Abstract
Most of industrial applications of statistical process control involve more than one quality characteristics to be monitored. These characteristics are usually correlated, causing challenges for the monitoring methods. These challenges are resolved using multivariate quality control charts that have been widely developed in recent years. Nonetheless, multivariate process monitoring methods encounter a problem when the quality characteristics are of the attribute type and follow nonnormal distributions such as multivariate binomial or multivariate Poisson. Since the data analysis in the latter case is not as easy as the normal case, more complexities are involved to monitor multiattribute processes. In this paper, a hybrid procedure is developed to monitor multiattribute correlated processes, in which number of defects in each characteristic is important. Two phases are proposed to design the monitoring scheme. In the first phase, the inherent skewness of multiattribute Poisson data is almost removed using a root transformation technique. In the second phase, a method based on the decision on belief concept is employed. The transformed data obtained from the first phase are implemented on the decision on belief (DOB) method. Finally, some simulation experiments are performed to compare the performances of the proposed methodology with the ones obtained using the Hotelling T 2 and the MEWMA charts in terms of in-control and out-of-control average run length criteria. The simulation results show that the proposed methodology outperforms the other two methods.
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References
Montgomery DC (2005) Introduction to statistical quality control, 5th edn. Wiley, New York, USA
Hotelling H (1947) Multivariate quality control. In: Eisenhart C, Hastay MW, Wallis WA (eds) Techniques of statistical analysis. Mac Graw-Hill, New York
Lowry CA, Montgomery DC (1995) A review of multivariate control charts. IIE Trans 27:800–810
Golnabi S, Houshmand AA (1999) Multivariate Shewhart X-bar charts. Inter Stat, No. 4
Woodall WH, Ncube MM (1985) Multivariate CUSUM quality control procedures. Technometrics 27:285–292
Healy JD (1987) A note on multivariate CUSUM procedures. Technometrics 29:409–412
Lucas JM, Crosier RB (1982) Fast initial response for CUSUM quality control schemes: give your CUSUM a head start. Technometrics 24:199–205
Pignatiello JJ, Runger GC (1990) Comparisons of multivariate CUSUM charts. J Qual Technol 22:173–186
Lucas JM, Saccucci MS (1990) Exponentially weighted moving average control schemes: properties and enhancements. Technometrics 32:1–10
Lowry CA, Woodall WH, Champ CW, Erigdon S (1992) A multivariate exponentially weighted moving average control chart. Technometrics 34:46–53
Niaki STA, Abbasi B (2005) Fault diagnosis in multivariate control charts using artificial neural networks. Qual Reliab Eng Int 21:825–840
Niaki STA, Falalh Nezhad MS (2009) Decision-making in detecting and diagnosing faults of multivariate statistical quality control systems. Int J Adv Manuf Technol 42:713–724
Eshragh A, Modarres M (2009) A New approach to distribution fitting: decision on beliefs. J Ind Syst Eng 3:56–71
Eshragh A (2003) The application of decision on beliefs in response surface methodology. Unpublished M.S. project, Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran
Fallah Nezhad MS, Niaki STA (2010) A new monitoring design for univariate statistical quality control charts. Inf Sci 180:1051–1059
Niaki STA, Nafar M (2008) An artificial neural network approach to monitor and diagnose multi-attribute quality control processes. J Ind Eng Int 4:10–24
Mukhopadhyay AR (2008) Multivariate attribute control chart using Mahalanobis D2 statistic. J Appl Stat 35:421–429
Yang SF, Yeh JT (2011) Using cause selecting control charts to monitor dependent process stages with attributes data. Expert Syst Appl 38:667–672
Li J, Tsung F, Zou C (2012) Directional control schemes for multivariate categorical processes. J Qual Technol 44:136–154
Chiu JE, Kuo TI (2010) Control charts for fraction nonconforming in a bivariate binomial process. J Appl Stat 37:1717–1728
Niaki STA, Abbasi B (2009) Monitoring multi-attribute processes based on NORTA inverse transformed vectors. Commun Stat Theory Methods 38:964–979
Niaki STA, Akbari-Nasaji S (2011) A hybrid method of artificial neural network and simulated annealing in monitoring auto-correlated multi-attribute processes. Int J Adv Manuf Technol 56:777–788
Niaki STA, Khedmati M (2012) Estimating the change point of the parameter vector of multivariate Poisson processes monitored by a multiattribute T2 control chart. Int J Adv Manuf Technol. doi:10.1007/s00170-012-4128-x
Patel HI (1973) Quality control methods for multivariate binomial in controlling high yield processes. Qual Reliab Eng Int 8:355–360
Lu XS, Xie M, Goh TN, Lai CD (1998) Control chart for multivariate attribute processes. Int J Prod Res 36:3477–3489
Larpkiattaworn S (2003) A neural network approach for multi-attributes processes control with comparison of two current techniques and guideline for practical use. University of Pittsburgh, USA, Dissertation
Niaki STA, Abbasi B (2007) On the monitoring of multi-attribute high-quality production processes. Metrika 66:373–388
Quesenberry CP (1995) Geometric Q-charts for high quality processes. J Qual Technol 27:304–315
Niaki STA, Abbasi B (2007) Bootstrap method approach in designing multi-attribute control charts. Int J Adv Manuf Technol 35:434–442
Niaki STA, Abbasi B (2008) A transformation technique in designing multi-attribute C control charts. Scientica Iran 15:125–130
Chiu JE, Kuo TI (2008) Attribute control chart for multivariate Poisson distribution. Commun Stat Theory Methods 37:146–158
Box G, Cox DR (1964) An analysis of transformation. J Roy Stat Soc 26:211–242
Niaki STA, Abbasi B (2011) A simple transformation method in skewness reduction. Int J Eng Trans A 24:169–175
Fallahnezhad MS (2012) A new EWMA monitoring design for multi-variate quality control problem. Int J Adv Manuf Technol 62(5):751–758
Niaki STA, Abbasi B (2008) Generating correlation matrices for normal random vectors in NORTA algorithm using artificial neural networks. J Uncertain Syst 2:192–201
Thisted RA (2000) Elements of statistical computing: numerical computation. Chapman & Hall/CRC, Boca Raton
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Niaki, S.T.A., Javadi, S. & Fallahnezhad, M.S. A hybrid root transformation and decision on belief approach to monitor multiattribute Poisson processes. Int J Adv Manuf Technol 75, 1651–1660 (2014). https://doi.org/10.1007/s00170-014-6263-z
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DOI: https://doi.org/10.1007/s00170-014-6263-z