Table 4 \({2}^{12-6}\) experiment using uniform distribution as the shift distribution.
From: Economic statistical model of the np chart for monitoring defectives
Run | Values of the input factors | Chart | Results | \({ETC}_{Traditional}\)/\({ETC}_{Optimal}\) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\({p}_{0}\) | \({\delta }_{max}\) | Ď„ | r | b | c | M | W | T | \(\varepsilon\) | e | D | n | h | UCL | ETC | |||
1 | 0.05 | 10 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 1320.665 | 2.032 |
Optimal np | 6 | 0.06 | 3 | 649.785 | ||||||||||||||
2 | 0.05 | 5 | 600 | 50 | 1 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 8 | 33.577 | 1.103 |
Optimal np | 56 | 1.12 | 8 | 30.446 | ||||||||||||||
3 | 0.05 | 5 | 600 | 50 | 1 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 8 | 82.959 | 1.204 |
Optimal np | 69 | 1.38 | 9 | 68.927 | ||||||||||||||
4 | 0.05 | 5 | 300 | 100 | 0.5 | 0.09 | 10,000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 100 | 1 | 12 | 725.784 | 1.987 |
Optimal np | 14 | 0.14 | 4 | 365.263 | ||||||||||||||
5 | 0.01 | 10 | 300 | 100 | 0.5 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 5 | 4.693 | 1.263 |
Optimal np | 50 | 0.5 | 3 | 3.714 | ||||||||||||||
6 | 0.01 | 10 | 600 | 100 | 0.5 | 0.01 | 1000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 26.365 | 1.625 |
Optimal np | 11 | 0.11 | 2 | 16.220 | ||||||||||||||
7 | 0.01 | 5 | 600 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 128.664 | 1.122 |
Optimal np | 99 | 1.98 | 4 | 114.627 | ||||||||||||||
8 | 0.05 | 10 | 600 | 100 | 1 | 0.01 | 1000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 134.989 | 1.897 |
Optimal np | 12 | 0.12 | 4 | 71.171 | ||||||||||||||
9 | 0.05 | 10 | 300 | 100 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 667.764 | 1.314 |
Optimal np | 23 | 0.23 | 5 | 508.199 | ||||||||||||||
10 | 0.05 | 10 | 600 | 100 | 1 | 0.01 | 10,000 | 50 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 1318.561 | 2.038 |
Optimal np | 6 | 0.06 | 3 | 646.836 | ||||||||||||||
11 | 0.01 | 10 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 3 | Traditional np | 50 | 1 | 3 | 4.650 | 1.128 |
Optimal np | 65 | 1.3 | 3 | 4.120 | ||||||||||||||
12 | 0.01 | 5 | 300 | 100 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 100 | 1 | 5 | 4.609 | 1.617 |
Optimal np | 99 | 0.99 | 4 | 2.851 | ||||||||||||||
13 | 0.01 | 10 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 280.854 | 1.473 |
Optimal np | 11 | 0.11 | 2 | 190.666 | ||||||||||||||
14 | 0.01 | 10 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.01 | 0.025 | 1 | Traditional np | 100 | 1 | 5 | 35.407 | 1.238 |
Optimal np | 80 | 0.8 | 4 | 28.603 | ||||||||||||||
15 | 0.05 | 5 | 600 | 50 | 1 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 8 | 58.145 | 1.239 |
Optimal np | 23 | 0.46 | 5 | 46.930 | ||||||||||||||
16 | 0.01 | 10 | 300 | 50 | 1 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 3.418 | 1.178 |
Optimal np | 65 | 1.3 | 3 | 2.902 | ||||||||||||||
17 | 0.01 | 5 | 300 | 100 | 0.5 | 0.09 | 1000 | 300 | 500 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 7.205 | 1.533 |
Optimal np | 50 | 0.5 | 3 | 4.700 | ||||||||||||||
18 | 0.05 | 10 | 300 | 50 | 0.5 | 0.09 | 1000 | 300 | 500 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 7 | 10.396 | 1.077 |
Optimal np | 26 | 0.52 | 5 | 9.651 | ||||||||||||||
19 | 0.01 | 5 | 600 | 100 | 1 | 0.01 | 10,000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 181.458 | 1.237 |
Optimal np | 39 | 0.39 | 3 | 146.733 | ||||||||||||||
20 | 0.05 | 5 | 300 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 7 | 521.330 | 1.274 |
Optimal np | 16 | 0.32 | 4 | 409.331 | ||||||||||||||
21 | 0.05 | 5 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 50 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 782.635 | 1.542 |
Optimal np | 20 | 0.2 | 5 | 507.667 | ||||||||||||||
22 | 0.01 | 5 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 4.543 | 1.496 |
Optimal np | 123 | 2.46 | 4 | 3.036 | ||||||||||||||
23 | 0.01 | 5 | 600 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 4.543 | 1.209 |
Optimal np | 99 | 1.98 | 4 | 3.759 | ||||||||||||||
24 | 0.01 | 5 | 600 | 100 | 1 | 0.09 | 1000 | 300 | 100 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 7.216 | 1.313 |
Optimal np | 39 | 0.39 | 3 | 5.495 | ||||||||||||||
25 | 0.01 | 5 | 300 | 50 | 0.5 | 0.01 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 4.403 | 1.520 |
Optimal np | 123 | 2.46 | 4 | 2.896 | ||||||||||||||
26 | 0.05 | 5 | 300 | 50 | 1 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.125 | 1 | Traditional np | 50 | 1 | 7 | 138.801 | 1.252 |
Optimal np | 26 | 0.52 | 5 | 110.824 | ||||||||||||||
27 | 0.01 | 5 | 300 | 50 | 1 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 4.561 | 1.499 |
Optimal np | 123 | 2.46 | 4 | 3.043 | ||||||||||||||
28 | 0.01 | 10 | 600 | 50 | 1 | 0.01 | 10,000 | 50 | 500 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 3 | 224.852 | 1.129 |
Optimal np | 16 | 0.32 | 2 | 199.223 | ||||||||||||||
29 | 0.01 | 10 | 600 | 100 | 0.5 | 0.01 | 10,000 | 50 | 100 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 5 | 160.903 | 1.119 |
Optimal np | 39 | 0.39 | 3 | 143.816 | ||||||||||||||
30 | 0.01 | 10 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 3.592 | 1.179 |
Optimal np | 65 | 1.3 | 3 | 3.046 | ||||||||||||||
31 | 0.01 | 5 | 600 | 50 | 0.5 | 0.09 | 10,000 | 50 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 128.354 | 1.123 |
Optimal np | 99 | 1.98 | 4 | 114.316 | ||||||||||||||
32 | 0.01 | 5 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 100 | 1 | 5 | 122.901 | 1.197 |
Optimal np | 131 | 1.31 | 5 | 102.711 | ||||||||||||||
33 | 0.05 | 10 | 300 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 1320.665 | 2.168 |
Optimal np | 7 | 0.07 | 3 | 609.037 | ||||||||||||||
34 | 0.05 | 10 | 300 | 50 | 0.5 | 0.01 | 10,000 | 300 | 100 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 7 | 972.900 | 1.521 |
Optimal np | 8 | 0.16 | 3 | 639.537 | ||||||||||||||
35 | 0.05 | 5 | 300 | 50 | 1 | 0.01 | 10,000 | 50 | 100 | 0.01 | 0.125 | 3 | Traditional np | 50 | 1 | 7 | 167.283 | 1.192 |
Optimal np | 26 | 0.52 | 5 | 140.347 | ||||||||||||||
36 | 0.05 | 5 | 300 | 50 | 0.5 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.125 | 1 | Traditional np | 50 | 1 | 7 | 14.283 | 1.238 |
Optimal np | 26 | 0.52 | 5 | 11.533 | ||||||||||||||
37 | 0.05 | 10 | 600 | 50 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 8 | 987.426 | 1.469 |
Optimal np | 7 | 0.14 | 3 | 672.269 | ||||||||||||||
38 | 0.01 | 5 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 4.527 | 1.494 |
Optimal np | 123 | 2.46 | 4 | 3.030 | ||||||||||||||
39 | 0.05 | 5 | 600 | 100 | 1 | 0.09 | 10,000 | 300 | 100 | 0.01 | 0.025 | 1 | Traditional np | 100 | 1 | 12 | 71.832 | 1.125 |
Optimal np | 62 | 0.62 | 9 | 63.829 | ||||||||||||||
40 | 0.01 | 5 | 300 | 50 | 1 | 0.09 | 10,000 | 300 | 500 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 43.788 | 1.522 |
Optimal np | 123 | 2.46 | 4 | 28.770 | ||||||||||||||
41 | 0.05 | 10 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 665.501 | 1.277 |
Optimal np | 20 | 0.2 | 5 | 520.951 | ||||||||||||||
42 | 0.01 | 5 | 300 | 50 | 1 | 0.01 | 1000 | 300 | 500 | 0.05 | 0.025 | 3 | Traditional np | 50 | 1 | 3 | 14.611 | 1.198 |
Optimal np | 123 | 2.46 | 4 | 12.194 | ||||||||||||||
43 | 0.05 | 10 | 600 | 100 | 0.5 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 1320.515 | 2.040 |
Optimal np | 6 | 0.06 | 3 | 647.285 | ||||||||||||||
44 | 0.01 | 5 | 300 | 50 | 0.5 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 43.674 | 1.525 |
Optimal np | 123 | 2.46 | 4 | 28.640 | ||||||||||||||
45 | 0.01 | 10 | 600 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.01 | 0.025 | 3 | Traditional np | 50 | 1 | 3 | 43.636 | 1.015 |
Optimal np | 99 | 1.98 | 4 | 42.981 | ||||||||||||||
46 | 0.05 | 10 | 600 | 50 | 0.5 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 8 | 40.656 | 1.149 |
Optimal np | 23 | 0.46 | 5 | 35.376 | ||||||||||||||
47 | 0.05 | 10 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.01 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 407.895 | 2.408 |
Optimal np | 12 | 0.12 | 4 | 169.425 | ||||||||||||||
48 | 0.05 | 10 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 7 | 99.035 | 1.489 |
Optimal np | 8 | 0.16 | 3 | 66.503 | ||||||||||||||
49 | 0.05 | 10 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 100 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 1320.566 | 2.033 |
Optimal np | 6 | 0.06 | 3 | 649.650 | ||||||||||||||
50 | 0.05 | 10 | 600 | 100 | 1 | 0.09 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 1323.065 | 2.029 |
Optimal np | 6 | 0.06 | 3 | 652.185 | ||||||||||||||
51 | 0.05 | 5 | 300 | 100 | 1 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 12 | 218.651 | 2.243 |
Optimal np | 14 | 0.14 | 4 | 97.479 | ||||||||||||||
52 | 0.05 | 10 | 600 | 100 | 1 | 0.01 | 1000 | 300 | 100 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 17.579 | 1.196 |
Optimal np | 29 | 0.29 | 6 | 14.694 | ||||||||||||||
53 | 0.05 | 10 | 600 | 100 | 1 | 0.09 | 1000 | 300 | 500 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 12 | 40.054 | 2.305 |
Optimal np | 12 | 0.12 | 4 | 17.376 | ||||||||||||||
54 | 0.01 | 5 | 300 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 3 | 160.846 | 1.135 |
Optimal np | 23 | 0.46 | 2 | 141.763 | ||||||||||||||
55 | 0.01 | 10 | 300 | 50 | 1 | 0.01 | 1000 | 50 | 100 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 3 | 22.654 | 1.206 |
Optimal np | 23 | 0.46 | 2 | 18.784 | ||||||||||||||
56 | 0.01 | 10 | 300 | 100 | 1 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 9.431 | 1.790 |
Optimal np | 16 | 0.16 | 2 | 5.268 | ||||||||||||||
57 | 0.05 | 10 | 300 | 100 | 1 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 70.265 | 1.267 |
Optimal np | 23 | 0.23 | 5 | 55.472 | ||||||||||||||
58 | 0.01 | 10 | 600 | 100 | 1 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 5 | 5.191 | 1.141 |
Optimal np | 80 | 0.8 | 4 | 4.549 | ||||||||||||||
59 | 0.05 | 10 | 600 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.01 | 0.125 | 1 | Traditional np | 50 | 1 | 8 | 223.001 | 1.777 |
Optimal np | 14 | 0.28 | 4 | 125.470 | ||||||||||||||
60 | 0.05 | 5 | 600 | 100 | 0.5 | 0.09 | 10,000 | 300 | 500 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 103.501 | 1.081 |
Optimal np | 62 | 0.62 | 9 | 95.762 | ||||||||||||||
61 | 0.01 | 5 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 100 | 0.01 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 72.504 | 1.311 |
Optimal np | 39 | 0.39 | 3 | 55.287 | ||||||||||||||
62 | 0.05 | 5 | 600 | 100 | 0.5 | 0.09 | 1000 | 50 | 500 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 42.964 | 1.080 |
Optimal np | 50 | 0.5 | 8 | 39.768 | ||||||||||||||
63 | 0.01 | 5 | 300 | 50 | 0.5 | 0.01 | 1000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 3 | 16.122 | 1.133 |
Optimal np | 23 | 0.46 | 2 | 14.236 | ||||||||||||||
64 | 0.01 | 5 | 600 | 100 | 0.5 | 0.09 | 1000 | 50 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 19.332 | 1.189 |
Optimal np | 39 | 0.39 | 3 | 16.263 | ||||||||||||||
