Table 1 Comparative analysis of existing EWMA and AEWMA-II with AEWMA-I ARL0 = 500 and p = 5.
From: Adaptive multivariate dispersion control chart with application to bimetal thermostat data
δ |  | ARL | SDRL | E (ARL) | P5th | P10th | P25th | P50th | P75th | P90th |
|---|---|---|---|---|---|---|---|---|---|---|
0.25 | EWMA | 5.26 | 1.27 | 5.06 | 4 | 4 | 5 | 6 | 7 | 8 |
AEWMA-II | 2.35 | 0.86 | 2.85 | 2 | 2 | 2 | 2 | 3 | 4 | |
AEWMA-I (proposed) | 4.44 | 1.31 | 4.64 | 2 | 4 | 4 | 5 | 6 | 6 | |
0.50 | EWMA | 13.63 | 7.27 | 13.03 | 6 | 9 | 12 | 17 | 23 | 28 |
AEWMA-II | 7.84 | 6.9 | 7.04 | 2 | 2 | 6 | 11 | 17 | 22 | |
AEWMA-I (proposed) | 10.6 | 5.13 | 9.66 | 5 | 7 | 10 | 13 | 18 | 21 | |
0.75 | EWMA | 82.5 | 74.19 | 80.25 | 16 | 30 | 60 | 111 | 179 | 231 |
AEWMA-II | 58.22 | 63.31 | 57.52 | 2 | 11 | 39 | 83 | 141 | 185 | |
AEWMA-I (proposed) | 39.9 | 23.58 | 40.39 | 12 | 22 | 37 | 54 | 72 | 83 | |
0.80 | EWMA | 137.96 | 129.97 | 138.9 | 22 | 46 | 99 | 188 | 307 | 398 |
AEWMA-II | 97.07 | 107.12 | 96.57 | 3 | 18 | 64 | 139 | 237 | 311 | |
AEWMA-I (proposed) | 55.94 | 33.58 | 54.34 | 16 | 31 | 51 | 75 | 101 | 118 | |
0.85 | EWMA | 237.03 | 229.11 | 237.93 | 32 | 74 | 167 | 325 | 534 | 697 |
AEWMA-II | 168.77 | 185.2 | 168.07 | 3 | 34 | 111 | 241 | 411 | 541 | |
AEWMA-I (proposed) | 82.65 | 51.66 | 82.05 | 23 | 45 | 75 | 111 | 151 | 179 | |
0.92 | EWMA | 480.14 | 473.16 | 481.24 | 57 | 144 | 337 | 663 | 1090 | 1430 |
AEWMA-II | 398.23 | 445.19 | 399.03 | 6 | 76 | 258 | 567 | 975 | 1286.05 | |
AEWMA-I (proposed) | 178.44 | 136.5 | 179.04 | 41 | 82 | 146 | 239 | 354 | 442 | |
1.00 | EWMA | 500.81 | 497.3 | 500.01 | 58 | 147 | 346 | 690 | 1149 | 1499.05 |
AEWMA-II | 502.14 | 553.11 | 500.40 | 7 | 102 | 331 | 713 | 1224 | 1610.05 | |
AEWMA-I (proposed) | 500.41 | 483.03 | 500.44 | 69 | 165 | 360 | 686 | 1128 | 1461 | |
1.03 | EWMA | 379.47 | 372.48 | 378.57 | 46 | 113 | 263 | 525 | 864 | 1131 |
AEWMA-II | 358.99 | 395.71 | 359.89 | 7 | 74 | 236 | 509 | 870.1 | 1147 | |
AEWMA-I (proposed) | 345.97 | 303.52 | 347.09 | 61 | 132 | 262 | 470 | 738 | 941 | |
1.05 | EWMA | 302.74 | 295.79 | 301.54 | 38 | 91 | 213 | 420 | 684 | 888.05 |
AEWMA-II | 272.41 | 298.34 | 272.31 | 6 | 57 | 178 | 385 | 667 | 878 | |
AEWMA-I (proposed) | 250.18 | 205.43 | 251.08 | 51 | 106 | 197 | 338 | 520 | 653 | |
1.08 | EWMA | 213.01 | 206.48 | 212.61 | 29 | 66 | 150 | 293 | 482 | 622 |
AEWMA-II | 180.11 | 193.38 | 180.01 | 6 | 40 | 120 | 255 | 435 | 565.05 | |
AEWMA-I (proposed) | 163.28 | 124.75 | 163.07 | 37 | 75 | 135 | 219 | 324 | 405 | |
1.10 | EWMA | 170.31 | 162.61 | 170.39 | 24 | 55 | 120 | 233 | 382 | 496 |
AEWMA-II | 140.36 | 150.01 | 140.76 | 5 | 32 | 94 | 198 | 336 | 441 | |
AEWMA-I (proposed) | 129.79 | 94.77 | 129.76 | 31 | 62 | 109 | 175 | 254 | 314 | |
1.15 | EWMA | 103.68 | 97.88 | 103.55 | 17 | 35 | 73 | 141 | 230 | 301 |
AEWMA-II | 80.98 | 84.08 | 80.66 | 4 | 20 | 56 | 114 | 192 | 249 | |
AEWMA-I (proposed) | 81.57 | 55.87 | 81.33 | 20 | 41 | 71 | 110 | 156 | 188 | |
1.30 | EWMA | 36.15 | 30.28 | 36.25 | 9 | 15 | 27 | 48 | 75 | 96 |
AEWMA-II | 26.92 | 26.16 | 26.99 | 2 | 8 | 19 | 38 | 62 | 79 | |
AEWMA-I (proposed) | 33.62 | 22.51 | 33.65 | 9 | 16 | 29 | 46 | 64 | 76 | |
1.75 | EWMA | 9.83 | 6.09 | 9.86 | 4 | 6 | 8 | 13 | 18 | 22 |
AEWMA-II | 6.73 | 5.55 | 6.79 | 2 | 2 | 5 | 9 | 14 | 18 | |
AEWMA-I (proposed) | 9.86 | 6.2 | 9.85 | 3 | 5 | 8 | 13 | 18 | 22 | |
3.50 | EWMA | 3.16 | 1.33 | 3.18 | 2 | 2 | 3 | 4 | 5 | 6 |
AEWMA-II | 2.37 | 0.89 | 2.35 | 2 | 2 | 2 | 2 | 3 | 4 | |
AEWMA-I (proposed) | 2.9 | 1.37 | 2.99 | 2 | 2 | 2 | 4 | 5 | 6 |
