Abstract
Identifying the change point or the starting time of a disturbance in a process can play an essential role in root cause analysis. Although, in univariate environment, change point identification by itself could be a significant step in process improvement but in multivariate environment without conducting diagnostic analysis which leads to the identification of the variable(s) responsible for the change in the process, one cannot effectively perform root cause analysis. In this paper, a supervised learning approach based on artificial neural networks is proposed which helps to identify the change point in a bivariate environment when the process mean vector is allowed to shift linearly and simultaneously a diagnostic analysis is conducted to identify the variable(s) responsible for the change in the process mean vector. To the best of our knowledge, this is the first time that this problem is addressed in the literature of change point estimation. The performance of the proposed model is investigated through several numerical examples. Results indicate that the proposed model provides practitioners with a very accurate estimate of the change point in the process mean vector and simultaneously helps to identify the variable(s) responsible with the out-of-control condition.
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References
Samuel TR, JR PJJ, Calvin JA (1998) Identifying the time of a step change with XBar control charts. J Qual Eng 10(3):521–527
Pignatiello JJ Jr, Samuel TR (2001) Identifying the time of a step change in the process fraction nonconforming. Qual Eng 13(3):375–385
JR PJJ, Samuel TR (2001) Estimation of the change point of a normal process mean in SPC applications. J Qual Technol 33(1):82–95
Hawkins DM, Qiu P (2003) The changepoint model for statistical process control. J Qual Technol 35(4):355–366
Perry MB, JR PJJ (2006) Estimation of the change point of a normal process mean with a linear trend disturbance. Quality Technology and Quantitative Management 3(3):325–334
Perry MB, JR PJJ, Simpson JR (2007) Estimation of the change point of the process fraction nonconforming with a monotonic change disturbance in SPC. Qual Reliab Eng Int 23(3):327–339
Gazanfari M, Alaeddini A, Niaki STA, Aryanezhad MB (2008) A clustering approach to identify the time of a step change in Shewhart control charts. Qual Reliab Eng Int 24(7):765–778
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
Noorossana R, Saghaei A, Paynabar K, Abdi S (2009) Identifying the period of a step change in high-yield processes. Qual Reliab Eng Int. doi:10.1002/qre.1007
Nedumaran G, JR PJJ, Calvin JA (2000) Identifying the time of a step-change with χ 2 control charts. Qual Eng 13(2):153–159
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. Communications in Statistics. 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
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
Bersimis S, Psarakis S, Panaretos J (2007) Multivariate statistical process control chart: an overview. Qual Reliab Eng Int 23(5):517–543
Guh RS, Shiue YR (2008) An effective application of decision tree learning for on-line detection of mean shifts in multivariate control charts. Comp Indust Eng 55(2):475–493
Ken N (1992) A comparison of control charts from the viewpoint of change-point estimation. Qual Reliab Eng Int 8(6):537–541
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
Li F, Runger GC, Tun E (2006) Supervised learning for change-point detection. Int J Prod Res 44(14):2853–2868
Hawkins DM, Zamba KD (2006) A multivariate change point model for statistical process control. Technometrics 48(4):539–549
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
Hwarng HB (2005) Simultaneous identification of mean shift and correlation change in AR(1) processes. Int J Prod Res 43(9):1761–1783
Zorriassatine F, Tannock JDT (1998) A review of neural networks for statistical process control. J Intell Manuf 9(3):209–224
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Atashgar, K., Noorossana, R. An integrating approach to root cause analysis of a bivariate mean vector with a linear trend disturbance. Int J Adv Manuf Technol 52, 407–420 (2011). https://doi.org/10.1007/s00170-010-2728-x
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DOI: https://doi.org/10.1007/s00170-010-2728-x