Research Article
Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions
Table 1
Constant multiplier and IC run length properties of max-EWMA control chart when
, , , , and
.
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| | Case 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0.05 | 2.718 | 370.293 | 357.630 | 51.00 | 114.00 | 260.00 | 507.00 | 839.00 | 2.913 | 500.901 | 484.018 | 66.90 | 155.00 | 352.00 | 683.25 | 1127.00 | | 0.10 | 3.050 | 370.458 | 362.651 | 47.00 | 114.00 | 259.00 | 503.25 | 852.00 | 3.210 | 499.010 | 483.872 | 60.00 | 151.00 | 350.00 | 694.00 | 1139.00 | | 0.15 | 3.195 | 370.843 | 362.010 | 46.00 | 115.00 | 260.00 | 505.00 | 841.10 | 3.352 | 500.784 | 497.616 | 59.00 | 149.00 | 349.00 | 706.00 | 1140.10 | | 0.20 | 3.222 | 370.892 | 368.258 | 44.00 | 110.00 | 258.00 | 512.00 | 848.00 | 3.375 | 497.327 | 499.830 | 55.00 | 144.00 | 344.00 | 679.00 | 1143.20 | | 0.25 | 3.329 | 367.599 | 368.560 | 41.00 | 105.00 | 252.50 | 504.00 | 833.10 | 3.489 | 497.583 | 501.449 | 55.00 | 144.00 | 345.00 | 684.00 | 1150.00 | | 0.30 | 3.384 | 373.593 | 368.582 | 43.00 | 113.75 | 263.00 | 512.00 | 855.10 | 3.543 | 500.492 | 503.290 | 55.00 | 146.00 | 343.00 | 688.00 | 1138.10 | | 0.35 | 3.394 | 370.134 | 370.493 | 41.90 | 108.75 | 259.00 | 514.00 | 844.00 | 3.560 | 502.520 | 495.290 | 58.00 | 150.00 | 351.00 | 692.00 | 1151.10 | | 0.40 | 3.407 | 367.501 | 365.593 | 41.00 | 106.00 | 254.50 | 510.00 | 846.00 | 3.572 | 500.229 | 494.105 | 55.00 | 147.00 | 346.00 | 698.00 | 1142.00 | | 0.45 | 3.461 | 370.338 | 362.491 | 41.00 | 109.00 | 260.00 | 514.00 | 854.10 | 3.625 | 500.339 | 494.290 | 55.00 | 144.00 | 349.00 | 696.00 | 1150.00 | | 0.50 | 3.456 | 367.458 | 370.280 | 39.00 | 104.00 | 253.00 | 509.00 | 844.10 | 3.620 | 497.380 | 502.596 | 52.00 | 141.00 | 342.00 | 684.00 | 1155.00 | | Case 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0.05 | 2.713 | 370.573 | 352.681 | 51.00 | 116.00 | 261.00 | 511.00 | 825.00 | 2.906 | 500.045 | 474.033 | 69.00 | 158.00 | 357.00 | 687.00 | 1142.00 | | 0.10 | 3.026 | 370.123 | 360.811 | 47.00 | 112.00 | 260.00 | 508.00 | 845.00 | 3.203 | 500.490 | 494.330 | 61.00 | 151.00 | 350.00 | 691.25 | 1142.20 | | 0.15 | 3.182 | 369.737 | 360.049 | 44.00 | 112.00 | 256.50 | 512.00 | 850.00 | 3.365 | 500.976 | 496.848 | 56.00 | 148.00 | 347.00 | 691.00 | 1145.00 | | 0.20 | 3.260 | 370.128 | 368.280 | 43.00 | 112.00 | 255.00 | 512.00 | 844.00 | 3.426 | 497.290 | 499.393 | 55.00 | 143.00 | 341.00 | 678.25 | 1139.00 | | 0.25 | 3.330 | 367.308 | 365.290 | 43.00 | 109.00 | 255.00 | 500.00 | 833.00 | 3.498 | 497.280 | 502.768 | 51.00 | 137.00 | 340.00 | 690.00 | 1159.00 | | 0.30 | 3.375 | 373.583 | 371.483 | 41.00 | 107.00 | 259.00 | 520.00 | 860.10 | 3.547 | 500.285 | 499.343 | 54.00 | 148.75 | 348.00 | 692.00 | 1152.00 | | 0.35 | 3.429 | 370.388 | 369.194 | 41.00 | 109.00 | 261.00 | 508.00 | 838.00 | 3.600 | 498.295 | 501.850 | 54.00 | 143.00 | 338.00 | 695.25 | 1156.10 | | 0.40 | 3.462 | 370.412 | 371.493 | 41.00 | 109.00 | 260.00 | 507.00 | 844.00 | 3.615 | 500.128 | 488.335 | 57.00 | 147.00 | 350.00 | 700.00 | 1144.00 | | 0.45 | 3.501 | 370.947 | 365.896 | 39.00 | 107.00 | 260.00 | 514.00 | 846.00 | 3.669 | 503.895 | 501.492 | 53.00 | 145.00 | 349.00 | 702.00 | 1164.00 | | 0.50 | 3.505 | 370.570 | 365.218 | 42.00 | 108.00 | 259.00 | 516.00 | 853.10 | 3.670 | 499.749 | 502.894 | 51.00 | 137.00 | 347.00 | 698.00 | 1147.10 | | Case 3 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0.05 | 2.711 | 370.786 | 357.297 | 51.00 | 117.00 | 262.00 | 506.00 | 831.10 | 2.909 | 500.294 | 484.821 | 67.00 | 155.00 | 346.00 | 683.00 | 1136.10 | | 0.10 | 3.034 | 370.837 | 354.197 | 49.00 | 115.00 | 267.00 | 513.00 | 842.00 | 3.210 | 500.029 | 484.467 | 59.00 | 149.00 | 355.00 | 695.25 | 1123.00 | | 0.15 | 3.191 | 369.015 | 363.016 | 45.00 | 111.00 | 255.00 | 505.00 | 850.00 | 3.368 | 500.117 | 491.441 | 62.00 | 150.00 | 355.00 | 687.00 | 1131.10 | | 0.20 | 3.270 | 372.558 | 366.104 | 43.00 | 113.00 | 260.00 | 516.00 | 846.00 | 3.447 | 502.583 | 501.448 | 56.00 | 144.00 | 348.00 | 690.00 | 1154.00 | | 0.25 | 3.354 | 371.859 | 365.327 | 42.00 | 110.00 | 261.00 | 518.00 | 848.00 | 3.524 | 500.338 | 484.789 | 53.00 | 144.00 | 355.00 | 694.00 | 1146.10 | | 0.30 | 3.446 | 368.284 | 361.668 | 41.00 | 108.00 | 257.00 | 512.00 | 844.00 | 3.632 | 498.280 | 502.532 | 54.00 | 142.00 | 335.00 | 696.00 | 1173.10 | | 0.35 | 3.468 | 370.782 | 374.503 | 40.00 | 105.00 | 258.00 | 510.00 | 850.00 | 3.648 | 503.294 | 497.307 | 56.00 | 149.00 | 359.00 | 696.00 | 1147.00 | | 0.40 | 3.499 | 367.339 | 365.058 | 40.00 | 107.00 | 353.50 | 507.00 | 854.00 | 3.687 | 497.283 | 497.100 | 52.00 | 144.00 | 347.50 | 691.00 | 1122.00 | | 0.45 | 3.653 | 368.480 | 366.583 | 42.00 | 107.00 | 256.00 | 510.00 | 830.00 | 3.822 | 497.280 | 493.684 | 53.00 | 143.00 | 342.00 | 689.00 | 1142.00 | | 0.50 | 3.650 | 373.943 | 370.048 | 41.00 | 108.00 | 263.00 | 521.00 | 850.10 | 3.838 | 502.297 | 495.786 | 56.00 | 147.00 | 352.00 | 707.00 | 1152.00 | | Case 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0.05 | 2.722 | 370.115 | 357.005 | 54.00 | 119.00 | 262.00 | 506.00 | 822.10 | 2.913 | 499.731 | 489.967 | 70.00 | 158.00 | 346.50 | 668.00 | 1131.10 | | 0.10 | 3.048 | 370.866 | 359.027 | 48.00 | 115.00 | 261.00 | 513.00 | 844.00 | 3.234 | 501.045 | 490.261 | 60.00 | 153.00 | 350.00 | 691.00 | 1143.00 | | 0.15 | 3.236 | 370.007 | 363.042 | 46.00 | 113.75 | 258.00 | 506.00 | 843.10 | 3.428 | 501.583 | 494.736 | 57.00 | 152.00 | 351.00 | 702.00 | 1139.10 | | 0.20 | 3.369 | 373.810 | 365.391 | 43.00 | 111.00 | 262.00 | 520.00 | 855.10 | 3.570 | 502.204 | 501.115 | 57.00 | 144.00 | 347.00 | 690.00 | 1153.10 | | 0.25 | 3.467 | 373.539 | 365.294 | 45.00 | 112.00 | 262.00 | 521.00 | 847.10 | 3.645 | 500.476 | 497.206 | 55.00 | 150.00 | 349.00 | 684.00 | 1144.00 | | 0.30 | 3.646 | 372.480 | 367.106 | 42.00 | 110.00 | 261.00 | 521.00 | 851.00 | 3.825 | 498.294 | 492.480 | 53.90 | 144.00 | 349.00 | 684.25 | 1149.00 | | 0.35 | 3.654 | 370.784 | 369.286 | 41.00 | 108.00 | 257.50 | 514.25 | 848.10 | 3.859 | 500.240 | 494.285 | 57.00 | 149.00 | 353.50 | 693.25 | 1147.00 | | 0.40 | 3.731 | 372.281 | 370.035 | 41.00 | 108.00 | 260.50 | 517.00 | 850.00 | 3.931 | 502.574 | 504.458 | 52.00 | 149.00 | 350.00 | 698.25 | 1153.10 | | 0.45 | 3.761 | 373.669 | 374.106 | 40.00 | 107.00 | 259.00 | 517.00 | 860.10 | 3.956 | 500.119 | 499.230 | 55.00 | 146.00 | 346.00 | 693.25 | 1147.10 | | 0.50 | 3.800 | 368.195 | 364.068 | 41.00 | 108.00 | 257.00 | 510.00 | 842.00 | 3.998 | 503.251 | 502.289 | 55.00 | 143.00 | 350.00 | 703.00 | 1164.10 |
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