Mathematical Problems in Engineering

Research Article

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

Table 3

The ARL₁ profile of the one-sided EDC and EDCC charts when δ ∈[0.25, 5] with ARL₀ = 300.


		DC	DCC	λ = 0.05						λ = 0.25						λ = 0.50						OC
				EDC	EDCC	ρ = 0.50		ρ = 0.75		EDC	EDCC	ρ = 0.50		ρ = 0.75		EDC	EDCC	ρ = 0.50		ρ = 0.75
				EDC	EDCC	AIB-EDC	AIB-EDCC	AIB-EDC	AIB-EDCC	EDC	EDCC	AIB-EDC	AIB-EDCC	AIB-EDC	AIB-EDCC	EDC	EDCC	AIB-EDC	AIB-EDCC	AIB-EDC	AIB-EDCC
[k₁ = 0.72, k₂ = 1.91]

δ	h₁	3.0085	2.9037	13.801	13.870	13.801	13.870	13.801	13.870	8.680	8.675	8.680	8.675	8.680	8.675	5.468	5.460	5.4680	5.460	5.468	5.460	k = δ/2
δ	h₂	1.1341	1.0946	5.2025	5.2285	5.2025	5.2285	5.2025	5.2285	3.272	3.2702	3.272	3.2702	3.272	3.2702	2.0612	2.0582	2.0612	2.0582	2.0612	2.0582	k = δ/2
0.25	ARL	91.59	88.98	45.50	45.58	31.81	38.97	28.96	29.08	53.58	53.55	44.59	44.43	30.77	30.64	63.77	63.31	52.58	52.58	35.22	35.26	52.31
	MRL	65.00	62.00	36.00	37.00	32.00	32.00	25.00	25.00	40.00	40.00	34.00	34.00	24.00	24.00	46.00	46.00	38.00	39.00	26.00	26.00	43
	SDRL	88.70	86.65	31.34	31.36	25.20	25.25	16.19	16.28	45.36	45.31	36.23	36.04	22.86	22.60	58.37	57.67	47.10	46.75	29.73	29.79	35.36
0.73	ARL	16.36	15.88	14.80	14.85	12.84	12.91	9.80	9.81	12.69	12.70	10.72	10.70	7.92	7.90	12.54	12.46	10.13	10.09	6.99	6.98	13.03
	MRL	12.00	12.00	14.00	14.00	12.00	12.00	10.00	10.00	11.00	11.00	10.00	10.00	8.00	7.00	10.00	10.00	9.00	9.00	6.00	6.00	11.00
	SDRL	13.39	13.15	5.59	5.60	4.57	4.60	3.27	3.28	6.25	6.33	4.77	4.75	2.94	2.93	7.91	7.81	5.79	5.80	3.28	3.27	7.66
1.20	ARL	6.44	6.26	8.95	8.97	7.66	7.69	5.67	5.68	7.23	7.23	6.18	6.19	4.60	4.60	6.28	6.28	5.27	5.26	3.85	3.84	6.21
	MRL	5.00	5.00	9.00	9.00	7.00	7.00	5.00	5.00	7.00	7.00	6.00	6.00	4.00	4.00	6.00	6.00	5.00	5.00	4.00	4.00	5.00
	SDRL	4.02	3.97	2.94	2.95	2.45	2.46	1.63	1.64	2.58	2.58	2.10	2.12	1.48	1.48	2.78	2.77	2.12	2.12	1.38	1.38	3.41
1.68	ARL	3.73	3.64	6.18	6.19	5.27	5.28	3.96	3.98	5.01	5.01	4.26	4.26	3.13	3.14	4.21	4.20	3.57	3.56	2.59	2.58	3.68
	MRL	3.00	3.00	6.00	6.00	5.00	5.00	4.00	4.00	5.00	5.00	4.00	4.00	3.00	3.00	4.00	4.00	4.00	3.00	2.00	2.00	3.00
	SDRL	1.91	1.89	1.84	1.85	1.47	1.47	0.96	0.96	1.64	1.64	1.35	1.36	0.91	0.91	1.54	1.54	1.27	1.26	0.90	0.90	1.94
2.15	ARL	2.60	2.54	4.71	4.73	4.06	4.07	3.09	3.10	3.78	3.79	3.22	3.22	2.41	2.41	3.16	3.15	2.66	2.66	1.93	1.93	2.51
	MRL	2.00	2.00	5.00	5.00	4.00	4.00	3.00	3.00	4.00	4.00	3.00	3.00	2.00	2.00	3.00	3.00	3.00	3.00	2.00	2.00	2.00
	SDRL	1.21	1.19	1.24	1.25	0.99	0.99	0.68	0.68	1.17	1.17	0.94	0.94	0.63	0.63	1.11	1.11	0.93	0.93	0.65	0.65	1.30
2.63	ARL	1.98	1.93	3.82	3.83	3.31	3.32	2.53	2.53	3.02	3.01	2.58	2.59	1.99	1.99	2.49	2.48	2.09	2.09	1.52	1.52	1.88
	MRL	2.00	2.00	4.00	4.00	3.00	3.00	2.00	3.00	3.00	3.00	3.00	3.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	2.00
	SDRL	0.89	0.87	0.91	0.91	0.74	0.75	0.56	0.56	0.86	0.86	0.69	0.69	0.47	0.47	0.86	0.86	0.71	0.71	0.54	0.54	0.93
3.10	ARL	1.58	1.56	3.24	3.25	2.80	2.82	2.16	2.17	2.53	2.53	2.19	2.19	1.70	1.70	2.04	2.04	1.72	1.72	1.24	1.24	1.46
	MRL	1.00	1.00	3.00	3.00	3.00	3.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	1.00
	SDRL	0.68	0.66	0.72	0.72	0.61	0.62	0.39	0.39	0.67	0.67	0.54	0.54	0.48	0.48	0.69	0.69	0.59	0.59	0.43	0.43	0.67
3.58	ARL	1.32	1.30	2.81	2.82	2.43	2.43	1.98	1.99	2.19	2.19	1.92	1.92	1.41	1.41	1.72	1.72	1.45	1.44	1.08	1.07	1.22
	MRL	1.00	1.00	3.00	3.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	2.00	2.00	1.00	1.00	1.00	1.00	1.00
	SDRL	0.51	0.50	0.62	0.62	0.53	0.53	0.27	0.26	0.54	0.54	0.46	0.46	0.49	0.49	0.59	0.59	0.52	0.52	0.26	0.26	0.47
4.05	ARL	1.16	1.15	2.48	2.48	2.16	2.17	1.84	1.85	1.96	1.96	1.71	1.70	1.17	1.17	1.48	1.48	1.24	1.24	1.02	1.02	1.10
	MRL	1.00	1.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	SDRL	0.38	0.37	0.54	0.54	0.39	0.40	0.37	0.37	0.46	0.47	0.48	0.49	0.38	0.38	0.53	0.53	0.43	0.43	0.12	0.12	0.31
4.53	ARL	1.07	1.06	2.22	2.23	2.02	2.02	1.60	1.61	1.76	1.76	1.48	1.48	1.05	1.05	1.29	1.29	1.10	1.11	1.00	1.00	1.04
	MRL	1.00	1.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	SDRL	0.26	0.25	0.43	0.44	0.27	0.27	0.49	0.49	0.47	0.47	0.50	0.50	0.21	0.21	0.46	0.46	0.31	0.31	0.05	0.04	0.19
5.00	ARL	1.03	1.02	2.07	2.07	1.92	1.92	1.33	1.34	1.58	1.58	1.28	1.27	1.01	1.01	1.15	1.15	1.04	1.04	1.00	1.00	1.01
	MRL	1.00	1.00	2.00	2.00	2.00	2.00	1.00	1.00	2.00	2.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	SDRL	0.16	0.15	0.31	0.31	0.30	0.30	0.47	0.47	0.50	0.50	0.45	0.45	0.09	0.09	0.36	0.36	0.19	0.19	0.01	0.01	0.11
EQL		14.44	14.20	26.76	26.82	23.58	23.67	18.23	18.32	21.20	21.20	18.02	17.99	13.35	13.36	16.78	16.78	14.28	14.29	11.47	11.46	13.49
IRARL		1.13	1.11	1.82	1.82	1.58	1.59	1.23	1.23	1.47	1.47	1.26	1.25	0.93	0.93	1.22	1.22	1.03	1.03	0.79	0.79	1.00