Research Article
Max-EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions
Table 2
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 | 2.688 | 370.573 | 357.498 | 53.00 | 118.00 | 261.00 | 501.00 | 831.00 | 2.893 | 500.062 | 482.891 | 66.00 | 154.00 | 349.00 | 688.00 | 1135.00 | | 0.10 | 3.016 | 371.465 | 363.243 | 47.00 | 113.00 | 257.00 | 516.00 | 844.10 | 3.203 | 499.944 | 506.414 | 61.00 | 147.00 | 341.00 | 683.00 | 1137.10 | | 0.15 | 3.194 | 370.018 | 367.745 | 41.00 | 107.00 | 255.00 | 514.00 | 841.00 | 3.375 | 500.824 | 493.943 | 56.00 | 148.00 | 350.00 | 692.00 | 1147.00 | | 0.20 | 3.315 | 370.897 | 364.675 | 40.00 | 109.00 | 260.00 | 517.00 | 838.00 | 3.475 | 498.786 | 492.890 | 60.00 | 145.00 | 348.00 | 683.25 | 1164.10 | | 0.25 | 3.420 | 373.710 | 372.589 | 41.00 | 110.00 | 260.00 | 517.00 | 855.10 | 3.579 | 501.585 | 498.849 | 55.00 | 148.00 | 349.00 | 693.00 | 1150.00 | | 0.30 | 3.424 | 370.053 | 361.593 | 42.00 | 114.00 | 262.00 | 512.00 | 836.00 | 3.575 | 503.754 | 495.329 | 57.00 | 150.00 | 352.00 | 692.00 | 1153.10 | | 0.35 | 3.460 | 368.540 | 369.097 | 41.00 | 106.00 | 255.00 | 510.00 | 857.00 | 3.604 | 497.001 | 490.793 | 56.00 | 147.00 | 346.00 | 692.00 | 1156.10 | | 0.40 | 3.479 | 370.574 | 369.909 | 41.00 | 109.00 | 260.00 | 512.00 | 845.00 | 3.621 | 501.571 | 500.310 | 55.00 | 146.00 | 351.00 | 691.00 | 1146.10 | | 0.45 | 3.456 | 372.057 | 370.922 | 42.00 | 106.00 | 259.00 | 520.00 | 854.00 | 3.590 | 498.140 | 482.700 | 55.00 | 146.00 | 349.00 | 704.00 | 1132.00 | | 0.50 | 3.400 | 370.461 | 373.091 | 39.00 | 107.00 | 255.00 | 511.00 | 857.00 | 3.538 | 502.511 | 498.690 | 55.00 | 149.00 | 352.00 | 695.00 | 1154.00 |
| | Case 2 | | = 148 | | 0.05 | 2.701 | 370.295 | 350.597 | 52.00 | 115.00 | 261.00 | 505.00 | 845.10 | 2.897 | 500.204 | 481.986 | 67.00 | 155.00 | 349.00 | 696.00 | 1126.10 | | 0.10 | 3.026 | 370.310 | 356.600 | 45.00 | 110.00 | 259.00 | 508.25 | 837.00 | 3.216 | 500.482 | 483.140 | 61.00 | 152.00 | 355.00 | 690.25 | 1127.10 | | 0.15 | 3.219 | 370.938 | 365.482 | 45.00 | 112.00 | 262.00 | 514.00 | 833.10 | 3.402 | 500.240 | 496.316 | 57.00 | 150.00 | 350.00 | 683.00 | 1147.10 | | 0.20 | 3.339 | 369.069 | 367.964 | 42.00 | 107.00 | 257.00 | 508.00 | 843.00 | 3.516 | 498.260 | 491.439 | 59.00 | 148.00 | 347.00 | 690.00 | 1132.10 | | 0.25 | 3.341 | 370.003 | 369.210 | 45.00 | 110.75 | 255.00 | 509.00 | 841.00 | 3.508 | 500.201 | 492.796 | 55.00 | 147.00 | 349.00 | 695.00 | 1145.10 | | 0.30 | 3.408 | 371.583 | 364.904 | 42.00 | 110.00 | 260.00 | 518.00 | 846.20 | 3.562 | 498.975 | 496.704 | 56.00 | 147.00 | 351.00 | 693.00 | 1136.00 | | 0.35 | 3.459 | 369.019 | 359.802 | 41.00 | 110.00 | 259.00 | 516.00 | 848.00 | 3.612 | 500.330 | 503.013 | 54.90 | 142.00 | 337.00 | 696.00 | 1161.00 | | 0.40 | 3.474 | 371.547 | 368.691 | 40.00 | 104.00 | 258.00 | 522.00 | 859.00 | 3.610 | 500.962 | 495.101 | 59.00 | 148.00 | 346.00 | 695.00 | 1146.00 | | 0.45 | 3.437 | 368.855 | 366.096 | 39.90 | 108.00 | 257.00 | 506.00 | 847.00 | 3.576 | 503.694 | 488.023 | 56.00 | 150.00 | 356.00 | 701.00 | 1147.10 | | 0.50 | 3.461 | 370.996 | 372.905 | 39.90 | 106.00 | 255.00 | 520.00 | 854.00 | 3.596 | 500.492 | 494.781 | 56.00 | 145.00 | 350.00 | 694.00 | 1156.10 |
| | Case 3 | | = 80 | | 0.05 | 2.686 | 370.896 | 357.014 | 53.00 | 116.00 | 262.00 | 503.00 | 846.00 | 2.880 | 500.104 | 488.094 | 67.00 | 157.00 | 349.00 | 672.00 | 1140.00 | | 0.10 | 3.015 | 370.785 | 365.286 | 46.00 | 111.00 | 259.00 | 509.00 | 845.00 | 3.204 | 499.594 | 484.227 | 62.00 | 152.00 | 343.00 | 694.00 | 1148.00 | | 0.15 | 3.209 | 370.858 | 370.921 | 42.00 | 107.00 | 253.00 | 520.00 | 860.00 | 3.387 | 499.567 | 501.873 | 55.00 | 145.00 | 340.00 | 687.00 | 1140.00 | | 0.20 | 3.314 | 368.244 | 365.435 | 40.00 | 108.00 | 258.00 | 513.00 | 845.00 | 3.501 | 500.465 | 485.071 | 59.90 | 156.00 | 353.00 | 693.00 | 1128.00 | | 0.25 | 3.425 | 369.114 | 364.794 | 43.00 | 111.00 | 255.00 | 514.00 | 839.10 | 3.595 | 503.579 | 498.596 | 57.00 | 148.00 | 353.00 | 695.25 | 1151.00 | | 0.30 | 3.458 | 370.577 | 367.574 | 43.00 | 110.00 | 258.00 | 514.25 | 848.00 | 3.632 | 498.584 | 500.348 | 57.00 | 147.75 | 342.00 | 688.00 | 1133.10 | | 0.35 | 3.475 | 370.459 | 366.664 | 42.00 | 108.75 | 257.00 | 513.75 | 845.00 | 3.646 | 500.035 | 495.041 | 54.00 | 147.00 | 350.00 | 687.00 | 1163.00 | | 0.40 | 3.476 | 373.584 | 362.321 | 42.00 | 109.00 | 264.00 | 520.00 | 862.00 | 3.630 | 501.585 | 495.564 | 57.00 | 147.00 | 347.00 | 698.00 | 1144.00 | | 0.45 | 3.506 | 368.577 | 363.570 | 40.00 | 109.00 | 260.00 | 509.00 | 845.10 | 3.652 | 500.039 | 487.289 | 57.00 | 145.00 | 353.00 | 696.00 | 1138.10 | | 0.50 | 3.485 | 370.115 | 372.840 | 41.00 | 107.00 | 255.00 | 513.00 | 847.00 | 3.624 | 497.782 | 499.021 | 51.90 | 143.00 | 344.00 | 692.00 | 1147.10 |
| | Case 4 | | = 31 | | 0.05 | 2.709 | 370.573 | 355.747 | 52.00 | 118.00 | 258.00 | 506.00 | 833.10 | 2.910 | 500.242 | 483.733 | 66.00 | 155.00 | 351.00 | 690.00 | 1129.00 | | 0.10 | 3.027 | 370.751 | 370.783 | 45.00 | 113.00 | 258.00 | 509.00 | 835.00 | 3.220 | 501.537 | 499.124 | 60.00 | 151.00 | 346.00 | 685.00 | 1157.00 | | 0.15 | 3.238 | 370.579 | 357.945 | 45.00 | 114.00 | 262.00 | 518.25 | 838.00 | 3.424 | 501.896 | 497.806 | 59.90 | 149.00 | 347.50 | 693.00 | 1160.10 | | 0.20 | 3.330 | 372.084 | 376.560 | 43.00 | 108.00 | 257.00 | 508.00 | 861.00 | 3.515 | 497.552 | 479.867 | 60.00 | 151.00 | 350.00 | 694.25 | 1129.00 | | 0.25 | 3.423 | 371.477 | 371.096 | 44.00 | 109.75 | 254.00 | 518.00 | 842.10 | 3.597 | 500.285 | 497.703 | 56.00 | 146.00 | 342.50 | 687.00 | 1173.00 | | 0.30 | 3.500 | 368.603 | 362.783 | 42.00 | 107.00 | 258.00 | 507.00 | 839.10 | 3.670 | 497.011 | 499.478 | 56.00 | 143.00 | 337.00 | 688.00 | 1139.10 | | 0.35 | 3.540 | 370.014 | 376.664 | 40.00 | 106.00 | 254.00 | 506.75 | 854.10 | 3.720 | 503.957 | 498.487 | 55.00 | 147.00 | 351.00 | 701.00 | 1148.00 | | 0.40 | 3.585 | 370.985 | 373.161 | 39.00 | 108.00 | 259.00 | 511.00 | 846.00 | 3.749 | 500.118 | 494.684 | 53.00 | 144.00 | 346.00 | 698.00 | 1155.10 | | 0.45 | 3.578 | 371.594 | 369.940 | 40.00 | 108.00 | 253.50 | 517.00 | 859.00 | 3.752 | 500.433 | 494.583 | 53.00 | 144.00 | 345.00 | 695.00 | 1170.10 | | 0.50 | 3.612 | 367.142 | 369.042 | 42.00 | 107.00 | 255.00 | 504.00 | 841.10 | 3.802 | 503.568 | 503.592 | 57.00 | 145.00 | 349.00 | 697.00 | 1156.10 |
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