Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Bootstrap method approach in designing multi-attribute control charts


In a production process, when the quality of a product depends on more than one correlated characteristic, multivariate quality control techniques are used. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In monitoring the quality of a product or process in multi-attribute environments in which the attributes are correlated, several issues arise. For example, a high number of false alarms (type I error) occur and the probability of not detecting defects (type II error) increases when the process is monitored by a set of independent uni-attribute control charts. In this paper, to overcome these problems, first we develop a new methodology to derive control limits on the attributes based on the bootstrap method in which we build simultaneous confidence intervals on the attributes. Then, based upon the in-control and out-of-control average run length criteria we investigate the performance of the proposed method and compare it with the ones from the Bonferroni and Sidak’s procedure using simulation. The results of the simulation study show that the proposed method performs better than the other two methods. At the end, we compare the bootstrap method with the T 2 control chart for attributes.

This is a preview of subscription content, log in to check access.


  1. 1.

    Montgomery DC (2003) Introduction to statistical quality control, 5th edn. Wiley, New York, NY

  2. 2.

    Hotelling H (1947) Multivariate quality control. In: Eisenhart C, Hastay H, Wallis WA (eds) In techniques of statistical analysis. McGraw-Hill, New York, NY

  3. 3.

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

  4. 4.

    Golnabi S, Houshmand AA (1999) Multivariate shewhart x-bar chart. Inter Stat, No. 4, -A web based journal

  5. 5.

    Woodall WH, Ncube MM (1985) Multivariate CUSUM quality-control procedures. Technometrics 27:285–292

  6. 6.

    Healy JD (1987) A note on multivariate CUSUM procedures. Technometrics 29:409–412

  7. 7.

    Lucas JM, Crosier RB (1982) Fast initial response for CUSUM quality control schemes: give your CUSUM a head start. Technometrics 24:199–2054

  8. 8.

    Pignatiello JJ, Runger GC (1990) Comparisons of multivariate CUSUM charts. J Qual Technol 22:173–186

  9. 9.

    Lucas JM, Saccucci MS (1990) Exponentially weighted moving average control schemes: properties and enhancements. Technometrics 32:1–10

  10. 10.

    Lowry CA, Woodall WH, Champ CW, Erigdon S (1992) A multivariate exponentially weighted moving average control chart. Technometrics 34:46–53

  11. 11.

    Kourti T, MacGregor JF (1996) Multivariate SPC methods for process and product monitoring. J Qual Technol 28:409–428

  12. 12.

    Runger GC (1996) Projections and the U2 multivariate control chart. J Qual Technol 2:313–319

  13. 13.

    Hawkins DM (1991) Regression adjustment for variables in multivariate quality control. J Qual Technol 25:175–182

  14. 14.

    Hayter AJ, Tsui KL (1994) Identification and qualification in multivariate quality control problems. J Qual Technol 26:197–208

  15. 15.

    Niaki STA, Abbasi B (2005) Fault diagnosis in multivariate control charts using artificial neural networks. J Qual Reliabil Eng Int 21:825–840

  16. 16.

    Bourke PD (1991) Detecting shift in fraction nonconforming using run-length control chart with 100% inspection. J Qual Technol 23:225–238

  17. 17.

    Xie M, Goh TN (1992) Some procedures for decision making in controlling high yield processes. Qual Reliabil Eng Int 8:355–360

  18. 18.

    Patel HI (1973) Quality control methods for multivariate binomial and Poisson distributions. Technometrics 15:103–112

  19. 19.

    Lu XS, Xie M, Goh TN, Lai CD (1998) Control chart for multivariate attribute processes. Int J Prod Res 36:3477–3489

  20. 20.

    Jolayemi JK (2000) An optimal design of multi-attribute control charts for processes subject to a multiplicity of assignable causes. Appl Math Comput 114:187–203

  21. 21.

    Jolayemi JK (1994) Convolution of independent binomial variables: an approximation method and a comparative study. Comput Stat Data Anal 18:403–417

  22. 22.

    Gibra IN (1978) Economically optimal determination of the parameters of np-control charts. J Qual Technol 10:12–19

  23. 23.

    Marcucci M (1985) Monitoring multinomial processes. J Qual Technol 17:86–91

  24. 24.

    Larpkiattaworn S (2003) A neural network approach for multi-attribute process control with comparison of two current techniques and guidelines for practical use. Dissertation, University of Pittsburgh

  25. 25.

    Gadre MP, Rattihalli RN (2005) Some group inspection based multi-attribute control charts to identify process deterioration. Econ Qual Control 2:151–164

  26. 26.

    Sahai H, Khurshid A (1993) Confidence intervals for the mean of a Poisson distribution: a review. Biometr J 7:857–867

  27. 27.

    Efron B (1979) Bootstrap method: another look at kackknife. Ann Stat 7:1–26

  28. 28.

    Holland BS, Copenhaver MD (1987) An improved sequentially rejective Bonferroni test procedure. Biometrics 43:417–424

  29. 29.

    Jhun M, Jeong H (2006) Simultaneous confidence intervals for multivariate Poisson distributions.

  30. 30.

    Cario MC, Nelson BL (1997) Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical Report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL

  31. 31.

    Niaki STA, Abbasi B (2006) NORTA and neural networks based method to generate random vectors with arbitrary marginal distributions and correlation matrix. Proc 17th IASTED International Conference on Modeling and Simulation, Montreal, Canada

Download references

Author information

Correspondence to Seyed Taghi Akhavan Niaki.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Niaki, S.T.A., Abbasi, B. Bootstrap method approach in designing multi-attribute control charts. Int J Adv Manuf Technol 35, 434–442 (2007).

Download citation


  • Bootstrap method
  • Multi-attribute control charts
  • Process monitoring
  • Simultaneous confidence intervals