Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 127 Accesses

  • 11 Citations


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 to check access.


  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 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

  7. 7.

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

  8. 8.

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

  9. 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

  10. 10.

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

  11. 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

  12. 12.

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

  13. 13.

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

  14. 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

  15. 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

Download references

Author information

Correspondence to L. L. Ho.

Rights and permissions

Reprints and Permissions

About this article

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).

Download citation


  • T 2’s Hotelling
  • Bivariate binomial distribution
  • Discriminating limits
  • Average run length