Skip to main content
SpringerLink
Log in

M a x D: an attribute control chart to monitor a bivariate process mean

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

Abstract

The aim of this paper is to propose a new attribute control chart, namely M a x D, to monitor a bivariate process mean. No measurement is taken but using a gauge ring each sampled unit is classified as failed/disapproved or not in each dimension. If the number of disapproved units of any dimension is larger than a control limit, a signal of out-of-control is triggered. The development of the control chart is based on a bivariate binomial distribution. The results show that the current proposal has a good performance and it is a feasible alternative to T 2 control chart mainly if the cost of the measurement of the quantitative characteristics is expensive or demands much time or the sampled units are damaged and have to be discarded in case of destructive experiments.

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. Alt FB (1985) Multivariate quality control. In: Kotz, S and Johnson, N (eds) Encyclopedia of statistical sciences, vol 6

  2. Bersimis S, Psarakis S, Panaretos J (2007) Multivariate statistical process control charts: an overview. Quality Reliab Eng Int 23(5):517–543

    Article  Google Scholar 

  3. Ho LL, Costa A (2015) Attribute charts for monitoring the mean vector of bivariate processes. Quality Reliab Eng Int 31(4):683–693

    Article  Google Scholar 

  4. Hotelling H (1947) Multivariate quality control illustrated by the air testing of sample bomb sights, techniques of statistical analysis, ch. ii

  5. Lowry CA, Montgomery DC (1995) A review of multivariate control charts. IIE Trans 27(6):800–810

    Article  Google Scholar 

  6. Marshall AW, Olkin I (1985) A family of bivariate distributions generated by the bivariate bernoulli distribution. J Amer Stat Assoc 80(390):332–338

    Article  MathSciNet  MATH  Google Scholar 

  7. Montgomery DC (2001) Introduction to statistical quality control, 4th edn. Wiley

  8. Development Core Team R (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

  9. Shewhart WA (1925) The application of statistics as an aid in maintaining quality of a manufactured product. J Amer Stat Assoc 20(152):546–548

    Article  Google Scholar 

  10. Steiner SH (1998) Grouped data exponentially weighted moving average control charts. J R Stat Soc Series C (Appl Stat) 47(2):203–216

    Article  MATH  Google Scholar 

  11. Steiner SH, Geyer PLEE, Wesolowsky GO (1996) Shewhart control charts to detect mean and standard deviation shifts based on grouped data. Quality Reliab Eng Int 12(5):345–353

    Article  Google Scholar 

  12. Stevens WL (1948) Control by gauging. J R Stat Soc Series B (Methodol) 10(1):54–108

    MATH  Google Scholar 

  13. Teicher H (1954) On the multivariate poisson distribution. Scand Actuar J 1954(1):1–9

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang W, Jiao J (2008) A control chart for monitoring process mean based on attribute inspection. Int J Prod Res 46(15):4331–4347

    Article  MATH  Google Scholar 

  15. Zhang W, Khoo MBC, Shu L, Jiang W (2009) An np control chart for monitoring the mean of a variable based on an attribute inspection. Int J Prod Econ 121(1):141–147

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of São Paulo and Federal University of Rio Grande de Norte, São Paulo, Brazil

    M. S. Melo & L. L. Ho

  2. Federal University of Rio Grande do Norte, Natal, Brazil

    M. S. Melo & P. G. Medeiros

Authors
  1. M. S. Melo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. L. Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. G. Medeiros
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. L. Ho.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Melo, M.S., Ho, L.L. & Medeiros, P.G. M a x D: an attribute control chart to monitor a bivariate process mean. Int J Adv Manuf Technol 90, 489–498 (2017). https://doi.org/10.1007/s00170-016-9368-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-016-9368-8

Keywords

Search

Navigation