Mathematical Problems in Engineering

Research Article

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

Table 5

The (ARL, MRL, SDRL) profiles of three different upper-sided run rules t charts when ARL₀ = 200 and n ∈ {5, 7, 9, 11}.


n	Chart	λ	UCL⁺	δ
n	Chart	λ	UCL⁺	0.1			0.3			0.5			0.7			1.0			1.5			2			3

5	RR_2,3-t	—	2.0762	(200.00	139	198.14)	(100.18	70	98.38)	(31.54	22	29.85)	(13.10	10	11.51)	(6.88	5	5.36)	(3.68	3	2.17)	(2.31	2	0.66)	(2.05	2	0.00)	(2.00	2	0.01)
	RR_3,4-t	—	1.2980	(200.00	139	197.17)	(87.36	61	84.64)	(24.10	17	21.59)	(10.12	8	7.76)	(5.84	4	3.50)	(3.79	3	1.32)	(3.08	3	0.31)	(3.01	3	0.07)	(3.00	3	0.00)
	RR_4,5-t	—	0.8755	(200.00	140	196.29)	(80.80	57	77.26)	(21.39	16	18.15)	(9.49	7	6.37)	(6.01	5	2.82)	(4.47	4	0.98)	(4.03	4	0.19)	(4.00	4	0.03)	(4.00	4	0.00)
	U-NEWMA	0.1	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)
	U-NEWMA	0.2	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)
	U-NEWMA	0.3	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)
	U-NEWMA	0.5	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)
	U-NEWMA	1	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	RR_2,3-t	—	1.8979	(200.00	139	198.14)	(85.39	60	83.60)	(21.92	16	20.27)	(8.45	6	6.91)	(4.50	3	3.00)	(2.68	2	1.11)	(2.06	2	0.26)	(2.00	2	0.05)	(2.00	2	0.00)
	RR_3,4-t	—	1.2319	(200.00	139	197.17)	(74.29	52	71.60)	(17.42	13	14.98)	(7.24	6	4.91)	(4.47	4	2.08)	(3.30	3	0.69)	(3.01	3	0.12)	(3.00	3	0.01)	(3.00	3	0.00)
	RR_4,5-t	—	0.8446	(200.00	140	196.29)	(68.81	49	65.31)	(15.99	12	12.81)	(7.28	5	4.15)	(5.02	4	1.70)	(4.17	4	0.50)	(4.00	4	0.07)	(4.00	4	0.01)	(4.00	4	0.00)
	U-NEWMA	0.1	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)
	U-NEWMA	0.2	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)
	U-NEWMA	0.3	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)
	U-NEWMA	0.5	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)
	U-NEWMA	1	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)
9	RR_2,3-t	—	1.8186	(200.00	139	198.14)	(75.03	53	73.25)	(16.67	12	15.05)	(6.26	5	4.74)	(3.48	3	1.97)	(3.68	3	0.67)	(2.32	2	0.12)	(2.01	2	0.01)	(2.00	2	0.00)
	RR_3,4-t	—	1.2011	(200.00	139	197.17)	(65.11	46	62.44)	(13.70	10	11.29)	(5.82	4	3.48)	(3.85	3	1.39)	(3.13	3	0.40)	(3.00	3	0.05)	(3.00	3	0.00)	(3.00	3	0.00)
	RR_4,5-t	—	0.8298	(200.00	140	196.29)	(60.33	43	56.86)	(12.91	10	9.76)	(6.15	5	2.97)	(4.57	4	1.12)	(4.07	4	0.28)	(4.00	4	0.02)	(4.00	4	0.00)	(4.00	4	0.00)
	U-NEWMA	0.1	0.5614	(200.00	140	195.72)	(35.53	27	29.59)	(8.61	8	4.53)	(4.74	4	1.88)	(3.33	3	1.12)	(2.38	3	0.76)	(1.73	2	0.50)	(1.73	2	0.50)	(1.02	1	0.15)
	U-NEWMA	0.2	0.9227	(201.93	141	199.81)	(44.74	32	40.96)	(9.12	8	5.92)	(4.50	4	2.16)	(3.01	3	1.18)	(2.11	2	0.70)	(1.73	2	0.50)	(1.73	2	0.50)	(1.00	1	0.02)
	U-NEWMA	0.3	1.2367	(200.65	140	199.17)	(54.12	38	51.22)	(10.42	8	7.82)	(4.60	4	2.57)	(2.93	2	1.31)	(1.98	2	0.73)	(1.36	1	0.49)	(1.36	1	0.49)	(1.00	1	1.01)
	U-NEWMA	0.5	1.8214	(200.51	139	199.81)	(70.77	50	69.31)	(14.61	11	12.98)	(5.50	4	3.96)	(3.08	3	1.77)	(1.89	2	0.84)	(1.24	1	0.44)	(1.24	1	0.44)	(1.00	1	0.00)
	U-NEWMA	1	3.3526	(198.40	138	197.83)	(100.79	70	100.13)	(30.40	21	29.85)	(11.56	8	11.04)	(5.31	4	4.77)	(2.33	2	1.77)	(1.20	1	0.49)	(1.20	1	0.49)	(2.00	2	0.00)
11	RR_2,3-t	—	1.7739	(200.00	139	198.14)	(67.18	47	65.41)	(13.39	10	11.80)	(5.03	4	3.52)	(2.95	2	1.40)	(2.16	3	0.44)	(2.00	2	0.05)	(2.00	2	0.05)	(3.00	3	0.00)
	RR_3,4-t	—	1.1833	(200.00	139	197.17)	(58.16	41	55.50)	(11.33	9	8.95)	(4.98	4	2.63)	(3.52	3	0.99)	(3.06	4	0.25)	(3.00	3	0.02)	(3.00	3	0.00)	(4.00	4	0.00)
	RR_4,5-t	—	0.8211	(200.00	140	196.29)	(53.90	38	50.45)	(10.93	8	7.80)	(5.49	5	2.25)	(4.34	4	0.78)	(4.03	2	0.17)	(4.00	4	0.01)	(4.00	4	0.00)	(1.00	1	0.04)
	U-NEWMA	0.1	0.5430	(199.45	140	195.98)	(30.77	24	24.80)	(7.52	7	3.71)	(4.19	4	1.56)	(2.97	3	0.94)	(2.15	2	0.60)	(1.58	2	0.50)	(1.20	1	0.40)	(1.00	1	0.00)
	U-NEWMA	0.2	0.8880	(200.19	139	197.80)	(37.86	27	34.08)	(7.62	7	4.61)	(3.87	4	1.70)	(2.65	3	0.96)	(1.89	2	0.60)	(1.32	1	0.47)	(1.05	1	0.22)	(1.00	1	0.00)
	U-NEWMA	0.3	1.1838	(199.62	139	197.84)	(45.53	32	43.01)	(8.33	7	5.85)	(3.85	3	1.96)	(2.52	2	1.03)	(1.74	2	0.62)	(1.20	1	0.40)	(1.02	1	0.14)	(1.00	1	0.00)
	U-NEWMA	0.5	1.7343	(200.63	139	200.26)	(61.15	43	59.69)	(11.14	8	9.43)	(4.31	4	2.84)	(2.52	2	1.31)	(1.61	2	0.66)	(1.11	1	0.31)	(1.01	1	0.07)	(1.00	1	0.00)
	U-NEWMA	1	3.1667	(199.08	139	197.97)	(91.00	63	90.52)	(24.05	17	23.66)	(8.34	6	7.81)	(3.76	3	3.22)	(1.73	1	1.12)	(1.07	1	0.40)	(1.00	1	0.05)	(1.00	1	0.00)