Self-starting single control charts for multivariate processes: a comparison of methods

Dogu, Eralp; Kim, Min Jung

doi:10.1590/0103-6513.20190136

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Sumário

Research Article • Prod. 30 • 2020 • https://doi.org/10.1590/0103-6513.20190136 copy

Self-starting single control charts for multivariate processes: a comparison of methods

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Paper aims

Based on challenges faced in real SPC application, this paper considers implementation and performance of self-starting methodology in multivariate process monitoring.

Originality

Traditional omnibus charts depend on in-control process parameters while parameters are generally known. However, in real settings, this information may not exist. This paper proposes and compares novel methods to overcome this difficulty.

Research method

This paper introduces, evaluates the performance and implements multivariate self-starting charts (SSMEC, SSMELR, and SSMME) for multivariate process monitoring.

Main findings

Proposed SSMME chart is the best choice in real application because it proves better performance in response to various simulation scenarios and gives diagnostic tools for further analysis.

Implications for theory and practice

The main contributions are the comparison of different self-starting approaches and introducing a novel multivariate self-starting chart that are suitable in real process monitoring and illustrate the benefit of the selected SPC chart with hypertension monitoring.

Keywords
Multivariate quality control; Self-starting method; Single control chart; Hypertension monitoring

Case	Mean vector		Covariance matrix
Case	$Δ_{1}$	$Δ_{2}$	$δ_{1}$	$δ_{2}$
0 (no shift)	0.0	0.0	1.0	1.0
3	0.5	0.0	1.0	1.5
6	1.0	1.0	1.5	1.5
8	2.0	1.0	2.0	1.0

Chart	Base sample size ( $τ$ )	Case	$ρ$ =0.5		$ρ$ =0.25		$ρ$ =0.75
Chart	Base sample size ( $τ$ )	Case	ARL	SDRL	ARL	SDRL	ARL	SDRL
SSMEC	50	3	88.25	233.58	118.17	256.68	40.62	121.34
		6	8.00	14.03	9.34	9.46	11.89	18.66
		8	4.12	2.89	4.47	2.90	4.08	2.88
	100	3	33.26	77.83	42.14	114.26	16.29	30.68
		6	8.20	6.37	7.12	5.23	7.89	5.77
		8	4.14	2.78	4.01	2.51	3.61	2.42
	200	3	19.86	17.89	23.30	22.26	13.00	9.71
		6	7.16	5.12	6.73	4.47	7.89	5.77
		8	3.85	2.42	3.69	2.42	3.43	2.26
	1000	3	16.37	12.36	19.27	14.44	11.54	7.74
		6	6.51	3.93	6.33	4.24	7.23	4.63
		8	3.71	2.42	3.78	2.36	3.35	2.20
SSMELR	50	3	114.69	279.57	137.06	284.51	42.80	134.89
		6	13.87	26.48	13.08	38.75	21.96	94.86
		8	5.91	3.89	5.71	3.24	5.23	2.93
	100	3	114.69	279.57	49.92	131.49	16.39	13.83
		6	13.87	26.48	9.05	5.83	10.44	8.13
		8	5.91	3.89	5.25	2.76	4.76	2.50
	200	3	37.26	84.70	49.92	131.49	14.36	9.37
		6	9.96	6.89	8.20	4.96	9.16	5.76
		8	5.28	2.83	4.89	2.39	4.62	2.32
	1000	3	18.39	13.27	20.15	14.35	12.77	7.44
		6	8.26	4.93	7.58	4.12	8.89	4.96
		8	4.79	2.30	4.91	2.44	4.51	2.29
SSMME	50	3	91.99	217.02	115.98	259.87	61.28	192.30
		6	9.99	11.86	8.83	8.73	10.20	9.61
		8	5.55	3.48	5.40	3.26	5.15	3.29
	100	3	30.97	78.95	40.36	87.37	20.00	63.68
		6	8.00	5.24	7.78	5.08	8.63	5.85
		8	4.79	2.76	4.60	2.59	4.58	2.70
	200	3	21.15	21.63	22.54	21.70	14.67	11.27
		6	7.74	4.68	6.73	3.81	8.03	5.04
		8	4.65	2.60	4.56	2.53	4.35	2.49
	1000	3	16.81	11.94	18.78	15.49	12.25	8.27
		6	7.16	4.08	6.62	3.77	7.62	4.20
		8	4.46	2.36	4.30	2.22	4.05	2.40

	SBP		DBP		Correlation
	mean	variance	mean	variance	Correlation
Pre-treatment period	135.76	9.86	92.32	5.90	0.27
Post-treatment period	119.35	29.06	80.85	12.74	0.16

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[1] * eralp.dogu@mu.edu.tr