Multi Task Scheme to Monitor Multivariate Environments Using Artificial Neural Network

Authors: K. Atashgar

Abstract:

When an assignable cause(s) manifests itself to a multivariate process and the process shifts to an out-of-control condition, a root-cause analysis should be initiated by quality engineers to identify and eliminate the assignable cause(s) affected the process. A root-cause analysis in a multivariate process is more complex compared to a univariate process. In the case of a process involved several correlated variables an effective root-cause analysis can be only experienced when it is possible to identify the required knowledge including the out-of-control condition, the change point, and the variable(s) responsible to the out-of-control condition, all simultaneously. Although literature addresses different schemes to monitor multivariate processes, one can find few scientific reports focused on all the required knowledge. To the best of the author’s knowledge this is the first time that a multi task model based on artificial neural network (ANN) is reported to monitor all the required knowledge at the same time for a multivariate process with more than two correlated quality characteristics. The performance of the proposed scheme is evaluated numerically when different step shifts affect the mean vector. Average run length is used to investigate the performance of the proposed multi task model. The simulated results indicate the multi task scheme performs all the required knowledge effectively.

Keywords: Artificial neural network, Multivariate process, Statistical process control, Change point.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077980

References:

[1] Montgomery D.C. (2005) Introduction to statistical quality control. Hoboken, N.J. John Weily & Sons, Inc..
[2] Shewhart, W.A. (1931) Economic Control of Quality of Manufactured Product. Milwaukee, WI: ASQ Quality Press. 1980.
[3] Hotelling H. (1947) Multivariate quality control-Illustrated by the air testing of sample bombsights. Techniques of Statistical Analysis, Eisenhart, C., Hastay, M.W., Wallis, W.A. (Eds). McGraw-Hill: New York.
[4] Woodall WH., Ncube MM. (1985) Multivariate CUSUM qualitycontrol procedures. Technometrics. 27(3): 285-292.
[5] Healy JD. (1987) A note on multivariate CUSUM procedures. Technometrics. 29(4): 409-412.
[6] Crosier R.B. (1988) Multivariate Generalization of Cumulative Sum Quality Control Schemes. Technometrics. 30(3): 291-302.
[7] Pignatiello JJ., Runger GC. (1990) Comparisons of multivariate CUSUM charts. Journal of Quality Technology. 22(3): 173-186.
[8] Ngai HM., Zhang J. (2001) Multivariate cumulative sum control charts based on projection pursuit. Statistica Sinica. 11(3): 747-766.
[9] Chan LK., Zhang J. (2001) Cumulative sum control charts for the covariance matrix. Statistica Sinica. 11(3): 767-790.
[10] Qiu PH., Hawkins DM. (2001) A rank-based multivariate CUSUM procedure. Technometrics. 43(2): 120-132
[11] Qiu, PH., Hawkins, DM. (2003) A nonparametric multivariate cumulative sum procedure for detecting shifts in all directions. Journal of the Royal Statistical Society Series D-The Statistician. 52(2): 151- 164.
[12] Runger GC., Testik MC. (2004) Multivariate extensions to cumulative sum control charts. Quality and Reliability Engineering International. 20(6): 587-606.
[13] Lowry CA., Woodall WH., Champ CW., Rigdon SE. (1992) A multivariate Exponential Weighted Moving Average control chart. Technometrics. 34(1): 46-53.
[14] Rigdon SE. (1995) An integral equation for the in-control average run length of a multivariate exponentially weighted moving average control chart. Journal of Statistical Computations and Simulation. 52(4): 351- 365.
[15] Yumin, L. (1996) An improvement for MEWMA in multivariate process control Computers and Industrial Engineering. 31(3-4): 779-781.
[16] Runger GC., Prabhu SS. (1996) A markov chain model for the multivariate exponentially weighted moving average control chart. Journal of the American Statistical Association. 91(436): 1701-1706.
[17] Kramer HG., Schmid W. (1997) EWMA charts for multivariate time series. Sequential Analysis. 16(2): 131-154.
[18] Prabhu SS., Runger GC. (1997)Designing a multivariate EWMA control chart. Journal of Quality Technology. 29(1): 8-15.
[19] Fasso A. (1999) One-sided MEWMA control charts. Communications in Statistics -Theory and Methods. 28(2): 381-401
[20] Borror CM., Montgomery DC., Runger GC. (1990) Robustness of the EWMA control chart to non-normality. Journal of Quality Technology. 31(3): 309-316.
[21] Runger GC., Keats JB., Montgomery DC., Scranton RD., (1999) Improving the performance of a multivariate exponentially weighted moving average control chart. Quality and Reliability Engineering International. 15(3): 161-166.
[22] Tseng S., Chou R., Lee S. (2002) A study on a multivariate EWMA controller. IIE Transactions. 34(6): 541-549.
[23] Yeh AB., Lin DKJ., Zhou H., Venkataramani C. (2003) A multivariate exponentially weighted moving average control chart for monitoring process variability. Journal of Applied Statistics. 30(5): 507-536.
[24] Testik MC., Runger GC., Borror CM. (2003) Robustness properties of multivariate EWMA control charts. Quality and Reliability Engineering International. 19(1): 31-38.
[25] Testik MC., Borror CM. (2004) Design strategies for the multivariate exponentially weighted moving average control chart. Quality and Reliability Engineering International. 20(6): 571- 577.
[26] Chen GM., Cheng SW., Xie HS. (2005) A new multivariate control chart for monitoring both location and dispersion. Communications in Statistics - Simulation and Computation. 34(1): 203-217.
[27] Atashgar, K. (2012). Identification of the change point: An overview. International Journal of Advanced Manufacturing Technology, DOI: 10.1007/s00170-012-4131-2.
[28] Mason Robert L., Tracy Nola D., Young John C. (1997) A Practical Approach for Interpreting Multivariate T2 control Chart Signals. Journal of Quality Technology. 29(4): 396:406.
[29] Aparisi F., Avendano G., Sanz J. (2006) Techniques to interpret T2 control chart signals. IIE Transaction. 38(8): 647-657.
[30] Niaki STA., Abbasi B. (2005) Fault diagnosis in multivariate control charts using artificial neural network. Quality and reliability Engineering International. 21(8): 825-840.
[31] Nedumaran G., Pignatiello JJ.Jr., Calvin J.A. (1998) Estimation of the time of a step-change with χ 2 control chart. Quality Engineering. 13(2):765-778.
[32] Noorossana R., Arbabzadeh N., Saghaei A., (2008) Painabar K. Development of procedure of detection change point in multi environment. 6th International Conference on Industrial Engineering, Iran-Tehran. (Written in Persian language)
[33] Noorossana R., Atashgar K., Saghaee, A. (2011) An integrated solution for monitoring process mean vector. International Journal of Advanced Manufacturing Technology. 56(5): 755-765.
[34] Atashgar K. and Noorossana R. (2010) An integrating approach to rootcause analysis of a bivariate mean vector with a linear trend disturbance. International Journal of Advance Manufacturing Technology. 52(1): 407-420.
[35] Guh, RS. (2007). On-line Identification and Quantification of Mean Shifts in Bivariate Processes using a Neural Network-based Approach. Quality and Reliability Engineering International, 23(3), 367-385
[36] Hwarng, HB. (2008). Toward identifying the source of mean shifts in multivariate SPC: a neural network approach. International Journal of Production Research, 46(20),5531–5559.