Research Article
Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions
Table 3
IC ARL and constant multiplier
L of the Max-EWMA control chart when
, , , , , and
(0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50).
| | | | | | | | | | | | | | | | | |
| | = 370 | = 500 | | Case 1 | | = 290 | | 0.05 | 2.687 | 370.125 | 351.717 | 53.00 | 117.00 | 263.00 | 512.25 | 821.00 | 2.887 | 500.934 | 478.084 | 67.00 | 160.00 | 356.00 | 695.00 | 1128.00 | | 0.10 | 2.988 | 370.022 | 359.925 | 45.00 | 111.00 | 256.50 | 507.00 | 845.00 | 3.162 | 501.845 | 494.182 | 65.00 | 154.00 | 350.00 | 700.00 | 1126.00 | | 0.15 | 3.105 | 370.360 | 360.606 | 44.00 | 110.00 | 260.00 | 512.00 | 851.00 | 3.267 | 500.683 | 496.854 | 56.00 | 149.00 | 351.00 | 691.00 | 1143.00 | | 0.20 | 3.177 | 368.326 | 361.352 | 43.00 | 110.00 | 260.00 | 510.00 | 829.10 | 3.339 | 500.877 | 492.443 | 57.00 | 148.00 | 352.00 | 701.00 | 1146.10 | | 0.25 | 3.250 | 372.437 | 373.003 | 42.00 | 107.00 | 257.00 | 512.25 | 852.00 | 3.410 | 503.770 | 504.429 | 58.00 | 149.00 | 352.50 | 689.00 | 1155.00 | | 0.30 | 3.310 | 369.483 | 366.082 | 40.00 | 109.00 | 250.00 | 511.00 | 850.10 | 3.462 | 501.180 | 496.507 | 56.00 | 146.00 | 353.00 | 690.00 | 1139.00 | | 0.35 | 3.320 | 370.449 | 370.009 | 40.00 | 105.00 | 259.00 | 519.00 | 850.10 | 3.470 | 497.231 | 490.686 | 53.90 | 143.00 | 345.00 | 700.00 | 1142.00 | | 0.40 | 3.336 | 373.882 | 374.799 | 39.00 | 108.00 | 257.00 | 514.00 | 864.00 | 3.487 | 500.583 | 497.339 | 52.00 | 144.00 | 344.00 | 693.00 | 1152.00 | | 0.45 | 3.330 | 370.497 | 362.019 | 42.00 | 111.00 | 262.00 | 513.00 | 841.00 | 3.482 | 502.583 | 511.258 | 56.00 | 143.00 | 345.00 | 685.25 | 1151.10 | | 0.50 | 3.348 | 372.947 | 368.228 | 40.00 | 106.75 | 258.00 | 523.00 | 860.00 | 3.491 | 497.740 | 497.238 | 52.00 | 144.00 | 344.00 | 680.00 | 1140.10 |
| | Case 2 | | = 148 | | 0.05 | 2.693 | 371.630 | 356.051 | 53.00 | 119.00 | 262.00 | 511.00 | 851.00 | 2.888 | 500.861 | 488.895 | 67.00 | 161.00 | 354.50 | 683.00 | 1124.00 | | 0.10 | 2.990 | 370.596 | 361.021 | 48.00 | 115.00 | 262.00 | 510.25 | 838.00 | 3.164 | 500.156 | 491.339 | 61.00 | 150.00 | 348.00 | 686.00 | 1147.00 | | 0.15 | 3.108 | 370.684 | 364.987 | 45.00 | 113.00 | 256.00 | 512.00 | 852.00 | 3.276 | 499.238 | 497.396 | 58.00 | 151.00 | 339.50 | 685.00 | 1141.00 | | 0.20 | 3.205 | 371.339 | 370.458 | 43.00 | 109.00 | 257.00 | 507.00 | 852.10 | 3.364 | 497.147 | 497.229 | 56.00 | 143.00 | 343.00 | 687.00 | 1135.10 | | 0.25 | 3.200 | 369.233 | 373.910 | 42.00 | 107.00 | 254.00 | 505.00 | 847.00 | 3.360 | 498.605 | 494.584 | 55.00 | 147.00 | 342.00 | 690.00 | 1150.00 | | 0.30 | 3.292 | 370.357 | 363.483 | 42.00 | 111.00 | 260.00 | 514.00 | 844.00 | 3.447 | 503.229 | 497.073 | 56.00 | 147.00 | 350.00 | 704.25 | 1160.00 | | 0.35 | 3.305 | 372.801 | 370.908 | 43.00 | 110.00 | 257.00 | 518.10 | 841.00 | 3.446 | 502.578 | 499.339 | 55.00 | 143.75 | 349.00 | 704.00 | 1154.00 | | 0.40 | 3.324 | 370.974 | 367.470 | 42.00 | 110.00 | 258.00 | 513.25 | 853.00 | 3.470 | 503.744 | 508.302 | 58.00 | 346.00 | 357.00 | 692.00 | 1171.10 | | 0.45 | 3.347 | 370.483 | 372.301 | 39.00 | 106.00 | 257.00 | 507.25 | 841.00 | 3.500 | 501.782 | 496.490 | 53.00 | 150.00 | 345.00 | 700.00 | 1162.00 | | 0.50 | 3.360 | 371.790 | 370.588 | 41.00 | 110.00 | 257.00 | 518.00 | 852.00 | 3.507 | 500.329 | 498.932 | 54.00 | 144.00 | 347.00 | 691.25 | 1162.10 |
| | Case 3 | | = 80 | | 0.05 | 2.707 | 370.278 | 351.550 | 53.00 | 117.00 | 257.00 | 512.00 | 834.00 | 2.887 | 500.015 | 480.233 | 66.00 | 154.00 | 350.00 | 690.00 | 1114.10 | | 0.10 | 2.989 | 369.285 | 363.063 | 47.00 | 111.00 | 257.00 | 509.00 | 827.00 | 3.165 | 500.538 | 486.596 | 61.00 | 147.00 | 346.00 | 702.00 | 1148.00 | | 0.15 | 3.117 | 371.785 | 363.854 | 44.00 | 112.00 | 262.50 | 511.00 | 842.10 | 3.290 | 500.964 | 488.821 | 57.00 | 150.00 | 353.00 | 703.00 | 1142.00 | | 0.20 | 3.247 | 372.514 | 367.564 | 43.00 | 110.00 | 260.00 | 514.00 | 861.00 | 3.403 | 500.589 | 498.487 | 57.00 | 143.00 | 344.00 | 702.00 | 1141.00 | | 0.25 | 3.220 | 373.994 | 377.628 | 44.00 | 108.00 | 259.00 | 517.00 | 861.10 | 3.380 | 500.294 | 493.483 | 56.00 | 148.00 | 352.00 | 692.00 | 1131.00 | | 0.30 | 3.293 | 372.312 | 374.228 | 40.00 | 109.00 | 258.00 | 516.00 | 856.10 | 3.445 | 497.150 | 491.477 | 54.00 | 143.00 | 353.00 | 691.00 | 1142.00 | | 0.35 | 3.314 | 367.220 | 365.391 | 43.00 | 110.00 | 252.00 | 502.00 | 831.10 | 3.485 | 500.662 | 508.339 | 53.00 | 143.00 | 339.00 | 694.25 | 1171.00 | | 0.40 | 3.348 | 370.380 | 374.010 | 41.00 | 105.00 | 253.00 | 515.00 | 863.00 | 3.500 | 503.220 | 505.692 | 55.00 | 147.00 | 352.00 | 692.00 | 1148.00 | | 0.45 | 3.400 | 369.380 | 365.924 | 42.00 | 109.00 | 255.00 | 515.25 | 845.00 | 3.580 | 500.338 | 502.458 | 55.00 | 146.00 | 345.00 | 685.25 | 1156.10 | | 0.50 | 3.410 | 372.003 | 375.300 | 42.00 | 110.00 | 257.00 | 509.25 | 863.00 | 3.589 | 500.828 | 502.584 | 54.00 | 141.00 | 342.00 | 689.25 | 1151.00 |
| | Case 4 | | = 31 | | 0.05 | 2.704 | 370.431 | 354.684 | 54.00 | 118.00 | 261.00 | 511.00 | 821.10 | 2.898 | 500.250 | 473.620 | 68.00 | 158.00 | 352.00 | 690.00 | 1129.10 | | 0.10 | 2.992 | 370.488 | 362.731 | 45.00 | 111.75 | 259.00 | 513.00 | 849.00 | 3.165 | 500.660 | 496.742 | 62.00 | 151.00 | 350.00 | 680.25 | 1146.10 | | 0.15 | 3.138 | 370.824 | 363.596 | 44.00 | 108.00 | 259.00 | 518.00 | 850.00 | 3.299 | 500.344 | 494.834 | 56.90 | 145.00 | 341.00 | 706.00 | 1147.00 | | 0.20 | 3.214 | 373.258 | 369.391 | 43.00 | 108.00 | 257.00 | 514.00 | 872.00 | 3.379 | 497.684 | 497.292 | 55.00 | 146.00 | 346.00 | 690.00 | 1138.00 | | 0.25 | 3.237 | 371.389 | 356.200 | 43.00 | 111.00 | 261.00 | 510.00 | 849.00 | 3.410 | 398.489 | 488.285 | 59.00 | 151.00 | 351.00 | 689.00 | 1118.00 | | 0.30 | 3.345 | 373.580 | 368.903 | 41.00 | 109.75 | 261.00 | 519.00 | 848.10 | 3.510 | 497.120 | 496.338 | 55.00 | 145.00 | 345.00 | 681.00 | 1139.00 | | 0.35 | 3.393 | 370.392 | 364.339 | 42.00 | 111.00 | 258.00 | 515.00 | 843.10 | 3.568 | 500.296 | 496.330 | 56.00 | 147.00 | 345.00 | 700.00 | 1147.10 | | 0.40 | 3.412 | 368.038 | 366.539 | 41.00 | 105.00 | 254.00 | 509.00 | 860.00 | 3.592 | 500.390 | 501.392 | 53.00 | 140.00 | 349.50 | 683.00 | 1153.10 | | 0.45 | 3.492 | 368.249 | 364.291 | 40.00 | 108.00 | 257.00 | 512.00 | 858.10 | 3.704 | 500.787 | 504.578 | 55.00 | 145.00 | 349.25 | 692.00 | 1146.00 | | 0.50 | 3.552 | 368.228 | 366.900 | 40.00 | 108.00 | 253.50 | 508.25 | 851.00 | 3.735 | 498.567 | 497.086 | 52.90 | 146.00 | 349.00 | 689.25 | 1132.10 |
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