Research Article
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) |
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