Abstract
When an out-of-control condition is detected by a control chart, a search begins to identify and eliminate the source(s) of the signal. Identification of the time when a process first changed is an important step in root cause analysis which helps a process engineer to eliminate the source(s) of assignable cause effectively. The time when a change takes place in the process is referred to as the change point. In multivariate environment, since there is more than one variable involved, then root cause analysis is relatively harder compared to the case of univariate because it is not clear exactly which variable has contributed to the out-of-control condition and in what direction its mean has shifted. Hence, a procedure that identifies the change point, performs diagnostic analysis, and specifies the direction of the shift in the mean of the contributing variable(s) all simultaneously could help to conduct root cause analysis effectively. Although different multivariate methods exist in the literature that allow to either estimate change point in the process mean vector or identify the contributing variables leading to the out-of-control condition, but in this research, an integrated supervised learning solution is proposed, which helps to (1) detect of an out-of-control condition, (2) identify the change point leading to shift in the mean vector, (3) specify the variable(s) contributing to the out-of-condition, and (4) identify the direction of the shift in the mean of each contributing variable simultaneously. A real case study is used to evaluate and compare the performance of the proposed integrated approach to existing methods in the literature.
Similar content being viewed by others
References
Pignatielo JR, Samuel TR (1988) Identifying the time of a step change with XBar control charts. J Qual Eng 10(3):521–527
Perry MB, Pignatielo JJ (2006) Estimation of the change point of a normal process mean with a linear trend disturbance. QTQM 3(3):101–115
Noorossana R, Shademan A (2009) Estimating the change point of a normal process mean with a monotonic change. Qual Reliab Eng Int 25(1):79–90
Sullivan JH, Woodall WH (2000) Change-point detection of mean vector or covariance matrix shifts using multivariate individual observation. IIE Trans 32(6):537–549
Nedumaran G, Pignatiello JJ, Calvin JA (2000) Identifying the time of a step-change with χ2 control charts. Qual Eng 13(2):153–159
Li F, Runger GC, Tun E (2006) Supervised learning for change-point detection. Int J Prod Res 44(14):2853–2868
Hotelling H (1947) Multivariate quality control illustrated by the air testing of sample bombsights. In: Eisenhart C, Hastay MW, Wallis WA (eds) Techniques of statistical analysis. McGraw-Hill, New York
Crosier RB (1988) Multivariate generalization of cumulative sum quality control schemes. Technometrics 30(3):291–302
Pignatiello JJ, Runger GC (1990) Comparison of multivariate CUSUM charts. J Qual Technol 22(2):173–186
Lowry CA, Woodall WH, Champ CW, Rigdon SE (1992) A multivariate exponentially weighted moving average control chart. Technometrics 34(1):46–53
Runger GC, Testik MC (2004) Multivariate extensions to cumulative sum control charts. Qual Reliab Int 20(6):587–606
Srivastava MS, Worsley KJ (1986) Likelihood ratio tests for a change in the multivariate normal mean. J Am Stat Assoc 81(393):199–204
Chua MK, Montgomery DC (1992) Investigation and characterization of a control scheme for multivariate quality control. Qual Reliab Eng Int 8(1):37–44
Wade MR, Woodall WH (1993) A review and analysis of cause-selecting control charts. J Qual Technol 25(3):161–170
Hawkins DM (1993) Regression adjustment for variables in multivariate quality control. J Qual Technol 25(3):170–182
Hayter AJ, Tsui KL (1994) Identification and quantification in multivariate quality control problems. J Qual Technol 26(3):197–208
Mason RL, Tracy ND, Young JC (1995) Decomposition of T 2 for multivariate control chart interpretation. J Qual Technol 27(2):99–108
Kourti T, MacGregor JF (1996) Multivariate SPC methods for process and product monitoring. J Qual Technol 28(4):409–428
Mason RL, Tracy ND, Young JC (1997) A practical approach for interpreting multivariate T 2 control chart signals. J Qual Technol 29(4):396–406
Nottingham QJ, Cook DF, Zobel CW (2001) Visualization of multivariate data with radial plots using SAS. Comput Ind Eng 41(1):17–35
Maravelakis PE, Bersimis S, Panaretos J, Psarakis S (2002) On identifying the out of control variable in a multivariate control chart. Commun Stat- Theory Methods 31(12):2391–2408
Niaki STA, Abbasi B (2005) Fault diagnosis in multivariate control charts using artificial neural network. Qual Reliab Eng Int 21(8):825–840
Bersimis S, Psarakis S, Panaretos J (2007) Multivariate statistical process control chart: an overview. Qual Reliab Eng Int 23(5):517–543
Hwang HB, Hubele NF (1993) Back-propagation pattern recognizers for \( \overline X \) control charts: methodology and performance. Comput Ind Eng 24(2):219–235
Cheng C (1995) A multi-layer neural network model for detecting changes in the process mean. Comput Ind Eng 28(1):51–61
Chang SI, Aw CA (1996) A neural fuzzy control chart for detecting and classifying process mean shifts. Int J Prod Res 34(8):2265–2278
Cheng CS (1997) A neural network approach for the analysis of control chart patterns. Int J Prod Res 35(3):667–697
Guh RS, Tannock TD (1997) A neural network approach to characterize pattern parameters in process control charts. J Intell Manuf 10(5):449–462
Noorossana R, Farrokhi M, Saghaei A (2003) Using neural networks to detect and classify out-of-control signals in autocorrelated processes. Qual Reliab Eng Int 19(6):493–504
Zorriassatine F, Tannockb JDT, O’Brienb C (2003) Using novelty detection to identify abnormalities caused by mean shifts in bivariate processes. Comput Ind Eng 44(3):385–408
Hwarng HB (2004) Detecting process mean shift in the presence of autocorrelation: a neural network based monitoring scheme. Int J Prod Res 42(3):573–595
Guh RS (2007) On-line identification and quantification of mean shifts in bivariate processes using a neural network-based approach. Qual Reliab Eng Int 23(3):367–385
Hwarng HB (2008) Toward identifying the source of mean shifts in multivariate SPC: a neural network approach. Int J Prod Res 46(20):5531–5559
Atashgar K, Noorossana R (2011) An integrating approach to root-cause analysis of a bivariate mean vector with a linear trend disturbance. Int J Adv Manuf Technol 52(1):407–420
Zorriassatine F, Tannock JDT (1998) A review of neural networks for statistical process control. J Intell Manuf 9(3):209–224
Hwarng HB (2005) Simultaneous identification of mean shift and correlation change in AR(1) processes. Int J Prod Res 43(9):1761–1783
Guo Y, Dooley KJ (1992) Identification of change structure in statistical process control. Int J Prod Res 30(7):1655–1669
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Noorossana, R., Atashgar, K. & Saghaei, A. An integrated supervised learning solution for monitoring process mean vector. Int J Adv Manuf Technol 56, 755–765 (2011). https://doi.org/10.1007/s00170-011-3188-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-011-3188-7