Research Article
New One-Sided EWMA t Charts without and with Variable Sampling Intervals for Monitoring the Process Mean
Table 4
The (ARL, MRL, SDRL) profiles of two upper-sided EWMA t charts when ARL0 = 200 and n ∈ {9, 11}.
| | N | λ | Chart | UCL+ | δ | | 0 | 0.1 | 0.3 | 0.5 | 0.7 | 1.0 | 1.5 | 2 | 3 |
| | 9 | 0.1 | U-EWMA | 0.6310 | (200.00 | 141 | 193.36) | (42.85 | 32 | 35.95) | (9.93 | 9 | 5.17) | (5.35 | 5 | 2.07) | (3.72 | 4 | 1.22) | (2.63 | 3 | 0.76) | (1.88 | 2 | 0.50) | (1.52 | 2 | 0.50) | (1.06 | 1 | 0.24) | | U-NEWMA | 0.5614 | (200.17 | 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) | (1.36 | 1 | 0.48) | (1.02 | 1 | 0.15) | | 0.2 | U-EWMA | 1.0009 | (200.00 | 140 | 196.43) | (52.95 | 38 | 48.86) | (10.44 | 9 | 6.92) | (4.97 | 5 | 2.38) | (3.29 | 3 | 1.28) | (2.26 | 2 | 0.74) | (1.60 | 2 | 0.52) | (1.23 | 1 | 0.42) | (1.00 | 1 | 0.08) | | U-NEWMA | 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) | (1.16 | 1 | 0.36) | (1.02 | 1 | 0.15) | | 0.3 | U-EWMA | 1.3200 | (200.00 | 139 | 197.67) | (62.75 | 44 | 59.99) | (12.00 | 9 | 9.24) | (5.09 | 4 | 2.89) | (3.17 | 3 | 1.42) | (2.10 | 2 | 0.77) | (1.44 | 1 | 0.51) | (1.12 | 1 | 0.33) | (1.00 | 1 | 0.03) | | U-NEWMA | 1.2367 | (200.65 | 140 | 199.17) | (54.12 | 38 | 51.22) | (10.42 | 8 | 7.82) | (4.60 | 4 | 2.57) | (2.93 | 3 | 1.31) | (1.98 | 2 | 0.73) | (1.36 | 1 | 0.49) | (1.08 | 1 | 0.28) | (1.00 | 1 | 0.02) | | 0.4 | U-EWMA | 1.6190 | (200.00 | 139 | 198.33) | (71.53 | 50 | 69.55) | (14.21 | 11 | 12.03) | (5.49 | 5 | 3.60) | (3.20 | 3 | 1.64) | (2.02 | 2 | 0.82) | (1.34 | 1 | 0.49) | (1.07 | 1 | 0.26) | (1.00 | 1 | 0.02) | | U-NEWMA | 1.5315 | (200.66 | 140 | 198.85) | (63.18 | 44 | 61.47) | (12.25 | 9 | 10.14) | (4.94 | 4 | 3.15) | (2.97 | 3 | 1.51) | (1.91 | 2 | 0.78) | (1.28 | 1 | 0.46) | (1.05 | 1 | 0.22) | (1.00 | 1 | 0.01) | | 0.5 | U-EWMA | 1.9095 | (200.00 | 139 | 198.74) | (79.11 | 55 | 77.62) | (16.88 | 12 | 15.16) | (6.13 | 5 | 4.52) | (3.34 | 3 | 1.95) | (1.99 | 2 | 0.90) | (1.28 | 1 | 0.47) | (1.05 | 1 | 0.22) | (1.00 | 1 | 0.01) | | U-NEWMA | 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) | (1.04 | 1 | 0.19) | (1.00 | 1 | 1.01) | | 0.75 | U-EWMA | 2.6283 | (200.00 | 139 | 199.27) | (92.94 | 65 | 92.13) | (24.25 | 17 | 23.32) | (8.57 | 6 | 7.58) | (4.10 | 3 | 3.14) | (2.07 | 2 | 1.22) | (1.22 | 1 | 0.45) | (1.03 | 1 | 0.16) | (1.00 | 1 | 0.00) | | U-NEWMA | 2.5577 | (199.74 | 140 | 198.68) | (87.52 | 61 | 86.51) | (22.06 | 16 | 20.97) | (7.90 | 6 | 6.94) | (3.83 | 3 | 2.88) | (1.98 | 2 | 1.15) | (1.19 | 1 | 0.42) | (1.02 | 1 | 0.14) | (1.00 | 1 | 0.01) | | 0.9 | U-EWMA | 3.0630 | (200.00 | 139 | 199.43) | (98.33 | 68 | 97.73) | (28.30 | 20 | 27.66) | (10.36 | 7 | 9.68) | (4.80 | 4 | 4.11) | (2.21 | 2 | 1.52) | (1.20 | 1 | 0.47) | (1.02 | 1 | 0.15) | (1.00 | 1 | 0.00) | | U-NEWMA | 3.0280 | (199.70 | 138 | 200.64) | (96.41 | 67 | 95.33) | (27.38 | 19 | 26.68) | (9.96 | 7 | 9.29) | (4.64 | 3 | 3.98) | (2.16 | 2 | 1.52) | (1.20 | 1 | 0.49) | (1.02 | 1 | 0.14) | (1.00 | 1 | 0.00) | | 1.0 | U-EWMA | 3.3554 | (200.00 | 139 | 199.50) | (101.01 | 70 | 100.51) | (30.62 | 21 | 30.12) | (11.54 | 8 | 11.03) | (5.33 | 4 | 4.80) | (2.34 | 2 | 1.77) | (1.20 | 1 | 0.49) | (1.02 | 1 | 0.14) | (1.00 | 1 | 0.00) | | U-NEWMA | 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) | (1.02 | 1 | 0.14) | (1.00 | 1 | 0.00) | | 11 | 0.1 | U-EWMA | 0.6101 | (200.00 | 141 | 193.18) | (36.98 | 28 | 30.12) | (8.57 | 8 | 4.14) | (4.70 | 4 | 1.69) | (3.30 | 3 | 1.01) | (2.36 | 2 | 0.64) | (1.73 | 2 | 0.48) | (1.34 | 1 | 0.47) | (1.01 | 1 | 0.10) | | U-NEWMA | 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 | 0.04) | | 0.2 | U-EWMA | 0.9631 | (200.00 | 140 | 196.25) | (45.16 | 33 | 40.99) | (8.63 | 7 | 5.30) | (4.24 | 4 | 1.87) | (2.87 | 3 | 1.03) | (2.02 | 2 | 0.62) | (1.42 | 1 | 0.50) | (1.09 | 1 | 0.29) | (1.00 | 1 | 0.02) | | U-NEWMA | 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) | | 0.3 | U-EWMA | 1.2645 | (200.00 | 139 | 197.52) | (53.57 | 38 | 50.69) | (9.53 | 8 | 6.87) | (4.21 | 4 | 2.17) | (2.71 | 3 | 1.11) | (1.84 | 2 | 0.64) | (1.26 | 1 | 0.44) | (1.03 | 1 | 0.18) | (1.00 | 1 | 0.00) | | U-NEWMA | 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) | | 0.4 | U-EWMA | 1.5450 | (200.00 | 139 | 198.22) | (61.51 | 43 | 59.41) | (10.96 | 8 | 8.81) | (4.38 | 4 | 2.61) | (2.66 | 2 | 1.24) | (1.75 | 2 | 0.67) | (1.18 | 1 | 0.39) | (1.02 | 1 | 0.13) | (1.00 | 1 | 0.00) | | U-NEWMA | 1.4634 | (201.39 | 140 | 200.23) | (54.05 | 38 | 52.27) | (9.56 | 7 | 7.56) | (4.01 | 3 | 2.34) | (2.49 | 2 | 1.15) | (1.66 | 2 | 0.64) | (1.14 | 1 | 0.35) | (1.01 | 1 | 0.10) | (1.00 | 1 | 0.00) | | 0.5 | U-EWMA | 1.8166 | (200.00 | 139 | 198.66) | (68.71 | 48 | 67.13) | (12.80 | 9 | 11.06) | (4.72 | 4 | 3.18) | (2.69 | 2 | 1.41) | (1.69 | 2 | 0.70) | (1.13 | 1 | 0.34) | (1.01 | 1 | 0.09) | (1.00 | 1 | 0.00) | | U-NEWMA | 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) | | 0.75 | U-EWMA | 2.4879 | (200.00 | 139 | 199.24) | (82.85 | 58 | 82.00) | (18.48 | 13 | 17.50) | (6.22 | 5 | 5.23) | (3.05 | 2 | 2.12) | (1.65 | 1 | 0.84) | (1.08 | 1 | 0.28) | (1.00 | 1 | 0.06) | (1.00 | 1 | 0.00) | | U-NEWMA | 2.4219 | (201.80 | 141 | 200.15) | (77.92 | 54 | 77.35) | (16.78 | 12 | 15.80) | (5.75 | 4 | 4.76) | (2.88 | 2 | 1.97) | (1.60 | 1 | 0.81) | (1.07 | 1 | 0.26) | (1.00 | 1 | 0.05) | (1.00 | 1 | 0.00) | | 0.9 | U-EWMA | 2.8949 | (200.00 | 139 | 199.42) | (88.72 | 62 | 88.11) | (21.96 | 15 | 21.30) | (7.47 | 5 | 6.78) | (3.44 | 3 | 2.75) | (1.69 | 1 | 1.00) | (1.07 | 1 | 0.27) | (1.00 | 1 | 0.05) | (1.00 | 1 | 0.00) | | U-NEWMA | 2.8575 | (199.58 | 139 | 199.33) | (86.06 | 60 | 85.47) | (21.02 | 15 | 20.39) | (7.14 | 5 | 6.44) | (3.33 | 3 | 2.64) | (1.66 | 1 | 0.97) | (1.07 | 1 | 0.26) | (1.00 | 1 | 0.05) | (1.00 | 1 | 0.00) | | 1.0 | U-EWMA | 3.1693 | (200.00 | 139 | 199.50) | (91.69 | 64 | 91.19) | (24.06 | 17 | 23.56) | (8.36 | 6 | 7.85) | (3.76 | 3 | 3.23) | (1.74 | 1 | 1.13) | (1.07 | 1 | 0.27) | (1.00 | 1 | 0.05) | (1.00 | 1 | 0.00) | | U-NEWMA | 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) |
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