Mathematical Problems in Engineering

Research Article

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

Table 7

The ARL₁ profile of the two-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	3.531	3.440	26.700	26.500	26.700	26.500	26.700	26.500	11.750	11.600	11.750	11.600	11.750	11.600	6.845	6.708	6.845	6.708	6.845	6.708	k = δ/2
δ	h₂	1.3311	1.2968	10.0649	9.9895	10.0649	9.9895	10.0649	9.9895	4.4293	4.3728	4.4293	4.3728	4.4293	4.3728	2.5803	2.5287	2.5803	2.5287	2.5803	2.5287
0.25	ARL	144.35	142.42	64.81	64.68	54.75	54.57	40.32	40.23	74.68	73.81	60.11	59.64	39.51	39.41	92.33	91.02	74.41	73.09	47.34	46.48	52.31
	MRL	101.00	100.00	54.00	53.00	46.00	46.00	36.00	36.00	56.00	55.00	46.00	45.00	31.00	31.00	66.00	65.00	54.00	53.00	35.00	35.00	43.00
	SDRL	140.50	139.40	40.63	40.93	31.46	31.46	19.35	19.39	62.85	62.58	48.56	48.06	28.55	28.70	85.14	84.34	66.71	66.04	40.20	39.45	35.36
0.73	ARL	20.76	20.28	20.50	20.42	17.68	17.62	13.18	13.16	15.41	15.26	12.88	12.74	9.43	9.36	15.03	14.74	11.96	11.85	8.15	8.04	13.03
	MRL	16.00	15.00	20.00	20.00	17.00	17.00	13.00	13.00	14.00	14.00	12.00	12.00	9.00	9.00	13.00	12.00	10.00	10.00	7.00	7.00	11.00
	SDRL	17.06	16.64	6.82	6.79	5.70	5.68	3.97	3.97	7.20	7.13	5.42	5.31	3.34	3.31	9.19	9.02	6.53	6.54	3.64	3.61	7.66
1.20	ARL	7.50	7.32	12.03	11.99	10.27	10.25	7.75	7.72	8.57	8.49	7.27	7.22	5.31	5.28	7.30	7.20	6.09	6.01	4.37	4.32	6.21
	MRL	6.00	6.00	12.00	11.00	10.00	10.00	8.00	8.00	8.00	8.00	7.00	7.00	5.00	5.00	7.00	7.00	6.00	6.00	4.00	4.00	5.00
	SDRL	4.50	4.47	3.50	3.51	2.77	2.77	1.76	1.77	2.93	2.91	2.40	2.38	1.64	1.62	3.07	3.04	2.35	2.32	1.53	1.52	3.41
1.68	ARL	4.27	4.19	8.38	8.34	7.24	7.21	5.57	5.55	5.81	5.78	4.91	4.88	3.62	3.61	4.80	4.75	4.04	3.98	2.89	2.87	3.68
	MRL	4.00	4.00	8.00	8.00	7.00	7.00	5.00	5.00	6.00	6.00	5.00	5.00	4.00	3.00	5.00	5.00	4.00	4.00	3.00	3.00	3.00
	SDRL	2.08	2.05	2.00	2.00	1.58	1.57	1.04	1.04	1.83	1.83	1.47	1.46	0.94	0.94	1.71	1.70	1.40	1.39	0.95	0.94	1.94
2.15	ARL	2.96	2.90	6.54	6.51	5.70	5.67	4.43	4.41	4.37	4.34	3.72	3.69	2.80	2.78	3.55	3.51	2.98	2.94	2.17	2.15	2.51
	MRL	3.00	3.00	6.00	6.00	6.00	6.00	4.00	4.00	4.00	4.00	4.00	4.00	3.00	3.00	3.00	3.00	3.00	3.00	2.00	2.00	2.00
	SDRL	1.33	1.31	1.34	1.34	1.08	1.07	0.73	0.73	1.24	1.24	0.98	0.98	0.67	0.66	1.22	1.20	0.98	0.97	0.64	0.64	1.30
2.63	ARL	2.21	2.16	5.39	5.36	4.72	4.70	3.70	3.68	3.49	3.47	3.00	2.98	2.29	2.28	2.78	2.74	2.34	2.32	1.74	1.72	1.88
	MRL	2.00	2.00	5.00	5.00	5.00	5.00	4.00	4.00	3.00	3.00	3.00	3.00	2.00	2.00	3.00	3.00	2.00	2.00	2.00	2.00	2.00
	SDRL	0.98	0.97	0.99	0.98	0.81	0.80	0.58	0.59	0.89	0.89	0.72	0.72	0.49	0.49	0.90	0.89	0.71	0.71	0.53	0.54	0.93
3.10	ARL	1.74	1.71	4.63	4.60	4.06	4.04	3.19	3.18	2.94	2.92	2.54	2.53	2.02	2.01	2.29	2.26	1.95	1.93	1.42	1.40	1.46
	MRL	2.00	2.00	5.00	5.00	4.00	4.00	3.00	3.00	3.00	3.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	1.00
	SDRL	0.77	0.76	0.78	0.78	0.65	0.65	0.44	0.44	0.71	0.71	0.59	0.59	0.34	0.34	0.69	0.69	0.57	0.57	0.50	0.50	0.67
3.58	ARL	1.42	1.40	4.06	4.05	3.56	3.55	2.89	2.88	2.54	2.52	2.21	2.20	1.83	1.81	1.95	1.93	1.67	1.65	1.18	1.17	1.22
	MRL	1.00	1.00	4.00	4.00	4.00	4.00	3.00	3.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	1.00
	SDRL	0.59	0.58	0.64	0.65	0.57	0.56	0.38	0.39	0.59	0.59	0.45	0.45	0.39	0.40	0.57	0.57	0.53	0.53	0.38	0.37	0.47
4.05	ARL	1.22	1.21	3.64	3.62	3.20	3.19	2.57	2.55	2.26	2.24	2.02	2.01	1.58	1.57	1.71	1.68	1.43	1.41	1.05	1.05	1.10
	MRL	1.00	1.00	4.00	4.00	3.00	3.00	3.00	3.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	2.00	1.00	1.00	1.00	1.00	1.00
	SDRL	0.44	0.43	0.58	0.58	0.45	0.44	0.50	0.50	0.47	0.47	0.34	0.34	0.49	0.50	0.53	0.53	0.50	0.50	0.22	0.21	0.31
4.53	ARL	1.10	1.09	3.28	3.27	2.96	2.95	2.21	2.20	2.06	2.05	1.88	1.87	1.31	1.29	1.49	1.47	1.23	1.21	1.01	1.01	1.04
	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	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	SDRL	0.30	0.29	0.48	0.48	0.36	0.37	0.41	0.40	0.36	0.36	0.36	0.37	0.46	0.45	0.51	0.51	0.42	0.41	0.10	0.09	0.19
5.00	ARL	1.04	1.04	3.05	3.04	2.75	2.73	2.04	2.03	1.94	1.92	1.71	1.70	1.11	1.10	1.31	1.29	1.10	1.09	1.00	1.00	1.01
	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	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	SDRL	0.20	0.19	0.37	0.38	0.45	0.46	0.19	0.18	0.34	0.34	0.45	0.46	0.31	0.30	0.46	0.45	0.30	0.29	0.03	0.03	0.11
EQL		15.95	15.73	38.48	38.32	33.97	33.82	26.25	26.12	24.96	24.77	21.83	21.70	16.14	16.01	19.26	18.99	16.14	15.94	12.32	12.25	13.49
IRARL		1.33	1.31	2.59	2.58	2.27	2.26	1.76	1.75	1.75	1.73	1.51	1.50	1.12	1.11	1.43	1.41	1.19	1.18	0.88	0.87	1.00