality evaluation of a manufactured product with multiple characteristics[J]. Quality and Reliability Engineering International, 2006, 22(2): 225–236.

    Article  Google Scholar 

  16. PEARN W L, WANG F K, YEN C H. Measuring production yield for processes with multiple quality characteristics[J]. International Journal of Production Research, 2006, 44(21): 4649–4661.

    Article  MATH  Google Scholar 

  17. PAN J N, LEE C Y. New capability indices for evaluating the performance of multivariate manufacturing processes[J]. Quality and Reliability Engineering International, 2010, 26(1): 3–15.

    Article  Google Scholar 

  18. ZHOU Chi, DENG Fumin. Solution method of multivariate process capability indices based on rough set and quartile method[J]. Industrial Engineering Journal, 2011, 14(4): 78–81.

    MathSciNet  Google Scholar 

  19. TANO I, VANNMAN K. A multivariate process capability index based on the first principal component only[J]. Quality and Reliability Engineering International, 2012, Online available, DOI: 10.1002/qre.1451.

  20. PERAKIS M, XEKALAKI E. On the implementation of the principal component analysis-based approach in measuring process capability[J]. Quality and Reliability Engineering International, 2012, 28(4): 467–480.

    Article  Google Scholar 

  21. WANG F K, CHEN J C. Capability index using principal component analysis[J]. Quality Engineering, 1998, 11(1): 21–27.

    Article  MATH  Google Scholar 

  22. WANG F K, Du T C T. Using principal component analysis in process performance for multivariate data[J]. Omega, 2000, 28(2): 185–194.

    Article  Google Scholar 

  23. SHINDE R L, KHADSE K G. Multivariate process capability using principal component analysis[J]. Quality and Reliability Engineering International, 2009, 25(1): 69–77.

    Article  Google Scholar 

  24. TAAM W, SUBBAIAH P. A note on multivariate capability indices[J]. Journal of Applied Statistics, 1993, 20(3): 339–351.

    Article  Google Scholar 

  25. PEARN W L, WANG F K, YEN C H. Multivariate capability indices: distributional and inferential properties[J]. Journal of Applied Statistics, 2007, 34(8): 941–962.

    Article  MathSciNet  Google Scholar 

  26. JOLLIFFE I T. Principal component analysis[M]. New York: Springer, 2002.

    Google Scholar 

  27. ANDREWS D F, GNANADESIKAN R, WARNER J L. Transformations of multivariate data[J]. Biometrics, 1971, 27(4): 825–840.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Tianjin University, Tianjin, 300072, China

    Min Zhang & Zhen He

  2. Department of Business Information Technology, Virginia Tech, Blacksburg, 24060, USA

    G. Alan Wang

  3. Department of Information Management and Management Science, Tianjin University, Tianjin, 300072, China

    Shuguang He

Authors
  1. Min Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Alan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuguang He
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhen He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuguang He.

Additional information

This project is supported by National Natural Science Foundation of China(Grant Nos. 70802043, 71225006 and 71002105)

ZHANG Min, born in 1979, is an associate professor at Department of Industrial Engineering, Tianjin University, China. She received her PhD degree in management science and engineering from Tianjin University, China, in 2006, and her MS and BS degrees in material engineering from Shandong University, China, in 2003 and 2000. Her research interests focus on quality engineering, statistical quality control and process monitoring application.

WANG G Alan, born in 1973, is an associate professor at Business Information Technology, Virginia Tech, USA. He received his PhD degree in management information systems from University of Arizona, USA, in 2006 and MS degree in industrial engineering from Louisiana State University, China, in 2001. His research interests include quality engineering and data mining. His publications have appeared in Decision Support Systems, IEEE Transactions on Systems, Man and Cybernetics(Part B), IEEE Computer, and Communications of the ACM.

HE Shuguang, born in 1975, is a professor at School of Management, Tianjin University, China. He received his PhD degree in 2002 and MS degree in 2000 from Tianjin University, China. His research interests include statistical process control and quality control using machine learning.

HE Zhen, born in 1967, is a professor at Department of Industrial Engineering, Tianjin University, China. He received his PhD degree in management science from Tianjin University, China, in 2002. His research interests include quality engineering, and six sigma management. His research appears in Total Quality Management and Business Excellence, Quality Progress, European Journal of Operational Research, Journal of Applied Statistics, Quality and Reliability Engineering International, Asian Journal on Quality, etc.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, M., Wang, G.A., He, S. et al. Modified multivariate process capability index using principal component analysis. Chin. J. Mech. Eng. 27, 249–259 (2014). https://doi.org/10.3901/CJME.2014.02.249

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2014.02.249

Keywords

Search

Navigation