Mathematical Problems in Engineering

Research Article

Triple Homogeneously Weighted Moving Average Charts for Monitoring Process Dispersion

Table 7

Performance measures for two-sided chart versus two-sided competing charts when = 15 for .





		1.2553	2.122	1.513	1.71	2.277	1.186	1.466	2.515	1.796	1.993	2.478
0.5	1.01	1.01	1.18	1.01	1.03	1.16	1.01	1.02	1.40	1.04	1.08	1.25
0.5	(0.11)	(0.13)	(0.54)	(0.12)	(0.17)	(0.37)	(0.11)	(0.21)	(0.72)	(0.20)	(0.27)	(0.45)
0.55	1.04	1.05	1.45	1.06	1.11	1.35	1.04	1.10	1.78	1.14	1.21	1.48
0.55	(0.28)	(0.32)	(0.81)	(0.26)	(0.32)	(0.52)	(0.29)	(0.43)	(0.92)	(0.38)	(0.44)	(0.58)
0.6	1.13	1.17	1.82	1.18	1.26	1.61	1.14	1.27	2.22	1.33	1.43	1.78
0.6	(0.50)	(0.56)	(1.02)	(0.47)	(0.52)	(0.69)	(0.52)	(0.69)	(1.05)	(0.64)	(0.65)	(0.75)
0.65	1.31	1.38	2.30	1.43	1.51	1.99	1.33	1.55	2.75	1.68	1.77	2.23
0.65	(0.76)	(0.82)	(1.21)	(0.81)	(0.78)	(0.92)	(0.77)	(0.95)	(1.20)	(0.99)	(0.92)	(1.01)
0.7	1.61	1.71	2.90	1.85	1.95	2.54	1.64	1.96	3.45	2.25	2.32	2.87
0.7	(1.05)	(1.11)	(1.46)	(1.31)	(1.19)	(1.29)	(1.06)	(1.24)	(1.50)	(1.52)	(1.36)	(1.41)
0.75	2.04	2.17	3.77	2.64	2.67	3.46	2.07	2.51	4.54	3.24	3.23	3.94
0.75	(1.39)	(1.46)	(1.97)	(2.12)	(1.86)	(1.94)	(1.41)	(1.61)	(2.12)	(2.36)	(2.05)	(2.13)
0.8	2.68	2.88	5.25	4.14	4.05	5.05	2.73	3.40	6.45	4.98	4.84	5.78
0.8	(1.95)	(2.05)	(3.02)	(3.60)	(3.09)	(3.11)	(1.98)	(2.31)	(3.39)	(3.77)	(3.30)	(3.44)
0.85	3.77	4.10	8.20	7.05	6.82	8.22	3.84	4.96	10.30	8.31	8.04	9.51
0.85	(3.08)	(3.31)	(5.41)	(6.43)	(5.59)	(5.63)	(3.13)	(3.84)	(6.08)	(6.42)	(5.79)	(6.31)
0.9	5.87	6.63	15.76	14.13	13.56	16.10	6.05	8.59	19.73	16.16	15.79	19.22
0.9	(6.05)	(6.75)	(11.81)	(13.13)	(11.80)	(12.29)	(6.23)	(8.29)	(12.82)	(12.80)	(12.43)	(14.98)
0.95	11.99	14.86	44.91	38.86	39.39	47.89	12.68	22.50	53.62	45.37	47.62	59.78
0.95	(18.92)	(22.49)	(37.87)	(39.36)	(39.26)	(44.43)	(19.88)	(29.84)	(39.19)	(42.54)	(45.65)	(55.78)
1	199.02	200.43	199.75	200.36	200.42	199.93	200.48	200.68	200.42	200.03	200.40	200.82
1	(2345.54)	(950.48)	(173.11)	(259.54)	(246.45)	(216.08)	(1697.43)	(418.10)	(157.24)	(226.73)	(218.14)	(205.66)
1.1	5.56	6.44	16.08	14.70	14.09	15.93	5.76	8.42	19.72	16.71	16.17	18.24
1.1	(6.33)	(7.35)	(13.57)	(15.14)	(13.78)	(13.63)	(6.59)	(9.27)	(14.22)	(14.71)	(14.21)	(15.29)
1.2	2.93	3.13	5.82	5.07	4.86	5.56	2.99	3.74	7.14	5.92	5.63	6.23
1.2	(2.46)	(2.62)	(4.27)	(5.20)	(4.49)	(4.25)	(2.50)	(3.08)	(4.79)	(5.26)	(4.66)	(4.58)
1.3	2.04	2.17	3.47	2.72	2.67	3.10	2.08	2.45	4.10	3.19	3.09	3.47
1.3	(1.52)	(1.62)	(2.30)	(2.59)	(2.24)	(2.16)	(1.55)	(1.79)	(2.52)	(2.83)	(2.42)	(2.33)
1.4	1.61	1.68	2.47	1.84	1.83	2.16	1.63	1.86	2.86	2.10	2.08	2.37
1.4	(1.11)	(1.17)	(1.60)	(1.52)	(1.33)	(1.36)	(1.13)	(1.30)	(1.72)	(1.71)	(1.49)	(1.47)
1.5	1.37	1.41	1.93	1.45	1.47	1.70	1.38	1.53	2.21	1.60	1.61	1.83
1.5	(0.85)	(0.90)	(1.25)	(0.98)	(0.89)	(0.96)	(0.87)	(1.01)	(1.33)	(1.13)	(1.01)	(1.03)
1.6	1.22	1.25	1.61	1.25	1.27	1.43	1.23	1.32	1.79	1.34	1.37	1.52
1.6	(0.66)	(0.70)	(1.01)	(0.67)	(0.63)	(0.71)	(0.67)	(0.78)	(1.08)	(0.78)	(0.72)	(0.77)
1.7	1.14	1.15	1.38	1.14	1.16	1.27	1.14	1.20	1.53	1.20	1.22	1.34
1.7	(0.52)	(0.55)	(0.81)	(0.47)	(0.45)	(0.54)	(0.52)	(0.62)	(0.90)	(0.56)	(0.53)	(0.61)
1.8	1.08	1.09	1.25	1.08	1.10	1.18	1.09	1.12	1.35	1.12	1.14	1.22
1.8	(0.41)	(0.43)	(0.67)	(0.34)	(0.34)	(0.43)	(0.41)	(0.48)	(0.74)	(0.41)	(0.4)	(0.47)
1.9	1.05	1.05	1.17	1.05	1.06	1.12	1.05	1.08	1.24	1.07	1.09	1.14
1.9	(0.31)	(0.33)	(0.54)	(0.25)	(0.26)	(0.34)	(0.32)	(0.39)	(0.62)	(0.30)	(0.31)	(0.38)
2	1.03	1.03	1.11	1.03	1.04	1.08	1.03	1.05	1.15	1.04	1.06	1.10
2	(0.25)	(0.26)	(0.43)	(0.19)	(0.20)	(0.28)	(0.25)	(0.30)	(0.49)	(0.23)	(0.24)	(0.31)
	13.16	13.48	16.36	15.45	15.39	16.21	13.29	14.15	17.57	16.15	16.16	17.15
	1.00	1.02	1.24	1.17	1.17	1.23	1.00	1.06	1.32	1.21	1.22	1.29
	1.00	1.05	1.69	1.38	1.38	1.60	1.00	1.17	1.95	1.53	1.53	1.75




		1.994	2.736	2.202	2.294	2.645	1.795	2.463	2.785	2.297	2.47	2.719
0.5	1.07	1.37	1.47	1.17	1.25	1.39	1.07	1.37	1.47	1.17	1.25	1.39
0.5	(0.36)	(0.70)	(0.59)	(0.39)	(0.45)	(0.52)	(0.36)	(0.70)	(0.59)	(0.39)	(0.45)	(0.52)
0.55	1.23	1.73	1.80	1.38	1.48	1.67	1.23	1.73	1.80	1.38	1.48	1.67
0.55	(0.63)	(0.92)	(0.75)	(0.58)	(0.59)	(0.66)	(0.63)	(0.92)	(0.75)	(0.58)	(0.59)	(0.66)
0.6	1.51	2.18	2.22	1.71	1.80	2.05	1.51	2.18	2.22	1.71	1.80	2.05
0.6	(0.89)	(1.06)	(0.89)	(0.82)	(0.78)	(0.86)	(0.89)	(1.06)	(0.89)	(0.82)	(0.78)	(0.86)
0.65	1.89	2.70	2.76	2.18	2.27	2.60	1.89	2.70	2.76	2.18	2.27	2.60
0.65	(1.12)	(1.21)	(1.12)	(1.13)	(1.05)	(1.19)	(1.12)	(1.21)	(1.12)	(1.13)	(1.05)	(1.19)
0.7	2.41	3.39	3.56	2.90	2.95	3.46	2.41	3.39	3.56	2.90	2.95	3.46
0.7	(1.39)	(1.49)	(1.58)	(1.57)	(1.48)	(1.77)	(1.39)	(1.49)	(1.58)	(1.57)	(1.48)	(1.77)
0.75	3.12	4.45	4.91	4.03	4.10	4.95	3.12	4.45	4.91	4.03	4.10	4.95
0.75	(1.81)	(2.10)	(2.48)	(2.29)	(2.24)	(2.91)	(1.81)	(2.10)	(2.48)	(2.29)	(2.24)	(2.91)
0.8	4.27	6.30	7.38	5.96	6.13	7.86	4.27	6.30	7.38	5.96	6.13	7.86
0.8	(2.67)	(3.35)	(4.27)	(3.58)	(3.77)	(5.45)	(2.67)	(3.35)	(4.27)	(3.58)	(3.77)	(5.45)
0.85	6.50	10.04	12.53	9.93	10.60	14.48	6.50	10.04	12.53	9.93	10.60	14.48
0.85	(4.68)	(6.01)	(8.32)	(6.79)	(7.68)	(11.69)	(4.68)	(6.01)	(8.32)	(6.79)	(7.68)	(11.69)
0.9	12.10	19.26	26.30	20.82	23.43	34.19	12.10	19.26	26.30	20.82	23.43	34.19
0.9	(10.42)	(12.71)	(20.28)	(17.20)	(20.44)	(31.54)	(10.42)	(12.71)	(20.28)	(17.20)	(20.44)	(31.54)
0.95	34.87	52.53	77.90	67.35	76.22	101.27	34.87	52.53	77.90	67.35	76.22	101.27
0.95	(35.92)	(38.63)	(68.91)	(65.03)	(73.91)	(99.67)	(35.92)	(38.63)	(68.91)	(65.03)	(73.91)	(99.67)
1	200.43	200.55	200.39	200.60	200.93	200.50	200.43	200.55	200.39	200.60	200.93	200.50
1	(234.77)	(156.29)	(191.41)	(205.54)	(203.46)	(201.16)	(234.77)	(156.29)	(191.41)	(205.54)	(203.46)	(201.16)
1.1	12.38	19.34	22.79	20.31	21.47	26.16	12.38	19.34	22.79	20.31	21.47	26.16
1.1	(12.19)	(14.14)	(18.24)	(17.85)	(19.3)	(24.19)	(12.19)	(14.14)	(18.24)	(17.85)	(19.30)	(24.19)
1.2	4.71	7.00	7.66	6.72	6.72	7.59	4.71	7.00	7.66	6.72	6.72	7.59
1.2	(3.69)	(4.76)	(5.21)	(4.97)	(5.04)	(5.9)	(3.69)	(4.76)	(5.21)	(4.97)	(5.04)	(5.9)
1.3	2.94	4.02	4.20	3.71	3.66	3.94	2.94	4.02	4.20	3.71	3.66	3.94
1.3	(2.06)	(2.49)	(2.59)	(2.66)	(2.51)	(2.69)	(2.06)	(2.49)	(2.59)	(2.66)	(2.51)	(2.69)
1.4	2.17	2.82	2.85	2.47	2.48	2.64	2.17	2.82	2.85	2.47	2.48	2.64
1.4	(1.47)	(1.70)	(1.67)	(1.71)	(1.60)	(1.64)	(1.47)	(1.70)	(1.67)	(1.71)	(1.60)	(1.64)
1.5	1.72	2.18	2.17	1.87	1.88	1.99	1.72	2.18	2.17	1.87	1.88	1.99
1.5	(1.13)	(1.33)	(1.22)	(1.21)	(1.12)	(1.13)	(1.13)	(1.33)	(1.22)	(1.21)	(1.12)	(1.13)
1.6	1.45	1.77	1.77	1.52	1.55	1.64	1.45	1.77	1.77	1.52	1.55	1.64
1.6	(0.91)	(1.08)	(0.97)	(0.88)	(0.83)	(0.84)	(0.91)	(1.08)	(0.97)	(0.88)	(0.83)	(0.84)
1.7	1.29	1.51	1.50	1.32	1.35	1.42	1.29	1.51	1.50	1.32	1.35	1.42
1.7	(0.72)	(0.90)	(0.77)	(0.66)	(0.63)	(0.66)	(0.72)	(0.90)	(0.77)	(0.66)	(0.63)	(0.66)
1.8	1.18	1.34	1.33	1.20	1.23	1.28	1.18	1.34	1.33	1.20	1.23	1.28
1.8	(0.58)	(0.73)	(0.62)	(0.51)	(0.50)	(0.53)	(0.58)	(0.73)	(0.62)	(0.51)	(0.50)	(0.53)
1.9	1.11	1.22	1.22	1.12	1.15	1.19	1.11	1.22	1.22	1.12	1.15	1.19
1.9	(0.46)	(0.59)	(0.50)	(0.38)	(0.40)	(0.43)	(0.46)	(0.59)	(0.50)	(0.38)	(0.40)	(0.43)
2	1.07	1.15	1.15	1.08	1.10	1.13	1.07	1.15	1.15	1.08	1.10	1.13
2	(0.36)	(0.49)	(0.41)	(0.31)	(0.31)	(0.36)	(0.36)	(0.49)	(0.41)	(0.31)	(0.31)	(0.36)
	13.99	15.99	18.18	16.96	17.21	18.58	15.29	17.44	18.84	17.67	18.17	19.94
	1.00	1.14	1.30	1.21	1.23	1.33	1.00	1.14	1.23	1.16	1.19	1.30
	1.00	1.34	1.75	1.44	1.46	1.68	1.00	1.32	1.43	1.23	1.27	1.46