Research Article
Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number
Table 1
Variables chain sampling plans indexed by AQL and LQL for
= 5% and
= 10%.
| | | Known sigma | Unknown sigma | | | | | | | | |
| 0.001 | 0.0020 | 119 | 1 | 2.883 | 3.013 | 650 | 1 | 2.888 | 3.013 | 0.0025 | 68 | 2 | 2.810 | 2.965 | 361 | 1 | 2.834 | 2.984 | 0.003 | 46 | 1 | 2.776 | 2.961 | 242 | 1 | 2.774 | 2.964 | 0.004 | 31 | 2 | 2.740 | 2.885 | 147 | 1 | 2.716 | 2.921 | 0.005 | 21 | 2 | 2.610 | 2.860 | 103 | 1 | 2.637 | 2.897 | 0.006 | 19 | 4 | 2.597 | 2.807 | 84 | 2 | 2.599 | 2.829 | 0.007 | 15 | 3 | 2.534 | 2.789 | 72 | 3 | 2.532 | 2.792 | 0.008 | 13 | 3 | 2.495 | 2.765 | 62 | 3 | 2.518 | 2.768 | 0.009 | 12 | 3 | 2.521 | 2.736 | 51 | 2 | 2.470 | 2.765 | 0.010 | 12 | 6 | 2.517 | 2.697 | 45 | 2 | 2.425 | 2.750 | 0.012 | 9 | 4 | 2.331 | 2.686 | 40 | 3 | 2.414 | 2.694 | 0.015 | 7 | 3 | 2.237 | 2.657 | 34 | 4 | 2.387 | 2.637 | 0.020 | 7 | 6 | 2.414 | 2.539 | 27 | 5 | 2.335 | 2.565 | 0.025 | 6 | 6 | 2.370 | 2.485 | 20 | 3 | 2.197 | 2.552 | 0.030 | 5 | 6 | 2.264 | 2.454 | 19 | 5 | 2.231 | 2.476 |
| 0.0025 | 0.004 | 230 | 2 | 2.658 | 2.738 | 1131 | 2 | 2.676 | 2.736 | 0.005 | 105 | 2 | 2.598 | 2.703 | 474 | 2 | 2.585 | 2.705 | 0.006 | 64 | 2 | 2.530 | 2.675 | 282 | 1 | 2.533 | 2.698 | 0.0075 | 39 | 2 | 2.441 | 2.641 | 171 | 1 | 2.464 | 2.669 | 0.010 | 26 | 3 | 2.379 | 2.579 | 106 | 1 | 2.430 | 2.610 | 0.012 | 19 | 2 | 2.335 | 2.555 | 76 | 1 | 2.321 | 2.601 | 0.015 | 16 | 4 | 2.296 | 2.491 | 55 | 1 | 2.237 | 2.572 | 0.020 | 12 | 4 | 2.260 | 2.425 | 38 | 1 | 2.139 | 2.529 | 0.025 | 10 | 6 | 2.206 | 2.366 | 32 | 2 | 2.163 | 2.413 | 0.030 | 8 | 5 | 2.114 | 2.334 | 29 | 5 | 2.107 | 2.342 | 0.035 | 7 | 6 | 2.307 | 2.297 | 25 | 5 | 2.092 | 2.302 | 0.040 | 6 | 6 | 1.884 | 2.274 | 21 | 5 | 1.952 | 2.282 |
| 0.005 | 0.0075 | 259 | 1 | 2.434 | 2.524 | 1113 | 2 | 2.442 | 2.512 | 0.010 | 86 | 1 | 2.326 | 2.486 | 347 | 1 | 2.348 | 2.483 | 0.012 | 53 | 1 | 2.277 | 2.457 | 211 | 1 | 2.299 | 2.454 | 0.015 | 33 | 1 | 2.211 | 2.421 | 128 | 1 | 2.233 | 2.418 | 0.020 | 24 | 4 | 2.161 | 2.316 | 75 | 2 | 2.100 | 2.345 | 0.025 | 16 | 3 | 2.046 | 2.281 | 55 | 2 | 2.083 | 2.293 | 0.030 | 14 | 6 | 1.989 | 2.224 | 43 | 3 | 1.974 | 2.249 | 0.035 | 12 | 6 | 2.002 | 2.182 | 36 | 3 | 1.979 | 2.209 | 0.040 | 10 | 4 | 1.976 | 2.156 | 31 | 3 | 1.964 | 2.174 | 0.050 | 8 | 5 | 1.893 | 2.098 | 25 | 4 | 1.925 | 2.105 |
| 0.0075 | 0.010 | 505 | 2 | 2.339 | 2.384 | 1817 | 1 | 2.329 | 2.394 | 0.012 | 173 | 1 | 2.259 | 2.369 | 690 | 2 | 2.278 | 2.353 | 0.015 | 78 | 1 | 2.185 | 2.335 | 286 | 1 | 2.182 | 2.337 | 0.020 | 43 | 2 | 2.146 | 2.251 | 133 | 1 | 2.083 | 2.293 | 0.025 | 29 | 5 | 2.008 | 2.198 | 83 | 1 | 2.003 | 2.258 | 0.030 | 19 | 2 | 1.968 | 2.178 | 61 | 1 | 1.984 | 2.214 | 0.035 | 17 | 5 | 1.888 | 2.123 | 47 | 1 | 1.925 | 2.190 | 0.040 | 13 | 3 | 1.837 | 2.107 | 41 | 3 | 1.851 | 2.111 | 0.050 | 10 | 3 | 1.792 | 2.052 | 28 | 2 | 1.756 | 2.081 | 0.060 | 9 | 5 | 1.792 | 1.982 | 26 | 4 | 1.815 | 1.990 |
| 0.010 | 0.015 | 248 | 1 | 2.212 | 2.257 | 786 | 1 | 2.187 | 2.267 | 0.020 | 74 | 1 | 2.090 | 2.220 | 247 | 1 | 2.071 | 2.226 | 0.025 | 42 | 1 | 2.027 | 2.177 | 135 | 1 | 2.011 | 2.186 | 0.030 | 27 | 1 | 1.906 | 2.161 | 93 | 2 | 1.954 | 2.124 | 0.035 | 21 | 2 | 1.846 | 2.096 | 66 | 1 | 1.900 | 2.125 | 0.040 | 18 | 3 | 1.804 | 2.054 | 53 | 2 | 1.846 | 2.066 | 0.045 | 15 | 3 | 1.762 | 2.027 | 46 | 3 | 1.811 | 2.026 | 0.050 | 13 | 3 | 1.731 | 2.001 | 39 | 2 | 1.824 | 2.004 | 0.060 | 11 | 5 | 1.662 | 2.942 | 30 | 3 | 1.730 | 1.955 | 0.070 | 9 | 5 | 1.573 | 1.903 | 26 | 4 | 1.728 | 1.898 | 0.080 | 7 | 3 | 1.486 | 1.891 | 21 | 5 | 1.579 | 1.869 |
| 0.02 | 0.030 | 187 | 2 | 1.896 | 1.976 | 528 | 1 | 1.886 | 1.991 | 0.035 | 96 | 2 | 1.835 | 1.945 | 272 | 2 | 1.831 | 1.946 | 0.040 | 59 | 1 | 1.779 | 1.939 | 169 | 2 | 1.770 | 1.920 | 0.045 | 45 | 2 | 1.749 | 1.889 | 117 | 1 | 1.734 | 1.919 | 0.050 | 34 | 2 | 1.693 | 1.868 | 88 | 1 | 1.683 | 1.903 | 0.060 | 22 | 2 | 1.563 | 1.833 | 63 | 2 | 1.670 | 1.820 | 0.070 | 18 | 3 | 1.544 | 1.779 | 44 | 2 | 1.577 | 1.792 | 0.080 | 14 | 3 | 1.434 | 1.749 | 36 | 3 | 1.525 | 1.745 | 0.090 | 13 | 4 | 1.502 | 1.697 | 27 | 2 | 1.423 | 1.737 | 0.10 | 10 | 2 | 1.436 | 1.691 | 22 | 1 | 1.386 | 1.766 | 0.11 | 10 | 4 | 1.457 | 1.632 | 23 | 4 | 1.476 | 1.636 | 0.12 | 7 | 1 | 1.235 | 1.725 | 17 | 1 | 1.379 | 1.699 | 0.13 | 8 | 5 | 1.360 | 1.580 | 17 | 4 | 1.356 | 1.596 | 0.15 | 6 | 4 | 1.110 | 1.560 | 14 | 5 | 1.279 | 1.544 |
| 0.030 | 0.040 | 341 | 2 | 1.771 | 1.821 | 1027 | 5 | 1.771 | 1.816 | 0.045 | 157 | 1 | 1.711 | 1.811 | 416 | 2 | 1.704 | 1.799 | 0.050 | 96 | 1 | 1.650 | 1.795 | 253 | 1 | 1.679 | 1.789 | 0.060 | 52 | 2 | 1.566 | 1.736 | 126 | 1 | 1.585 | 1.760 | 0.070 | 33 | 1 | 1.508 | 1.728 | 81 | 1 | 1.539 | 1.724 | 0.080 | 26 | 3 | 1.427 | 1.657 | 62 | 2 | 1.514 | 1.659 | 0.090 | 23 | 5 | 1.449 | 1.609 | 44 | 2 | 1.401 | 1.641 | 0.100 | 17 | 3 | 1.378 | 1.593 | 36 | 2 | 1.384 | 1.609 | 0.110 | 13 | 2 | 1.268 | 1.588 | 29 | 2 | 1.305 | 1.590 | 0.120 | 11 | 1 | 1.270 | 1.605 | 26 | 3 | 1.274 | 1.549 | 0.130 | 11 | 4 | 1.204 | 1.514 | 23 | 3 | 1.289 | 1.519 | 0.150 | 10 | 6 | 1.273 | 1.443 | 18 | 3 | 1.230 | 1.475 | 0.200 | 6 | 5 | 0.950 | 1.365 | 12 | 5 | 1.134 | 1.354 |
| 0.04 | 0.060 | 145 | 2 | 1.568 | 1.663 | 339 | 2 | 1.564 | 1.664 | 0.070 | 73 | 1 | 1.513 | 1.643 | 166 | 1 | 1.507 | 1.647 | 0.080 | 50 | 2 | 1.478 | 1.588 | 102 | 1 | 1.425 | 1.625 | 0.090 | 34 | 2 | 1.394 | 1.564 | 71 | 1 | 1.374 | 1.600 | 0.100 | 27 | 3 | 1.324 | 1.529 | 53 | 1 | 1.315 | 1.580 | 0.110 | 24 | 5 | 1.309 | 1.489 | 42 | 1 | 1.294 | 1.554 | 0.120 | 18 | 3 | 1.233 | 1.478 | 34 | 1 | 1.234 | 1.539 | 0.130 | 14 | 2 | 1.130 | 1.475 | 31 | 2 | 1.271 | 1.461 | 0.140 | 14 | 4 | 1.158 | 1.423 | 27 | 3 | 1.193 | 1.433 | 0.150 | 11 | 2 | 1.108 | 1.428 | 23 | 3 | 1.130 | 1.415 | 0.170 | 10 | 4 | 1.070 | 1.360 | 17 | 2 | 1.061 | 1.396 | 0.200 | 8 | 5 | 0.990 | 1.295 | 15 | 4 | 1.120 | 1.290 |
| 0.050 | 0.070 | 188 | 1 | 1.487 | 1.582 | 427 | 2 | 1.485 | 1.570 | 0.080 | 93 | 1 | 1.408 | 1.558 | 203 | 1 | 1.422 | 1.557 | 0.090 | 60 | 2 | 1.359 | 1.509 | 127 | 2 | 1.365 | 1.510 | 0.100 | 46 | 3 | 1.331 | 1.471 | 86 | 1 | 1.331 | 1.506 | 0.110 | 33 | 2 | 1.288 | 1.453 | 63 | 1 | 1.261 | 1.491 | 0.120 | 26 | 1 | 1.270 | 1.450 | 49 | 1 | 1.213 | 1.473 | 0.130 | 20 | 1 | 1.157 | 1.452 | 45 | 3 | 1.235 | 1.395 | 0.140 | 19 | 3 | 1.160 | 1.375 | 34 | 2 | 1.148 | 1.393 | 0.150 | 17 | 4 | 1.108 | 1.348 | 30 | 2 | 1.165 | 1.365 | 0.160 | 13 | 2 | 1.011 | 1.356 | 25 | 1 | 1.134 | 1.384 | 0.170 | 12 | 2 | 1.045 | 1.330 | 24 | 3 | 1.112 | 1.312 | 0.200 | 11 | 6 | 1.059 | 1.229 | 17 | 3 | 1.023 | 1.258 |
|
|