Research Article
Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling
Table 6
RL characteristics of the
control chart under various 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, 2.011) | Normal | ARL | 502.18 | 126.47 | 47.44 | 24.83 | 15.55 | 3.86 | 1.56 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 450.00 | 108.00 | 41.00 | 22.00 | 14.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 369.20 | 93.57 | 32.86 | 16.66 | 10.06 | 1.91 | 0.87 | 0.24 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| | | CN | ARL | 498.95 | 131.67 | 49.92 | 26.01 | 16.50 | 4.06 | 1.65 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 447.00 | 114.00 | 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 | 354.98 | 96.62 | 35.19 | 17.65 | 10.85 | 2.00 | 0.93 | 0.31 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Laplace | ARL | 503.02 | 89.97 | 31.42 | 16.34 | 10.24 | 2.93 | 1.31 | 1.03 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 447.00 | 78.00 | 28.00 | 14.00 | 9.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 357.84 | 66.10 | 21.28 | 10.81 | 6.45 | 1.46 | 0.69 | 0.20 | 0.07 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | | | Logistic | ARL | 502.13 | 115.25 | 42.13 | 22.17 | 13.63 | 3.57 | 1.45 | 1.03 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 447.00 | 99.00 | 36.00 | 19.00 | 12.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 357.84 | 83.49 | 29.56 | 14.54 | 8.81 | 1.75 | 0.81 | 0.23 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(4) | ARL | 503.11 | 153.20 | 59.65 | 31.34 | 19.66 | 4.77 | 1.97 | 1.22 | 1.03 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 449.00 | 130.00 | 52.00 | 27.00 | 17.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 361.52 | 115.04 | 42.01 | 21.93 | 13.15 | 2.47 | 1.07 | 0.59 | 0.23 | 0.02 | 0.03 | 0.00 | 0.00 | 0.00 | | | t(8) | ARL | 500.36 | 138.20 | 53.18 | 28.35 | 17.56 | 4.24 | 1.74 | 1.10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 437.00 | 115.50 | 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 | 369.84 | 105.14 | 36.77 | 19.05 | 11.45 | 2.15 | 0.98 | 0.40 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | (0.10, 2.268) | Normal | ARL | 501.08 | 141.18 | 53.78 | 28.36 | 17.91 | 4.33 | 1.69 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 416.00 | 116.00 | 47.00 | 25.00 | 16.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 409.43 | 104.61 | 35.48 | 17.45 | 10.47 | 2.03 | 0.92 | 0.30 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | CN | ARL | 498.89 | 188.39 | 84.69 | 47.51 | 31.26 | 7.05 | 2.63 | 1.35 | 1.10 | 1.02 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 401.00 | 123.00 | 49.00 | 27.00 | 17.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 392.85 | 106.58 | 37.05 | 18.45 | 11.47 | 2.12 | 0.97 | 0.36 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Laplace | ARL | 499.36 | 100.25 | 35.70 | 18.93 | 11.97 | 3.22 | 1.42 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 409.00 | 84.00 | 32.00 | 17.00 | 11.00 | 3.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 401.09 | 72.33 | 22.59 | 11.48 | 6.81 | 1.50 | 0.76 | 0.27 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | Logistic | ARL | 500.14 | 129.12 | 47.66 | 25.23 | 15.93 | 3.92 | 1.58 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 409.00 | 108.00 | 41.00 | 22.00 | 14.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 401.09 | 94.77 | 31.64 | 15.46 | 9.24 | 1.78 | 0.86 | 0.25 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | t(4) | ARL | 498.01 | 169.35 | 66.27 | 36.09 | 22.57 | 5.34 | 2.19 | 1.28 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 398.50 | 141.00 | 56.00 | 32.00 | 20.00 | 5.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 395.19 | 124.85 | 45.22 | 22.77 | 13.46 | 2.65 | 1.12 | 0.63 | 0.27 | 0.03 | 0.01 | 0.00 | 0.00 | 0.00 | | | t(8) | ARL | 499.21 | 153.55 | 60.16 | 32.02 | 20.27 | 4.77 | 1.92 | 1.15 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | MDRL | 400.50 | 125.00 | 52.00 | 29.00 | 18.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | | | SDRL | 400.94 | 119.02 | 39.91 | 19.71 | 11.99 | 2.23 | 1.02 | 0.46 | 0.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
|
|
