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A transformation-based multivariate chart to monitor process dispersion

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Abstract

Multivariate monitoring techniques such as multivariate control charts are used to control the processes that contain more than one correlated characteristic. Although the majority of previous researches are focused on controlling only the mean vector of multivariate processes, little work has been performed to monitor the covariance matrix. In this research, a new method is presented to detect possible shifts in the covariance matrix of multivariate processes. The basis of the proposed method is to eliminate the correlation structure between the quality characteristics by transformation technique and then use an S chart for each variable. The performance of the proposed method is then compared to the ones from other existing methods and a real case is presented.

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References

  1. Hotelling H (1947) Multivariate Quality Control. In: Eisenhart C, Hastay M, Wallis WA (eds) Techniques of statistical analysis. McGraw-Hill, New York

    Google Scholar 

  2. Jackson JE, Morris RH (1957) An application of multivariate quality control to photographic processes. J Am Stat Assoc 52:186–199. doi:10.2307/2280844

    Article  Google Scholar 

  3. Hayter AJ, Tsui K-L (1994) Identification and qualification in multivariate quality control problems. J Qual Tech 26:197–208

    Google Scholar 

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

    Google Scholar 

  5. Mason RL, Tracy ND, Young JC (1997) A practical approach for interpreting multivariate T2 control chart signals. J Qual Tech 29:396–406

    Google Scholar 

  6. Niaki STA, Abbasi B (2005) Fault diagnosis in multivariate control charts using artificial neural networks. Qual Reliab Eng Int 21:825–840. doi:10.1002/qre.689

    Article  Google Scholar 

  7. Alt FB (1985) Multivariate quality control. Encyclopedia of Statistical Sciences 6:110–122

    Google Scholar 

  8. Tang PF, Barnett NS (1996a) Dispersion control for multivariate processes. Aust J Stat 38:235–251. doi:10.1111/j.1467-842X.1996.tb00680.x

    Article  MATH  MathSciNet  Google Scholar 

  9. Anderson TW (1984) An introduction to multivariate statistical analysis. Wiley, New York

    MATH  Google Scholar 

  10. Tang PF, Barnett NS (1996b) Dispersion control for multivariate processes—some comparisons. Aust J Stat 38:253–273. doi:10.1111/j.1467-842X.1996.tb00681.x

    Article  MATH  MathSciNet  Google Scholar 

  11. Aparisi F, Jabaloyes J, Carrion A (1999) Statistical properties of the |S| multivariate control chart. Comm Statist Theory Methods 28:2671–2686. doi:10.1080/03610929908832445

    Article  MATH  MathSciNet  Google Scholar 

  12. Aparisi F, Jabaloyes J, Carrion A (2001) Generalized variance chart design with adaptive sample sizes; the bivariate case. Comm Statist Simulation Comput 30:931–948. doi:10.1081/SAC-100107789

    Article  MATH  MathSciNet  Google Scholar 

  13. Grigoryan A, He D (2005) Multivariate double sampling |S| charts for controlling process variability. Int J Prod Res 43:715–730. doi:10.1080/00207540410001716525

    Article  MATH  Google Scholar 

  14. Daudin JJ (1992) Double sampling X-bar charts. J Qual Tech 24:78–87

    Google Scholar 

  15. He D, Grigoryan A (2002) Construction of double sampling S-control charts for agile manufacturing. Qual Reliab Eng Int 18:343–355. doi:10.1002/qre.466

    Article  Google Scholar 

  16. He D, Grigoryan A (2003) An improved double sampling S chart. Int J Prod Res 41:2663–2679. doi:10.1080/0020754031000093187

    Article  MATH  Google Scholar 

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

    Google Scholar 

  18. Tracy ND, Young JC, Mason RL (1992) Multivariate control charts for individual observations. J Qual Tech 24:89–125

    Google Scholar 

  19. García-Díaz CJ (2007) The effective variance control chart for monitoring the dispersion process with missing data. Eur J Ind Eng 1:40–55. doi:10.1504/EJIE.2007.012653

    Article  Google Scholar 

  20. Costa AFB, Machado MAG (2008) A new chart based on sample variances for monitoring the covariance matrix of multivariate processes. Int J Adv Manuf Tech. doi:10.1007/s00170-008-1502-9

  21. Chang SI, Zhang K (2007) Statistical Process Control for Variance Shift Detections of Multivariate Autocorrelated Processes. Qual Technol Quant Manag 4:413–435

    MathSciNet  Google Scholar 

  22. Golnabi S, Houshmand AA (1999) Multivariate Shewhart X-bar Chart. Internet Statistics, 4,—A web based journal: http://interstat.stat.vt.edu/interstat/index/Sep99.html

  23. Montgomery DC (2005) Introduction to statistical quality control, 5th edn. Wiley, New York, NY

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

    S. T. A. Niaki

  2. Department of Statistics and Operations Research, RMIT University, Melbourne, Australia

    M. Abdollahian

  3. Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran

    S. Z. Hosseinifard

  4. Department of Industrial Engineering, Buali Sina University, Hamedan, Iran

    B. Abbasi

Authors
  1. B. Abbasi
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  2. S. T. A. Niaki
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  3. M. Abdollahian
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  4. S. Z. Hosseinifard
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Correspondence to B. Abbasi.

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Abbasi, B., Niaki, S.T.A., Abdollahian, M. et al. A transformation-based multivariate chart to monitor process dispersion. Int J Adv Manuf Technol 44, 748–756 (2009). https://doi.org/10.1007/s00170-008-1882-x

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  • DOI: https://doi.org/10.1007/s00170-008-1882-x

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