Variable selection-based SPC procedures for high-dimensional multistage processes

doi:10.21629/JSEE.2019.01.14

Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (1): 144-153.doi: 10.21629/JSEE.2019.01.14

收稿日期:2017-05-26 出版日期:2019-02-27 发布日期:2019-02-27

Variable selection-based SPC procedures for high-dimensional multistage processes

Sangahn KIM*()

Department of Business Analytics and Acturial Science, Siena College, New York 12211, U.S.A

Received:2017-05-26 Online:2019-02-27 Published:2019-02-27
Contact: Sangahn KIM E-mail:skim@siena.edu
About author:KIM Sangahn received his Ph.D. degree in Department of Industrial and Systems Engineering, Rutgers University, New Jersey, USA. He is an assistant professor in Department of Business Analytics and Acturial Science, Siena College, New York, USA. He is a recipient of the Richard A. Freund International Scolarship by the American Society of Quality (ASQ) in 2016. He also won the Tayfur Altiok Memaorial Scholarship and the Best Ph.D. Student Award in 2017 by Rutgers University. His research interests include statistical process modeling and monitoring, data mining and stochastic process. E-mail:skim@siena.edu
Supported by:
the Qatar National Research Fund(NPRP 5-364-2-142);the Qatar National Research Fund(NPRP 7-1040-2-293);This work was supported by the Qatar National Research Fund (NPRP 5-364-2-142; NPRP 7-1040-2-293)

摘要/Abstract

Abstract:

Monitoring high-dimensional multistage processes becomes crucial to ensure the quality of the final product in modern industry environments. Few statistical process monitoring (SPC) approaches for monitoring and controlling quality in highdimensional multistage processes are studied. We propose a deviance residual-based multivariate exponentially weighted moving average (MEWMA) control chart with a variable selection procedure. We demonstrate that it outperforms the existing multivariate SPC charts in terms of out-of-control average run length (ARL) for the detection of process mean shift.

Key words: diagnosis procedure, deviance residual, fault identification, model-based control chart, multistage process monitoring, variable selection

. [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 144-153.

Sangahn KIM. Variable selection-based SPC procedures for high-dimensional multistage processes[J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 144-153.

图/表 11

参考文献 37

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Shift	Shewhart	Hotelling $T^2$	MEWMA	CVS-MEWMA
(0.2, 0.2)	189.68	171.07	84.48	73.04
(0.4, 0.4)	161.98	111.86	24.41	20.24
(0.6, 0.6)	121.98	63.34	11.14	9.38
(0.8, 0.8)	86.52	31.86	6.99	5.95
(1.0, 1.0)	57.48	16.61	5.11	4.34
(1.5, 1.5)	18.66	4.16	3.18	2.70
(2.0, 2.0)	7.03	1.70	2.37	2.03
(2.5, 2.5)	3.23	1.13	2.02	1.68
(3.0, 3.0)	1.82	1.02	1.88	1.43

Shift	Shewhart	Hotelling $T^2$	MEWMA	CVS-MEWMA
(0.1, 0.3)	184.92	164.23	71.06	61.25
(0.2, 0.6)	149.04	98.01	19.51	16.46
(0.4, 0.8)	111.70	55.77	10.17	8.58
(0.6, 1.0)	77.95	29.64	6.67	5.65
(0.8, 1.2)	51.66	15.70	4.99	4.22
(1.0, 2.0)	12.09	3.43	3.02	2.55
(1.5, 2.5)	5.23	1.57	2.31	1.98
(2.0, 3.0)	2.63	1.11	2.01	1.65
(2.5, 3.5)	1.69	1.01	1.86	1.42

Shift	Shewhart	Hotelling $T^2$	MEWMA	CVS-MEWMA
(0.4, 0.2)	176.83	136.72	39.77	32.64
(0.6, 0.4)	139.38	81.72	15.03	12.57
(0.8, 0.6)	102.45	43.73	8.45	7.14
(1.0, 0.8)	68.92	22.70	5.84	4.93
(1.5, 1.0)	28.27	7.32	3.79	3.22
(2.0, 1.5)	9.98	2.39	2.69	2.29
(2.5, 2.0)	4.32	1.30	2.13	1.82
(3.0, 2.5)	2.28	1.05	1.95	1.56
(3.0, 3.0)	1.82	1.01	1.88	1.44

Shift	VS-MSPC	VS-MEWMA	CVS-MEWMA
0.2	170.49	77.09	76.65
0.4	107.86	22.11	21.16
0.6	58.15	10.15	9.71
0.8	29.94	6.50	6.15
1.0	15.77	4.76	4.51
1.5	4.12	2.97	2.79
2.0	1.82	2.23	2.10
2.5	1.22	1.82	1.74
3.0	1.05	1.56	1.48

Shift	γ
Shift	0.01	0.1	0.2	0.3
0.2	84.36	80.14	76.20	73.04
0.4	23.05	22.32	20.89	20.24
0.6	10.36	10.11	9.71	9.38
0.8	6.44	6.32	6.08	5.95
1.0	4.66	4.57	4.45	4.34
1.5	2.86	2.81	2.74	2.70
2.0	2.15	2.10	2.06	2.03
2.5	1.75	1.73	1.71	1.68
3.0	1.52	1.49	1.46	1.43

Variable selection-based SPC procedures for high-dimensional multistage processes

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Shift	$\gamma $
Shift	0.01	0.10	0.20	0.30	$\gamma ^\ast $
0.2	0.958 1	0.629 9	0.349 7	0.164 6	0.036 5
0.4	0.975 0	0.777 8	0.565 1	0.359 8	0.086 7
0.6	0.981 2	0.830 6	0.661 4	0.482 7	0.128 3
0.8	0.984 3	0.857 2	0.707 2	0.544 4	0.154 1
1.0	0.987 4	0.873 5	0.739 0	0.594 9	0.180 7
1.5	0.990 4	0.913 2	0.813 9	0.694 4	0.228 4
2.0	0.994 9	0.949 9	0.879 6	0.779 8	0.277 7
2.5	0.997 3	0.976 7	0.932 2	0.868 0	0.335 5
3.0	0.999 3	0.990 1	0.973 2	0.930 5	0.388 1

Shift	$\gamma $
Shift	0.01	0.10	0.20	0.30	$\gamma ^\ast $
0.2	0.782 0	0.620 8	0.464 2	0.343 6	0.141 4
0.4	0.781 6	0.615 9	0.452 9	0.329 2	0.118 8
0.6	0.781 2	0.614 6	0.451 2	0.323 5	0.108 2
0.8	0.781 9	0.617 0	0.450 4	0.323 7	0.102 1
1.0	0.781 4	0.615 6	0.454 1	0.325 1	0.097 9
1.5	0.781 8	0.617 2	0.453 9	0.324 0	0.087 7
2.0	0.780 6	0.618 1	0.456 4	0.329 2	0.078 8
2.5	0.782 5	0.620 8	0.459 2	0.331 2	0.070 1
3.0	0.781 8	0.622 2	0.461 4	0.335 9	0.062 8

Shift	VS-MEWMA		CVS-MEWMA
Shift	CR	EER	CR	EER
0.2	0.019 8	0.152 5	0.036 5	0.141 4
0.4	0.041 4	0.140 8	0.086 7	0.118 8
0.6	0.006 2	0.133 4	0.128 3	0.108 2
0.8	0.075 7	0.129 0	0.154 1	0.102 1
1.0	0.092 8	0.123 6	0.180 7	0.097 9
1.5	0.126 9	0.114 9	0.228 4	0.087 7
2.0	0.162 9	0.106 2	0.277 7	0.078 8
2.5	0.208 5	0.097 0	0.335 5	0.070 1
3.0	0.241 8	0.089 6	0.388 1	0.062 8