Research Article
Triple Homogeneously Weighted Moving Average Charts for Monitoring Process Dispersion
Table 2
Performance measures for upper-sided
chart versus upper-sided competing charts when
ā=ā5 for
.
| ā | | | | | | | | | | | | | | |
| | | 0.1095 | 1.408 | 0.981 | 1.223 | 1.876 | 0.06 | 0.507 | 1.956 | 1.355 | 1.587 | 2.145 | 1 | 200.68 | 200.77 | 200.23 | 200.76 | 200.52 | 200.05 | 200.61 | 200.69 | 200.65 | 200.10 | 200.52 | 200.69 | (2560.33) | (1859.27) | (261.01) | (264.43) | (250.72) | (221.37) | (1878.20) | (714.61) | (203.99) | (230.54) | (222.91) | (207.67) | 1.1 | 3.92 | 4.35 | 21.08 | 23.52 | 23.48 | 27.18 | 4.01 | 7.46 | 29.67 | 28.09 | 28.31 | 32.15 | (7.25) | (8.16) | (24.49) | (29.03) | (27.71) | (27.82) | (7.49) | (13.24) | (26.46) | (29.45) | (29.29) | (30.94) | 1.2 | 2.38 | 2.56 | 8.60 | 9.42 | 9.22 | 10.83 | 2.46 | 3.69 | 12.62 | 11.63 | 11.40 | 12.79 | (2.91) | (3.17) | (9.06) | (11.69) | (10.57) | (10.40) | (3.00) | (4.65) | (10.82) | (11.97) | (11.27) | (11.49) | 1.3 | 1.89 | 1.98 | 5.18 | 5.40 | 5.28 | 6.21 | 1.92 | 2.63 | 7.41 | 6.77 | 6.54 | 7.31 | (1.87) | (1.98) | (4.93) | (6.75) | (5.95) | (5.73) | (1.95) | (2.70) | (6.18) | (7.08) | (6.38) | (6.27) | 1.4 | 1.63 | 1.69 | 3.76 | 3.64 | 3.57 | 4.29 | 1.64 | 2.13 | 5.09 | 4.54 | 4.40 | 4.91 | (1.40) | (1.46) | (3.32) | (4.39) | (3.83) | (3.74) | (1.40) | (1.94) | (4.08) | (4.77) | (4.23) | (4.02) | 1.5 | 1.46 | 1.52 | 2.97 | 2.73 | 2.71 | 3.23 | 1.48 | 1.83 | 3.91 | 3.37 | 3.29 | 3.69 | (1.11) | (1.18) | (2.44) | (3.11) | (2.72) | (2.68) | (1.13) | (1.54) | (2.96) | (3.46) | (3.03) | (2.89) | 1.6 | 1.36 | 1.40 | 2.49 | 2.23 | 2.23 | 2.61 | 1.38 | 1.64 | 3.18 | 2.65 | 2.61 | 2.96 | (0.95) | (0.99) | (1.95) | (2.36) | (2.08) | (2.04) | (0.97) | (1.27) | (2.34) | (2.62) | (2.31) | (2.23) | 1.7 | 1.28 | 1.32 | 2.18 | 1.88 | 1.89 | 2.20 | 1.30 | 1.51 | 2.70 | 2.23 | 2.22 | 2.50 | (0.81) | (0.86) | (1.64) | (1.85) | (1.62) | (1.61) | (0.85) | (1.10) | (1.94) | (2.11) | (1.85) | (1.81) | 1.8 | 1.23 | 1.25 | 1.95 | 1.66 | 1.68 | 1.96 | 1.24 | 1.41 | 2.39 | 1.91 | 1.92 | 2.18 | (0.71) | (0.76) | (1.43) | (1.48) | (1.32) | (1.36) | (0.74) | (0.95) | (1.68) | (1.69) | (1.50) | (1.51) | 1.9 | 1.19 | 1.21 | 1.78 | 1.51 | 1.54 | 1.77 | 1.19 | 1.33 | 2.14 | 1.73 | 1.74 | 1.95 | (0.65) | (0.67) | (1.26) | (1.22) | (1.11) | (1.15) | (0.64) | (0.84) | (1.47) | (1.45) | (1.29) | (1.28) | 2 | 1.15 | 1.17 | 1.65 | 1.40 | 1.42 | 1.62 | 1.16 | 1.27 | 1.95 | 1.56 | 1.57 | 1.76 | (0.58) | (0.61) | (1.14) | (1.03) | (0.93) | (0.99) | (0.59) | (0.76) | (1.32) | (1.20) | (1.08) | (1.10) | | 13.59 | 13.76 | 18.95 | 18.96 | 18.90 | 20.37 | 13.64 | 14.79 | 22.10 | 20.75 | 20.68 | 22.04 | | 1.00 | 1.01 | 1.39 | 1.39 | 1.39 | 1.50 | 1.00 | 1.08 | 1.62 | 1.52 | 1.52 | 1.62 | | 1.00 | 1.04 | 2.39 | 2.38 | 2.36 | 2.75 | 1.00 | 1.29 | 3.16 | 2.81 | 2.78 | 3.12 |
| ā | | | ā | | | | | | | | | | | | |
| | | 1.245 | 2.352 | 1.738 | 1.954 | 2.355 | 0.986 | 1.877 | 2.474 | 1.965 | 2.162 | 2.449 | 1 | 200.57 | 200.66 | 200.56 | 200.16 | 200.56 | 200.10 | 200.77 | 200.83 | 200.55 | 200.99 | 200.39 | 200.27 | (828.92) | (294.71) | (195.00) | (210.95) | (207.38) | (201.96) | (372.45) | (208.90) | (197.29) | (206.10) | (203.68) | (200.27) | 1.1 | 6.66 | 18.30 | 34.12 | 32.60 | 33.64 | 37.58 | 13.96 | 28.59 | 36.85 | 35.86 | 37.35 | 41.65 | (12.16) | (23.28) | (28.39) | (31.87) | (32.88) | (35.86) | (20.45) | (26.33) | (32.30) | (34.75) | (36.13) | (40.34) | 1.2 | 3.49 | 7.51 | 14.76 | 13.28 | 13.42 | 14.77 | 5.89 | 12.08 | 15.38 | 14.23 | 14.61 | 16.24 | (4.50) | (8.36) | (11.47) | (12.14) | (12.25) | (13.25) | (7.11) | (10.66) | (12.46) | (12.80) | (13.31) | (14.91) | 1.3 | 2.48 | 4.58 | 8.57 | 7.72 | 7.53 | 8.14 | 3.77 | 7.13 | 8.79 | 8.06 | 8.08 | 8.84 | (2.57) | (4.46) | (6.42) | (6.93) | (6.62) | (6.85) | (3.83) | (6.07) | (6.68) | (6.96) | (6.94) | (7.63) | 1.4 | 2.01 | 3.37 | 5.91 | 5.19 | 5.08 | 5.45 | 2.87 | 4.91 | 6.06 | 5.46 | 5.40 | 5.84 | (1.82) | (3.01) | (4.29) | (4.65) | (4.33) | (4.34) | (2.62) | (4.01) | (4.43) | (4.57) | (4.41) | (4.73) | 1.5 | 1.76 | 2.72 | 4.51 | 3.87 | 3.78 | 4.10 | 2.36 | 3.75 | 4.55 | 4.11 | 4.06 | 4.28 | (1.47) | (2.27) | (3.19) | (3.45) | (3.14) | (3.14) | (2.00) | (2.88) | (3.21) | (3.39) | (3.21) | (3.29) | 1.6 | 1.59 | 2.32 | 3.63 | 3.08 | 3.03 | 3.25 | 2.04 | 3.09 | 3.62 | 3.28 | 3.22 | 3.38 | (1.21) | (1.83) | (2.51) | (2.71) | (2.45) | (2.38) | (1.63) | (2.30) | (2.49) | (2.66) | (2.47) | (2.48) | 1.7 | 1.46 | 2.04 | 3.04 | 2.57 | 2.54 | 2.71 | 1.83 | 2.62 | 3.04 | 2.69 | 2.67 | 2.81 | (1.04) | (1.55) | (2.05) | (2.21) | (1.98) | (1.91) | (1.38) | (1.90) | (2.03) | (2.14) | (1.97) | (1.99) | 1.8 | 1.37 | 1.84 | 2.63 | 2.21 | 2.19 | 2.35 | 1.65 | 2.31 | 2.62 | 2.31 | 2.31 | 2.43 | (0.91) | (1.35) | (1.74) | (1.83) | (1.64) | (1.59) | (1.19) | (1.63) | (1.72) | (1.78) | (1.65) | (1.64) | 1.9 | 1.30 | 1.68 | 2.33 | 1.94 | 1.93 | 2.07 | 1.54 | 2.09 | 2.32 | 2.05 | 2.04 | 2.15 | (0.81) | (1.19) | (1.53) | (1.55) | (1.37) | (1.35) | (1.07) | (1.45) | (1.51) | (1.54) | (1.40) | (1.39) | 2 | 1.25 | 1.57 | 2.10 | 1.74 | 1.76 | 1.89 | 1.45 | 1.90 | 2.09 | 1.84 | 1.84 | 1.93 | (0.73) | (1.07) | (1.36) | (1.32) | (1.19) | (1.17) | (0.97) | (1.30) | (1.32) | (1.32) | (1.21) | (1.20) | | 14.54 | 18.08 | 23.82 | 22.35 | 22.42 | 23.55 | 16.74 | 21.68 | 24.31 | 23.27 | 23.43 | 24.62 | | 1.00 | 1.24 | 1.64 | 1.54 | 1.54 | 1.62 | 1.00 | 1.30 | 1.45 | 1.39 | 1.40 | 1.47 | | 1.00 | 1.66 | 2.77 | 2.46 | 2.45 | 2.67 | 1.00 | 1.61 | 1.94 | 1.77 | 1.78 | 1.92 |
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