Skip to main content
SpringerLink
Log in

A CUSUM-based method for monitoring simple linear profiles

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

Abstract

In most statistical process control applications, the quality of a process or product is characterized by univariate or multivariate quality characteristics and monitored by the corresponding univariate and multivariate control charts, respectively. However, sometimes, the quality of a process or a product is better characterized by a relationship between a response variable and one or more explanatory variables. This relationship, which can be linear, nonlinear, or even a complicated model, is referred to as a profile. So far, several methods have been proposed for monitoring simple linear profiles. In this paper, a new method based on cumulative sum statistics is proposed to enhance monitoring of linear profiles in phase II. The performance of the proposed method is evaluated by average run length criterion. A comprehensive comparison is also conducted between the performance of the proposed method and the existing methods for monitoring simple linear profiles. The results show that the proposed method performs satisfactorily. In addition, the effects of reference value, sample size, and corrected sum of squares of explanatory variables on the performance of the proposed method are investigated.

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. Croarkin C, Varner R (1982) Measurement assurance for dimensional measurements on integrated-circuit photomasks. NBS Technical Note 1164. US Department of Commerce, Washington, D.C

    Google Scholar 

  2. Ding Y, Zeng L, Zhou S (2006) Phase I analysis for monitoring nonlinear profiles in manufacturing processes. J Qual Technol 38(3):199–216

    Google Scholar 

  3. Gupta S, Montgomery DC, Woodall WH (2006) Performance evaluation of two methods for online monitoring of linear calibration profiles. Int J Prod Res 44(10):1927–1942. doi:10.1080/00207540500409855

    Article  Google Scholar 

  4. Jensen WA, Birch JB (2009) Profile monitoring via nonlinear mixed model. J Qual Technol 41(1):18–34

    Google Scholar 

  5. Kang L, Albin SL (2000) On-line monitoring when the process yields a linear profile. J Qual Technol 32(4):418–426

    Google Scholar 

  6. Kazemzadeh RB, Noorossana R, Amiri A (2008) Phase I monitoring of polynomial profiles. Commun Stat Theory Methods 37(10):1671–1686. doi:10.1080/03610920701691714

    Article  MATH  Google Scholar 

  7. Kazemzadeh RB, Noorossana R, Amiri A (2008) Monitoring polynomial profiles in quality control applications. Int J Adv Manuf Technol. doi:10.1007/s00170-008-1633-z

  8. Kim K, Mahmoud MA, Woodall WH (2003) On the monitoring of linear profiles. J Qual Technol 35(3):317–328

    Google Scholar 

  9. Mahmoud MA, Parker PA, Woodall WH, Hawkins DM (2007) A change point method for linear profile data. Qual Reliab Eng Int 23(2):247–268. doi:10.1002/qre.788

    Article  Google Scholar 

  10. Mahmoud MA, Woodall WH (2004) Phase I analysis of linear profiles with calibration applications. Technometrics 46(4):380–391. doi:10.1198/004017004000000455

    Article  MathSciNet  Google Scholar 

  11. Mahmoud MA, Woodall WH (2005) The inertial properties of quality control charts. Technometrics 47(4):425–436

    Article  MathSciNet  Google Scholar 

  12. Montgomery DC (2005) Introduction to statistical quality control. Wiley, New York

    MATH  Google Scholar 

  13. Niaki STA, Abbasi B, Arkat J (2007) A generalized linear statistical model approach to monitor profiles. Int J Eng Trans A Basics 20(3):233–242

    Google Scholar 

  14. Noorossana R, Amiri A (2007) Enhancement of linear profiles monitoring in Phase II. AmirKabir J Sci Technol 18(No. 66-B):19–27 in Farsi

    Google Scholar 

  15. Stover FS, Brill RV (1998) Statistical quality control applied to ion chromatography calibrations. J Chromatogr 804(1–2):37–43

    Article  Google Scholar 

  16. Walker E, Wright S (2002) Comparing curves using additive models. J Qual Technol 34(1):118–129

    Google Scholar 

  17. Wang K, Tsung F (2005) Using profile monitoring techniques for a data-rich environment with huge sample size. Qual Reliab Eng Int 21(7):677–688. doi:10.1002/qre.711

    Article  Google Scholar 

  18. Williams JD, Woodall WH, Birch JB (2007) Statistical monitoring of nonlinear product and process quality profiles. Qual Reliab Eng Int 23(8):925–941. doi:10.1002/qre.858

    Article  Google Scholar 

  19. Woodall WH (2007) Current research on profile monitoring. Rev Producao 17(3):420–425

    Google Scholar 

  20. Woodall WH, Spitzner DJ, Montgomery DC, Gupta S (2004) Using control charts to monitor process and product quality profiles. J Qual Technol 36(3):309–320

    Google Scholar 

  21. Zou C, Tsung F, Wang Z (2007) Monitoring general linear profiles using multivariate exponentially weighted moving average schemes. Technometrics 49(4):395–408. doi:10.1198/004017007000000164

    Article  MathSciNet  Google Scholar 

  22. Zou C, Zhang Y, Wang Z (2006) Control chart based on change-point model for monitoring linear profiles. IIE Trans 38(12):1093–1103. doi:10.1080/07408170600728913

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Science and Research Branch, Islamic Azad University, Tehran, Iran

    Abbas Saghaei & Marzieh Mehrjoo

  2. North Tehran Branch, Islamic Azad University, Tehran, Iran

    Amirhossein Amiri

Authors
  1. Abbas Saghaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marzieh Mehrjoo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amirhossein Amiri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abbas Saghaei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saghaei, A., Mehrjoo, M. & Amiri, A. A CUSUM-based method for monitoring simple linear profiles. Int J Adv Manuf Technol 45, 1252 (2009). https://doi.org/10.1007/s00170-009-2063-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00170-009-2063-2

Keywords

Search

Navigation