Research Article
An Efficient Robust Nonparametric Triple EWMA Wilcoxon Signed-Rank Control Chart for Process Location
Table 4
RL characteristics of the proposed
control chart under different distributions with nominal
and
.
| | | | | | | | 0.00 | 0.025 | 0.03 | 0.05 | 0.075 | 0.10 | 0.15 | 0.20 | 0.25 | 0.50 | 0.75 | 1.00 | 1.50 | 2.00 |
| | (0.05, 1.3635) | N(0, 1) | ARL | 369.61 | 96.01 | 71.86 | 34.99 | 19.89 | 12.62 | 6.24 | 3.75 | 2.47 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | | MDRL | 240.0 | 67.0 | 54.0 | 29.0 | 16.0 | 10.0 | 5.0 | 3.0 | 2.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | | SDRL | 418.41 | 101.64 | 70.49 | 30.60 | 16.96 | 10.99 | 5.50 | 3.19 | 1.95 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | | CN | ARL | 369.54 | 98.54 | 77.99 | 37.52 | 20.21 | 13.22 | 6.20 | 3.85 | 2.65 | 1.11 | 1.01 | 1.00 | 1.00 | 1.00 | | MDRL | 244.00 | 69.00 | 61.00 | 32.00 | 16.00 | 11.00 | 5.00 | 3.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 429.63 | 102.05 | 74.36 | 31.93 | 17.22 | 11.36 | 5.24 | 3.25 | 2.18 | 0.37 | 0.07 | 0.00 | 0.00 | 0.00 | | Logistic | ARL | 370.04 | 85.10 | 65.60 | 30.63 | 16.53 | 10.77 | 5.08 | 3.09 | 2.19 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | | MDRL | 215.50 | 64.00 | 53.00 | 25.00 | 13.00 | 8.00 | 4.00 | 2.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 451.55 | 83.95 | 61.17 | 27.07 | 14.16 | 9.51 | 4.44 | 2.54 | 1.64 | 0.26 | 0.04 | 0.00 | 0.00 | 0.00 | | Laplace | ARL | 371.04 | 65.82 | 51.95 | 23.68 | 12.32 | 7.75 | 4.03 | 2.36 | 1.74 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | | MDRL | 218.00 | 55.00 | 42.00 | 19.00 | 9.00 | 6.00 | 3.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 452.29 | 61.73 | 46.09 | 20.99 | 11.01 | 6.81 | 3.50 | 1.90 | 1.19 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | | ARL | 370.73 | 116.79 | 91.87 | 43.49 | 24.36 | 15.90 | 7.42 | 4.85 | 3.29 | 1.23 | 1.02 | 1.00 | 1.00 | 1.00 | | MDRL | 228.50 | 84.00 | 69.00 | 35.00 | 20.00 | 13.00 | 5.00 | 4.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 421.19 | 125.85 | 92.98 | 40.01 | 20.16 | 13.58 | 6.69 | 4.04 | 2.71 | 0.54 | 0.14 | 0.00 | 0.00 | 0.00 | | ARL | 369.67 | 107.75 | 85.82 | 40.15 | 23.71 | 14.78 | 7.08 | 4.29 | 2.87 | 1.11 | 1.01 | 1.00 | 1.00 | 1.00 | | MDRL | 225.00 | 77.00 | 65.00 | 33.00 | 20.00 | 12.00 | 5.00 | 3.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 441.35 | 113.15 | 83.92 | 36.90 | 18.63 | 12.45 | 6.15 | 3.58 | 2.35 | 0.39 | 0.09 | 0.00 | 0.00 | 0.00 |
| | (0.10, 1.57) | N(0, 1) | ARL | 369.43 | 109.52 | 84.48 | 39.80 | 21.08 | 13.55 | 6.82 | 4.30 | 2.87 | 1.13 | 1.00 | 1.00 | 1.00 | 1.00 | | MDRL | 242.50 | 76.00 | 61.00 | 33.00 | 18.00 | 12.00 | 6.00 | 4.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 401.47 | 109.19 | 79.78 | 32.99 | 16.75 | 10.21 | 5.30 | 3.26 | 2.14 | 0.39 | 0.04 | 0.00 | 0.00 | 0.00 | | CN | ARL | 369.18 | 117.33 | 91.87 | 41.32 | 23.19 | 14.61 | 7.15 | 4.58 | 3.14 | 1.17 | 1.01 | 1.00 | 1.00 | 1.00 | | MDRL | 244.50 | 84.00 | 68.00 | 32.50 | 21.00 | 13.00 | 6.00 | 4.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 401.76 | 115.00 | 87.66 | 36.27 | 16.79 | 10.75 | 5.59 | 3.48 | 2.30 | 0.46 | 0.07 | 0.00 | 0.00 | 0.00 | | Logistic | ARL | 369.92 | 104.66 | 73.89 | 35.34 | 19.33 | 12.30 | 6.06 | 3.73 | 2.46 | 1.09 | 1.00 | 1.00 | 1.00 | 1.00 | | MDRL | 243.00 | 77.00 | 54.00 | 29.50 | 17.00 | 10.00 | 5.00 | 3.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 419.02 | 99.93 | 71.94 | 29.90 | 14.51 | 9.21 | 4.56 | 2.78 | 1.76 | 0.33 | 0.06 | 0.00 | 0.00 | 0.00 | | Laplace | ARL | 369.92 | 80.30 | 57.70 | 25.08 | 13.95 | 8.93 | 4.65 | 2.88 | 2.01 | 1.08 | 1.00 | 1.00 | 1.00 | 1.00 | | MDRL | 243.00 | 60.00 | 45.00 | 22.00 | 12.00 | 7.50 | 4.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 419.02 | 73.03 | 52.34 | 19.71 | 10.63 | 6.76 | 3.66 | 2.16 | 1.38 | 0.29 | 0.07 | 0.00 | 0.00 | 0.00 | | ARL | 370.86 | 137.04 | 109.45 | 50.21 | 25.91 | 17.07 | 9.22 | 5.67 | 3.94 | 1.33 | 1.04 | 1.00 | 1.00 | 1.00 | | MDRL | 251.00 | 98.00 | 80.00 | 39.00 | 23.00 | 15.00 | 8.00 | 5.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 388.38 | 138.72 | 108.92 | 43.31 | 19.84 | 12.63 | 6.93 | 4.30 | 3.07 | 0.66 | 0.20 | 0.05 | 0.00 | 0.00 | | ARL | 370.56 | 126.76 | 101.54 | 48.45 | 23.01 | 15.84 | 8.16 | 5.04 | 3.33 | 1.21 | 1.01 | 1.00 | 1.00 | 1.00 | | MDRL | 257.50 | 87.00 | 68.50 | 38.00 | 20.00 | 14.00 | 7.00 | 4.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 387.66 | 130.74 | 104.01 | 41.84 | 17.88 | 11.16 | 6.14 | 3.68 | 2.39 | 0.53 | 0.10 | 0.00 | 0.00 | 0.00 |
| | (0.25, 1.867) | N(0, 1) | ARL | 370.25 | 148.30 | 114.50 | 53.87 | 26.46 | 15.29 | 7.57 | 4.94 | 3.56 | 1.25 | 1.02 | 1.00 | 1.00 | 1.00 | | MDRL | 271.50 | 103.00 | 78.00 | 40.00 | 20.00 | 13.00 | 7.00 | 4.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 353.98 | 143.90 | 113.04 | 49.08 | 22.94 | 11.38 | 5.06 | 2.97 | 2.09 | 0.52 | 0.13 | 0.00 | 0.00 | 0.00 | | CN | ARL | 371.05 | 154.57 | 129.10 | 59.23 | 26.81 | 16.47 | 7.95 | 5.34 | 3.66 | 1.30 | 1.02 | 1.00 | 1.00 | 1.00 | | MDRL | 255.50 | 105.50 | 90.00 | 44.00 | 21.00 | 14.00 | 7.00 | 5.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 383.00 | 152.56 | 124.95 | 56.42 | 22.54 | 12.56 | 4.99 | 3.36 | 2.09 | 0.56 | 0.14 | 0.00 | 0.00 | 0.00 | | Logistic | ARL | 369.80 | 142.12 | 110.97 | 45.00 | 22.01 | 13.10 | 6.86 | 4.23 | 3.03 | 1.20 | 1.01 | 1.00 | 1.00 | 1.00 | | MDRL | 249.00 | 97.00 | 78.00 | 32.00 | 18.00 | 11.00 | 6.00 | 4.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 402.95 | 147.38 | 102.81 | 41.45 | 16.83 | 9.21 | 4.22 | 2.72 | 1.85 | 0.46 | 0.09 | 0.03 | 0.00 | 0.00 | | Laplace | ARL | 369.80 | 111.92 | 78.38 | 33.46 | 16.67 | 9.76 | 5.28 | 3.30 | 2.50 | 1.14 | 1.02 | 1.00 | 1.00 | 1.00 | | MDRL | 249.00 | 81.00 | 54.00 | 26.00 | 14.00 | 9.00 | 5.00 | 3.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 402.95 | 105.95 | 75.98 | 28.81 | 12.94 | 6.80 | 3.23 | 2.04 | 1.50 | 0.37 | 0.14 | 0.00 | 0.00 | 0.00 | | ARL | 368.97 | 186.35 | 140.23 | 71.38 | 34.86 | 19.43 | 9.78 | 6.19 | 4.22 | 1.56 | 1.09 | 1.01 | 1.00 | 1.00 | | MDRL | 262.00 | 131.00 | 97.50 | 50.00 | 26.00 | 16.00 | 9.00 | 6.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 359.24 | 181.23 | 140.44 | 67.16 | 29.67 | 14.58 | 6.51 | 4.05 | 2.63 | 0.79 | 0.30 | 0.11 | 0.00 | 0.00 | | ARL | 371.13 | 177.20 | 148.49 | 62.09 | 30.50 | 17.80 | 9.01 | 5.81 | 3.75 | 1.41 | 1.04 | 1.00 | 1.00 | 1.00 | | MDRL | 259.00 | 125.00 | 101.50 | 44.50 | 23.00 | 15.00 | 8.00 | 5.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 367.57 | 173.08 | 155.73 | 54.46 | 25.64 | 13.55 | 5.73 | 3.45 | 2.21 | 0.69 | 0.20 | 0.05 | 0.00 | 0.00 |
| | (0.50, 2.1185) | N(0, 1) | ARL | 370.25 | 203.92 | 181.53 | 81.69 | 39.73 | 21.85 | 8.99 | 5.16 | 3.64 | 1.35 | 1.02 | 1.00 | 1.00 | 1.00 | | MDRL | 261.00 | 144.00 | 131.50 | 55.00 | 29.00 | 16.00 | 7.00 | 5.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 361.13 | 203.76 | 174.27 | 81.56 | 36.79 | 19.27 | 6.49 | 3.35 | 2.03 | 0.56 | 0.15 | 0.00 | 0.00 | 0.00 | | CN | ARL | 371.05 | 220.20 | 176.01 | 89.51 | 45.28 | 23.66 | 9.17 | 5.40 | 3.82 | 1.40 | 1.05 | 1.00 | 1.00 | 1.00 | | MDRL | 266.50 | 144.00 | 129.50 | 63.00 | 33.00 | 17.00 | 7.00 | 5.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 355.54 | 224.64 | 167.97 | 86.11 | 44.09 | 20.66 | 6.81 | 3.40 | 2.19 | 0.59 | 0.21 | 0.04 | 0.00 | 0.00 | | Logistic | ARL | 369.71 | 207.36 | 144.94 | 72.68 | 33.57 | 18.75 | 7.77 | 4.62 | 3.28 | 1.26 | 1.01 | 1.00 | 1.00 | 1.00 | | MDRL | 262.00 | 140.50 | 107.50 | 53.00 | 25.00 | 15.00 | 7.00 | 4.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 389.82 | 220.88 | 139.79 | 69.42 | 31.08 | 15.69 | 5.48 | 2.89 | 1.81 | 0.49 | 0.12 | 0.04 | 0.00 | 0.00 | | Laplace | ARL | 369.71 | 165.97 | 118.11 | 47.01 | 21.84 | 12.14 | 5.65 | 3.50 | 2.55 | 1.22 | 1.02 | 1.00 | 1.00 | 1.00 | | MDRL | 262.00 | 112.00 | 81.50 | 33.50 | 16.00 | 9.00 | 5.00 | 3.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 389.82 | 177.25 | 114.36 | 42.64 | 19.12 | 9.66 | 3.58 | 2.00 | 1.38 | 0.45 | 0.14 | 0.05 | 0.00 | 0.00 | | ARL | 369.17 | 242.08 | 202.82 | 104.20 | 55.12 | 29.44 | 12.56 | 7.09 | 4.64 | 1.64 | 1.12 | 1.03 | 1.00 | 1.00 | | MDRL | 261.50 | 172.00 | 141.00 | 76.00 | 38.00 | 22.00 | 9.00 | 6.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 359.03 | 241.26 | 199.81 | 101.71 | 54.08 | 26.61 | 10.82 | 4.73 | 2.73 | 0.79 | 0.34 | 0.16 | 0.04 | 0.00 | | ARL | 369.74 | 240.61 | 203.22 | 99.49 | 48.13 | 26.55 | 10.96 | 5.74 | 4.13 | 1.56 | 1.06 | 1.01 | 1.00 | 1.00 | | MDRL | 253.00 | 173.00 | 138.00 | 67.00 | 34.50 | 20.00 | 9.00 | 5.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | SDRL | 366.34 | 229.90 | 209.30 | 100.88 | 44.50 | 24.28 | 8.71 | 3.80 | 2.32 | 0.74 | 0.24 | 0.08 | 0.00 | 0.00 |
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