Interpreting the Out-of-Control Signals of Multivariate Control Charts Employing Neural Networks
Multivariate quality control charts show some advantages to monitor several variables in comparison with the simultaneous use of univariate charts, nevertheless, there are some disadvantages. The main problem is how to interpret the out-ofcontrol signal of a multivariate chart. For example, in the case of control charts designed to monitor the mean vector, the chart signals showing that it must be accepted that there is a shift in the vector, but no indication is given about the variables that have produced this shift. The MEWMA quality control chart is a very powerful scheme to detect small shifts in the mean vector. There are no previous specific works about the interpretation of the out-of-control signal of this chart. In this paper neural networks are designed to interpret the out-of-control signal of the MEWMA chart, and the percentage of correct classifications is studied for different cases.
[1] Lowry, C.A., Woodall, W.H., Champ, C.W., and Rigdon, S.E. A
multivariate exponentially weighted moving average control chart.
Technometrics, 1992, 34 (1), 46-53.
[2] Prabhu, SS. And Runger, GC. Designing a multivariate EWMA control
chart. Journal of Quality Technology, 1997, 29:8-15.
[3] Roberts, S. W. (1959). Control Chart Test Based on Geometrics Moving
Averages. Technometrics, 1959, 1, pp. 239-250.
[4] Montgomery, D.C. Introduction to Statistical Quality Control .4rd. John
Wiley. New York. 2001
[5] Lowry CA. and, Montgomery, DC. A review of multivariate control
charts. IIE Transactions, 1995; 27: 800-810.
[6] Blazek, L.W., Novic B .and Scott M.D. Displaying Multivariate Data
Using Polyplots. Journal of Quality Technology, 1987, 19(2), 69-74.
[7] Subramanyan, N. and Houshmand, A.A. Simultaneous representation of
multivariate and corresponding univariate charts using line graph.
Quality Engineering, 1995, 4, 681-682.
[8] Fuchs, C. and Benjamin, Y. Multivariate profile charts for statistical
process control. Technometrics, 1994, 36(2), 182-195.
[9] Iglewicz, B. and Hoaglin, D.C. Use of boxplots for process evaluation.
Journal of Quality Technology, 1987, 19(4), 180-190.
[10] Atienza, O.O., Ching L.T. and Wah, B.A. Simultaneous monitoring of
univariante and multivariate SPC information using boxplots.
International Journal of Quality Science, 1988, 3(2).
[11] Doganaksoy, N., Faltin, F.W. and Tucker, W.T. Identification of-out-of
control characteristics in a multivariate manufacturing environment.
Communications in Statistics Theory and Methods, 1991, 20, 2775-
2790.
[12] Runger, G.C., Alt, F.B., and Montgomery, D.C. Contributors to a
multivariate statistical process control chart signal. Communications in
Statistics. Theory Methods, 1996, 25, 2203-2213.
[13] Mason, R. L., Tracy, N.D. and Young, J.C. Decomposition of T2
multivariate control chart interpretation. Journal of Quality Technology,
1995, 27(2), 99-108.
[14] Mason, R.L., Tracy, N.D. and Young, J.C. A practical approach for
interpreting multivariate T2 control chart signals. Journal of Quality
Technology, 1997, 29(4), 396-406.
[15] Aparisi, F., Avenda├▒o, G. and Sanz, J. Interpreting T2 Control Chart
Signals: Effectiveness of MTY decomposition vs. a Neural Network, IIE
Transactions, 2006, 38(8), 647-657.
[1] Lowry, C.A., Woodall, W.H., Champ, C.W., and Rigdon, S.E. A
multivariate exponentially weighted moving average control chart.
Technometrics, 1992, 34 (1), 46-53.
[2] Prabhu, SS. And Runger, GC. Designing a multivariate EWMA control
chart. Journal of Quality Technology, 1997, 29:8-15.
[3] Roberts, S. W. (1959). Control Chart Test Based on Geometrics Moving
Averages. Technometrics, 1959, 1, pp. 239-250.
[4] Montgomery, D.C. Introduction to Statistical Quality Control .4rd. John
Wiley. New York. 2001
[5] Lowry CA. and, Montgomery, DC. A review of multivariate control
charts. IIE Transactions, 1995; 27: 800-810.
[6] Blazek, L.W., Novic B .and Scott M.D. Displaying Multivariate Data
Using Polyplots. Journal of Quality Technology, 1987, 19(2), 69-74.
[7] Subramanyan, N. and Houshmand, A.A. Simultaneous representation of
multivariate and corresponding univariate charts using line graph.
Quality Engineering, 1995, 4, 681-682.
[8] Fuchs, C. and Benjamin, Y. Multivariate profile charts for statistical
process control. Technometrics, 1994, 36(2), 182-195.
[9] Iglewicz, B. and Hoaglin, D.C. Use of boxplots for process evaluation.
Journal of Quality Technology, 1987, 19(4), 180-190.
[10] Atienza, O.O., Ching L.T. and Wah, B.A. Simultaneous monitoring of
univariante and multivariate SPC information using boxplots.
International Journal of Quality Science, 1988, 3(2).
[11] Doganaksoy, N., Faltin, F.W. and Tucker, W.T. Identification of-out-of
control characteristics in a multivariate manufacturing environment.
Communications in Statistics Theory and Methods, 1991, 20, 2775-
2790.
[12] Runger, G.C., Alt, F.B., and Montgomery, D.C. Contributors to a
multivariate statistical process control chart signal. Communications in
Statistics. Theory Methods, 1996, 25, 2203-2213.
[13] Mason, R. L., Tracy, N.D. and Young, J.C. Decomposition of T2
multivariate control chart interpretation. Journal of Quality Technology,
1995, 27(2), 99-108.
[14] Mason, R.L., Tracy, N.D. and Young, J.C. A practical approach for
interpreting multivariate T2 control chart signals. Journal of Quality
Technology, 1997, 29(4), 396-406.
[15] Aparisi, F., Avenda├▒o, G. and Sanz, J. Interpreting T2 Control Chart
Signals: Effectiveness of MTY decomposition vs. a Neural Network, IIE
Transactions, 2006, 38(8), 647-657.
@article{"International Journal of Information, Control and Computer Sciences:57872", author = "Francisco Aparisi and José Sanz", title = "Interpreting the Out-of-Control Signals of Multivariate Control Charts Employing Neural Networks", abstract = "Multivariate quality control charts show some advantages to monitor several variables in comparison with the simultaneous use of univariate charts, nevertheless, there are some disadvantages. The main problem is how to interpret the out-ofcontrol signal of a multivariate chart. For example, in the case of control charts designed to monitor the mean vector, the chart signals showing that it must be accepted that there is a shift in the vector, but no indication is given about the variables that have produced this shift. The MEWMA quality control chart is a very powerful scheme to detect small shifts in the mean vector. There are no previous specific works about the interpretation of the out-of-control signal of this chart. In this paper neural networks are designed to interpret the out-of-control signal of the MEWMA chart, and the percentage of correct classifications is studied for different cases.
", keywords = "Multivariate quality control, Artificial Intelligence, Neural Networks, Computer Applications", volume = "4", number = "1", pages = "112-5", }
