Research Article
Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling
Table 1
RL characteristics of the proposed
control chart under different distributions with nominal
and
.
| | (, L) | Distr. | Metrics | | | 0 | 0.025 | 0.05 | 0.075 | 0.1 | 0.25 | 0.5 | 0.75 | 1 | 1.5 | 2 | 2.5 | 3 | 5 |
| | (0.05, 1.064) | Normal | ARL | 499.49 | 31.74 | 13.25 | 7.96 | 5.65 | 1.94 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 12.00 | 9.00 | 7.00 | 5.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 1,851.30 | 55.84 | 17.04 | 8.31 | 5.23 | 1.33 | 0.31 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| | | CN | ARL | 503.08 | 34.36 | 13.86 | 8.41 | 5.84 | 2.02 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 12.00 | 9.00 | 7.00 | 5.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 1,890.28 | 61.32 | 18.38 | 9.16 | 5.56 | 1.40 | 0.37 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(4) | ARL | 498.70 | 40.62 | 16.39 | 9.83 | 6.64 | 2.30 | 1.14 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 11.00 | 10.00 | 7.00 | 6.00 | 5.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 1,850.07 | 74.61 | 22.42 | 11.14 | 6.56 | 1.63 | 0.53 | 0.13 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(8) | ARL | 499.22 | 36.60 | 14.81 | 8.75 | 6.19 | 2.11 | 1.09 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 12.00 | 10.00 | 7.00 | 5.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 1,852.41 | 68.10 | 19.91 | 9.73 | 5.93 | 1.48 | 0.43 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Laplace | ARL | 498.40 | 24.06 | 9.46 | 5.83 | 4.23 | 1.55 | 1.02 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 13.00 | 9.00 | 6.00 | 4.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 1,856.38 | 37.19 | 10.66 | 5.45 | 3.50 | 1.01 | 0.19 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Logistic | ARL | 498.55 | 30.34 | 12.03 | 7.21 | 5.21 | 1.82 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 12.00 | 9.00 | 6.00 | 5.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 1,869.47 | 50.49 | 14.94 | 7.38 | 4.64 | 1.23 | 0.27 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| | (0.10, 1.306) | Normal | ARL | 499.48 | 61.76 | 21.72 | 11.82 | 7.79 | 2.46 | 1.12 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 81.00 | 28.00 | 13.00 | 8.00 | 6.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 781.09 | 80.85 | 23.95 | 11.14 | 6.59 | 1.52 | 0.45 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | CN | ARL | 499.16 | 65.72 | 23.07 | 12.44 | 8.17 | 2.55 | 1.15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 78.00 | 29.00 | 14.00 | 8.00 | 6.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 772.97 | 86.04 | 25.58 | 11.96 | 6.97 | 1.58 | 0.51 | 0.08 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(4) | ARL | 498.28 | 79.24 | 27.20 | 14.72 | 9.64 | 2.92 | 1.31 | 1.03 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 83.00 | 34.00 | 16.00 | 10.00 | 7.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 779.49 | 105.11 | 30.95 | 14.68 | 8.63 | 1.83 | 0.72 | 0.22 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(8) | ARL | 499.07 | 70.30 | 24.31 | 12.99 | 8.66 | 2.67 | 1.20 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 87.00 | 30.00 | 14.00 | 9.00 | 6.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 781.02 | 94.06 | 27.71 | 12.61 | 7.60 | 1.65 | 0.58 | 0.12 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Laplace | ARL | 499.21 | 42.49 | 14.75 | 8.18 | 5.54 | 1.90 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 81.00 | 22.00 | 10.00 | 6.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 780.79 | 51.83 | 14.91 | 6.94 | 4.26 | 1.18 | 0.30 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Logistic | ARL | 498.88 | 57.01 | 19.44 | 10.56 | 7.02 | 2.26 | 1.09 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 82.00 | 27.50 | 12.00 | 7.00 | 5.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 771.67 | 72.06 | 21.01 | 9.77 | 5.65 | 1.40 | 0.38 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | (0.25, 2.113) | Normal | ARL | 502.19 | 132.32 | 49.74 | 26.33 | 16.57 | 4.07 | 1.58 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 435.00 | 112.00 | 44.00 | 23.00 | 15.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 369.43 | 96.29 | 33.30 | 16.99 | 10.30 | 1.98 | 0.91 | 0.25 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | CN | ARL | 500.19 | 137.93 | 52.65 | 27.93 | 17.65 | 4.27 | 1.68 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 432.00 | 118.00 | 46.00 | 25.00 | 16.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 368.45 | 100.15 | 35.14 | 18.15 | 10.96 | 2.08 | 0.96 | 0.33 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(4) | ARL | 499.91 | 160.20 | 61.99 | 33.15 | 21.17 | 4.96 | 2.02 | 1.22 | 1.03 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 434.00 | 136.00 | 54.00 | 30.00 | 19.00 | 5.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 365.58 | 115.71 | 42.60 | 21.67 | 13.36 | 2.51 | 1.12 | 0.60 | 0.24 | 0.04 | 0.01 | 0.00 | 0.00 | 0.00 | | | t(8) | ARL | 498.30 | 145.75 | 55.91 | 29.76 | 18.82 | 4.52 | 1.82 | 1.10 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 428.00 | 123.00 | 49.00 | 26.00 | 17.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 366.98 | 107.89 | 37.87 | 19.27 | 11.84 | 2.27 | 1.02 | 0.41 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Laplace | ARL | 501.05 | 92.85 | 33.30 | 17.52 | 10.99 | 3.07 | 1.33 | 1.03 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 435.00 | 80.00 | 30.00 | 16.00 | 10.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 368.41 | 64.68 | 21.87 | 10.98 | 6.61 | 1.53 | 0.72 | 0.24 | 0.09 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | | | Logistic | ARL | 502.04 | 119.77 | 44.62 | 23.70 | 14.70 | 3.75 | 1.47 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 439.00 | 103.00 | 39.00 | 21.00 | 13.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 364.68 | 85.82 | 29.84 | 14.94 | 9.23 | 1.78 | 0.83 | 0.25 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| | (0.50, 2.376) | Normal | ARL | 498.71 | 201.01 | 70.69 | 34.34 | 20.17 | 4.26 | 1.67 | 1.08 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 355.00 | 147.00 | 55.00 | 28.00 | 17.00 | 4.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 482.39 | 184.95 | 58.24 | 25.76 | 13.71 | 2.05 | 0.76 | 0.28 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | CN | ARL | 497.95 | 210.08 | 75.05 | 36.35 | 21.56 | 4.49 | 1.76 | 1.12 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 349.00 | 155.00 | 58.00 | 30.00 | 18.00 | 4.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 486.93 | 191.48 | 62.24 | 27.33 | 14.78 | 2.20 | 0.80 | 0.33 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(4) | ARL | 499.23 | 234.12 | 89.78 | 44.68 | 26.26 | 5.37 | 2.08 | 1.29 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 353.00 | 172.00 | 68.00 | 36.00 | 22.00 | 5.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 483.45 | 216.30 | 76.45 | 34.47 | 18.70 | 2.80 | 0.93 | 0.53 | 0.25 | 0.05 | 0.01 | 0.01 | 0.00 | 0.00 | | | t(8) | ARL | 501.84 | 220.42 | 79.56 | 39.20 | 23.38 | 4.77 | 1.88 | 1.16 | 1.02 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 355.50 | 160.50 | 60.00 | 31.00 | 20.00 | 4.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 490.89 | 206.08 | 67.97 | 29.98 | 16.20 | 2.36 | 0.85 | 0.40 | 0.13 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | | | Laplace | ARL | 498.36 | 142.19 | 44.47 | 21.30 | 12.97 | 3.14 | 1.39 | 1.06 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 351.00 | 106.00 | 36.00 | 18.00 | 11.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 489.74 | 126.58 | 33.90 | 14.60 | 8.05 | 1.41 | 0.62 | 0.24 | 0.07 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | | | Logistic | ARL | 499.28 | 186.35 | 62.61 | 29.79 | 17.68 | 3.84 | 1.56 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 358.00 | 138.00 | 49.00 | 25.00 | 15.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 479.40 | 170.70 | 50.14 | 21.40 | 12.02 | 1.76 | 0.71 | 0.26 | 0.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
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