Skip to main content
SpringerLink
Log in

Multivariate process capability using principal component analysis in the presence of measurement errors

  • Original Paper
  • Published:
AStA Advances in Statistical Analysis Aims and scope Submit manuscript

Abstract

Various different definitions of multivariate process capability indices have been proposed in the literature. Most of the research works related to multivariate process capability indices assume no gauge measurement errors. However, in industrial applications, despite the use of highly advanced measuring instruments, account needs to be taken of gauge imprecision. In this paper we are going to examine the effects of measurement errors on multivariate process capability indices computed using the principal components analysis. We show that measurement errors alter the results of a multivariate process capability analysis, resulting in either a decrease or an increase in the capability of the process. In order to achieve accurate process capability assessments, we propose a method useful for overcoming the effects of gauge measurement errors.

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

  • Bordignon, S., Scagliarini, M.: Statistical analysis of process capability indices with measurement errors. Qual. Reliab. Eng. Int. 18, 321–332 (2002)

    Article  Google Scholar 

  • Bordignon, S., Scagliarini, M.: Estimation of C pm when measurement error is present. Qual. Reliab. Eng. Int. 22, 787–801 (2006)

    Article  Google Scholar 

  • Burdick, R.K., Borror, C.M., Montgomery, D.C.: A review of methods for measurements systems capability analysis. J. Qual. Technol. 35, 342–354 (2003)

    Google Scholar 

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

    MATH  Google Scholar 

  • Chen, K.S., Pearn, W.L., Lin, P.C.: Capability measures for processes with multivariate Characteristics. Qual. Reliab. Eng. Int. 19, 101–110 (2003)

    Article  Google Scholar 

  • González, I., Sánchez, I.: Capability indices and nonconforming proportion in univariate and multivariate processes. Int. J. Adv. Manuf. Technol. 44, 1036–1050 (2009)

    Article  Google Scholar 

  • Huwang, L., Hung, Y.: Effect of measurement error on monitoring multivariate process variability. Stat. Sin. 17, 749–760 (2007)

    MATH  MathSciNet  Google Scholar 

  • Jackson, J.E.: Principal components and factor analysis: part I. J. Qual. Technol. 12, 201–213 (1980)

    Google Scholar 

  • Kotz, S., Johnson, N.L.: Process capability indices—a review, 1992–2000. J. Qual. Technol. 34, 2–19 (2002)

    Google Scholar 

  • Kotz, S., Lovelace, C.R.: Process Capability Indices in Theory and Practices. Arnold, London (1998)

    Google Scholar 

  • Linna, K.W., Woodall, W.H., Busby, K.L.: The performance of multivariate control chart in the presence of measurement error. J. Qual. Technol. 33, 349–355 (2001)

    Google Scholar 

  • Majeske, K.D.: Approval criteria for multivariate measurement systems. J. Qual. Technol. 40, 140–153 (2008)

    Google Scholar 

  • Mittag, H.J.: Measurement error effects on the performance of process capability indices. In: Lenz, H.J., Wirlich, P.T. (eds.) Frontiers in Statistical Quality Control, vol. 5, pp. 195–206. Physica-Verlag, Heidelberg (1997)

    Google Scholar 

  • Montgomery, D.C.: Introduction to Statistical Quality Control, 5th edn. Wiley, New York (2005)

    MATH  Google Scholar 

  • Pearn, W.L., Liao, M.-Y.: Measuring process capability based on C pk with gauge measurement errors. Microelectron. Reliab. 45, 739–751 (2005)

    Article  Google Scholar 

  • Pearn, W.L., Kotz, S.: Encyclopedia and Handbook of Process Capability Indices. Series on Quality, Reliability and Engineering Statistics, vol. 12. World Scientific, Singapore (2006)

    MATH  Google Scholar 

  • Pearn, W.L., Shu, M.H., Hsu, B.: Testing process capability based on C pm in the presence of random measurement errors. J. Appl. Stat. 32, 1003–1024 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Pearn, W.L., Wang, F.K., Yen, C.H.: Multivariate capability indices: distributional and inferential properties. J. Appl. Stat. 34, 941–962 (2007)

    MathSciNet  Google Scholar 

  • Scagliarini, M.: Estimation of C p for autocorrelated data and measurement errors. Commun. Stat. A, Theory 31, 1647–1664 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Scagliarini, M.: Inference on C pk for autocorrelated data in the presence of random measurement errors. J. Appl. Stat. 37, 147–158 (2010)

    Article  Google Scholar 

  • Shahriari, H., Hubele, N.F., Lawrence, F.P.: A Multivariate Process Capability Vector, Proceedings of the 4th Industrial Engineering Research Conference, Nashville, TN, pp. 303–308 (1995)

    Google Scholar 

  • Shinde, R.L., Khadse, K.G.: Multivariate process capability using principal component analysis. Qual. Reliab. Eng. Int. 25, 69–77 (2009)

    Article  Google Scholar 

  • Shishebori, D., Hamadani, A.Z.: The effect of gauge measurement capability on MC p and its statistical properties. Int. J. Qual. Reliab. Manag. 26, 564–582 (2009)

    Article  Google Scholar 

  • Shishebori, D., Hamadani, A.Z.: Properties of multivariate process capability in the presence of gauge measurement errors and dependency measure of process variables. J. Manuf. Syst. 29, 10–18 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Villeta, M., Rubio, E.M., Sebastián, M.A., Sanz, A.: New criterion for evaluating the aptitude of measurement systems in process capability determination. Int. J. Adv. Manuf. Technol. (2010). doi:10.1007/s00170-010-2545-2

    Google Scholar 

  • Wang, C.H.: Constructing multivariate process capability indices for short-run production. Int. J. Adv. Manuf. Technol. 26, 1306–1311 (2005)

    Article  Google Scholar 

  • Wang, F.K., Chen, J.C.: Capability index using principal components analysis. Qual. Eng. 11, 21–27 (1998)

    Article  MATH  Google Scholar 

  • Wierda, S.J.: A multivariate process capability index. In: ASQC-Quality Congress Transactions, Boston, pp. 342–348 (1993)

    Google Scholar 

  • Wu, C.-W.: Using a novel approach to assess process performance in the presence of measurement errors. J. Stat. Comput. Simul. (2010). doi:10.1080/00949650903313761

    Google Scholar 

  • Wu, C.-W., Pearn, W.L., Kotz, S.: An overview of theory and practice on process capability indices for quality assurance. Int. J. Prod. Econ. 117, 338–359 (2009)

    Article  Google Scholar 

  • Xekalaki, E., Perakis, M.: The Use of principal component analysis in the assessment of process capability indices. In: Proceedings of the Joint Statistical Meetings of the American Statistical Association, The Institute of Mathematical Statistics, The Canadian Statistical Society, New York, pp. 3819–3823 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Bologna, Via Belle Arti 41, 40126, Bologna, Italy

    Michele Scagliarini

Authors
  1. Michele Scagliarini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michele Scagliarini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Scagliarini, M. Multivariate process capability using principal component analysis in the presence of measurement errors. AStA Adv Stat Anal 95, 113–128 (2011). https://doi.org/10.1007/s10182-011-0156-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10182-011-0156-3

Keywords

Search

Navigation