New One-Sided EWMA t Charts without and with Variable Sampling Intervals for Monitoring the Process Mean

Table 3

The (ARL, MRL, SDRL) profiles of two upper-sided EWMA t charts when ARL₀ = 200 and n ∈ {5, 7}.

n	λ	Chart	UCL^+	δ
				0			0.1			0.3			0.5			0.7			1.0			1.5			2			3
5	0.1	U-EWMA	0.7695	(200.00	140	194.60)	(68.82	50	62.30)	(17.10	14	11.24)	(8.59	8	4.23)	(5.72	5	2.36)	(3.88	4	1.38)	(2.64	3	0.85)	(2.07	2	0.65)	(1.56	2	0.51)
		U-NEWMA	0.6811	(200.45	140	198.20)	(56.71	41	51.02)	(14.41	12	9.35)	(7.45	7	3.69)	(5.04	5	2.11)	(3.46	3	1.26)	(2.38	2	0.78)	(1.90	2	0.60)	(1.43	1	0.50)
	0.2	U-EWMA	1.2555	(200.00	139	197.35)	(86.78	61	83.41)	(21.80	17	17.91)	(9.37	8	5.99)	(5.67	5	2.93)	(3.59	3	1.51)	(2.34	2	0.84)	(1.83	2	0.61)	(1.35	1	0.48)
		U-NEWMA	1.1493	(201.26	141	198.92)	(74.34	53	70.89)	(17.96	14	14.27)	(8.09	7	5.04)	(5.02	5	2.56)	(3.26	3	1.37)	(2.17	2	0.78)	(1.71	2	0.58)	(1.27	1	0.44)
	0.3	U-EWMA	1.6957	(200.00	139	198.33)	(99.93	70	97.84)	(28.37	21	25.69)	(11.34	9	8.69)	(6.26	5	3.93)	(3.65	3	1.80)	(2.25	2	0.89)	(1.72	2	0.62)	(1.25	1	0.44)
		U-NEWMA	1.5763	(199.58	139	198.32)	(87.67	61	85.70)	(23.31	17	20.65)	(9.66	8	7.16)	(5.52	5	3.37)	(3.33	3	1.61)	(2.10	2	0.82)	(1.63	2	0.59)	(1.19	1	0.39)
	0.4	U-EWMA	2.1198	(200.00	139	198.80)	(109.09	76	107.64)	(35.14	25	33.25)	(14.08	11	12.04)	(7.30	6	5.36)	(3.91	3	2.26)	(2.25	2	0.99)	(1.67	2	0.64)	(1.20	1	0.40)
		U-NEWMA	1.9932	(198.73	138	199.89)	(98.38	68	97.67)	(29.40	21	27.53)	(12.02	9	8.69)	(6.41	5	4.54)	(3.56	3	2.01)	(2.10	2	0.91)	(1.58	2	0.61)	(1.15	1	0.36)
	0.5	U-EWMA	2.5371	(200.00	139	199.06)	(115.52	80	114.43)	(41.25	29	39.86)	(17.17	12	15.60)	(8.69	7	7.11)	(4.33	4	2.90)	(2.30	2	1.14)	(1.65	2	0.68)	(1.17	1	0.38)
		U-NEWMA	2.4137	(198.78	138	198.32)	(107.58	75	106.77)	(35.70	25	34.22)	(14.96	11	13.43)	(7.71	6	6.19)	(3.94	3	2.55)	(2.17	2	1.05)	(1.57	1	0.64)	(1.13	1	0.34)
	0.75	U-EWMA	3.5711	(200.00	139	199.37)	(124.84	87	124.17)	(52.36	37	51.60)	(24.40	17	23.57)	(12.75	9	11.85)	(5.94	4	5.03)	(2.64	2	1.77)	(1.69	1	0.88)	(1.13	1	0.35)
		U-NEWMA	3.4872	(200.43	140	198.53)	(120.81	84	121.95)	(49.60	35	48.92)	(22.90	16	22.02)	(11.88	9	10.91)	(5.60	4	4.68)	(2.52	2	1.67)	(1.63	1	0.84)	(1.11	1	0.33)
	0.9	U-EWMA	4.1907	(200.00	139	199.46)	(127.93	89	127.37)	(56.65	39	56.07)	(27.77	19	27.16)	(15.00	11	14.37)	(7.07	5	6.41)	(2.96	2	2.28)	(1.76	1	1.08)	(1.12	1	0.35)
		U-NEWMA	4.1474	(199.43	138	199.15)	(126.47	88	126.08)	(55.29	39	54.83)	(27.10	19	26.49)	(14.56	10	13.98)	(6.86	5	6.20)	(2.90	2	2.22)	(1.73	1	1.05)	(1.11	1	0.33)
	1.0	U-EWMA	4.6041	(200.00	139	199.50)	(129.40	90	128.90)	(58.79	41	58.30)	(29.57	21	29.06)	(16.31	11	15.80)	(7.79	6	7.27)	(3.20	2	2.65)	(1.83	1	1.23)	(1.12	1	0.36)
		U-NEWMA	4.5961	(198.50	138	197.91)	(129.07	90	128.30)	(58.35	40	58.02)	(29.23	20	28.74)	(16.17	11	15.73)	(7.75	6	7.23)	(3.19	2	2.64)	(1.82	1	1.22)	(1.12	1	0.36)
7	0.1	U-EWMA	0.6704	(200.00	141	193.73)	(51.88	38	45.01)	(12.19	11	6.98)	(6.40	6	2.72)	(4.38	4	1.57)	(3.05	3	0.95)	(2.12	2	0.61)	(1.72	2	0.50)	(1.24	1	0.42)
		U-NEWMA	0.5958	(200.09	139	196.95)	(43.21	32	37.14)	(10.51	9	5.99)	(5.64	5	2.45)	(3.90	4	1.44)	(2.75	3	0.88)	(1.94	2	0.57)	(1.58	2	0.51)	(1.13	1	0.34)
	0.2	U-EWMA	1.0726	(200.00	140	196.73)	(64.93	46	61.03)	(13.72	11	9.98)	(6.25	6	3.35)	(4.00	4	1.73)	(2.67	3	0.96)	(1.84	2	0.59)	(1.46	1	0.51)	(1.07	1	0.25)
		U-NEWMA	0.9854	(199.34	139	197.69)	(54.50	39	51.08)	(11.74	10	8.34)	(5.58	5	2.96)	(3.63	3	1.58)	(2.47	2	0.89)	(1.72	2	0.57)	(1.36	1	0.48)	(1.04	1	0.18)
	0.3	U-EWMA	1.4253	(200.00	139	197.90)	(76.51	54	73.96)	(16.65	13	13.83)	(6.76	6	4.34)	(4.02	4	2.05)	(2.55	2	1.03)	(1.70	2	0.60)	(1.33	1	0.47)	(1.03	1	0.16)
		U-NEWMA	1.3314	(200.22	140	198.80)	(66.24	47	63.94)	(14.12	11	11.51)	(5.98	5	3.76)	(3.66	3	1.83)	(2.38	2	0.96)	(1.61	2	0.57)	(1.26	1	0.44)	(1.01	1	0.12)
	0.4	U-EWMA	1.7594	(200.00	139	198.51)	(86.05	60	84.25)	(20.36	15	18.23)	(7.71	6	5.70)	(4.25	4	2.52)	(2.53	2	1.16)	(1.62	2	0.61)	(1.25	1	0.44)	(1.01	1	0.11)
		U-NEWMA	1.6610	(199.18	139	197.63)	(76.68	54	74.88)	(17.23	13	15.17)	(6.79	5	4.88)	(3.87	3	2.23)	(2.36	2	1.07)	(1.54	1	0.58)	(1.20	1	0.40)	(1.01	1	0.08)
	0.5	U-EWMA	2.0857	(200.00	139	198.87)	(93.66	65	92.32)	(24.42	17	22.79)	(9.02	7	7.37)	(4.67	4	3.16)	(2.59	2	1.34)	(1.57	1	0.63)	(1.20	1	0.41)	(1.01	1	0.09)
		U-NEWMA	1.9866	(199.84	139	199.15)	(84.97	59	83.88)	(21.03	15	19.47)	(7.94	6	6.34)	(4.25	4	2.82)	(2.42	2	1.24)	(1.50	1	0.60)	(1.16	1	0.37)	(1.00	1	0.07)
	0.75	U-EWMA	2.8940	(200.00	139	199.31)	(106.26	74	105.51)	(33.97	24	33.10)	(13.21	9	12.27)	(6.35	5	5.39)	(3.00	2	2.09)	(1.54	1	0.75)	(1.15	1	0.37)	(1.00	1	0.06)
		U-NEWMA	2.8192	(201.52	140	200.46)	(101.69	71	101.23)	(31.24	22	30.33)	(12.04	9	11.10)	(5.88	4	4.93)	(2.84	2	1.94)	(1.50	1	0.71)	(1.13	1	0.35)	(1.00	1	0.05)
	0.9	U-EWMA	3.3810	(200.00	139	199.44)	(110.81	77	110.23)	(38.48	27	37.86)	(15.78	11	15.13)	(7.63	5	6.95)	(3.40	3	2.72)	(1.58	1	0.88)	(1.14	1	0.37)	(1.00	1	0.05)
		U-NEWMA	3.3416	(198.65	137	198.27)	(109.32	76	108.69)	(37.10	26	36.57)	(15.24	11	14.55)	(7.34	5	6.69)	(3.30	3	2.62)	(1.55	1	0.85)	(1.13	1	0.36)	(1.00	1	0.04)
	1.0	U-EWMA	3.7074	(200.00	139	199.50)	(113.02	78	112.52)	(40.90	29	40.40)	(17.33	12	16.82)	(8.49	6	7.97)	(3.72	3	3.18)	(1.62	1	1.00)	(1.13	1	0.39)	(1.00	1	0.04)
		U-NEWMA	3.7043	(199.48	138	198.99)	(112.28	78	111.99)	(40.68	28	39.97)	(17.30	12	16.79)	(8.44	6	7.86)	(3.70	3	3.17)	(1.61	1	1.00)	(1.13	1	0.39)	(1.00	1	0.04)