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

doi:10.21629/JSEE.2019.01.14

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

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

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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