Table 6 \({2}^{12-6}\) experiment using Rayleigh distribution as the shift distribution.
From: Economic statistical model of the np chart for monitoring defectives
Run | Values of the input factors | Chart | Results | \({ETC}_{Traditional}\)/\({ETC}_{Optimal}\) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\({p}_{0}\) | \({\mu }_{\delta }\) | Ď„ | r | b | c | M | W | T | \(\varepsilon\) | e | D | n | h | UCL | ETC | |||
1 | 0.05 | 0.217 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 897.269 | 1.683 |
Optimal np | 12 | 0.12 | 4 | 533.107 | ||||||||||||||
2 | 0.05 | 0.117 | 600 | 50 | 1 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 8 | 42.420 | 1.273 |
Optimal np | 110 | 2.2 | 12 | 33.329 | ||||||||||||||
3 | 0.05 | 0.117 | 600 | 50 | 1 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 8 | 158.374 | 1.609 |
Optimal np | 125 | 2.5 | 13 | 98.439 | ||||||||||||||
4 | 0.05 | 0.117 | 300 | 100 | 0.5 | 0.09 | 10,000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 100 | 1 | 12 | 542.795 | 1.372 |
Optimal np | 23 | 0.23 | 5 | 395.680 | ||||||||||||||
5 | 0.01 | 0.040 | 300 | 100 | 0.5 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 5 | 4.621 | 1.390 |
Optimal np | 99 | 0.99 | 4 | 3.324 | ||||||||||||||
6 | 0.01 | 0.040 | 600 | 100 | 0.5 | 0.01 | 1000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 19.659 | 1.298 |
Optimal np | 39 | 0.39 | 3 | 15.147 | ||||||||||||||
7 | 0.01 | 0.023 | 600 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 140.226 | 1.118 |
Optimal np | 99 | 1.98 | 4 | 125.435 | ||||||||||||||
8 | 0.05 | 0.202 | 600 | 100 | 1 | 0.01 | 1000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 91.671 | 1.605 |
Optimal np | 12 | 0.12 | 4 | 57.105 | ||||||||||||||
9 | 0.05 | 0.202 | 300 | 100 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 467.710 | 1.201 |
Optimal np | 33 | 0.33 | 6 | 389.433 | ||||||||||||||
10 | 0.05 | 0.202 | 600 | 100 | 1 | 0.01 | 10,000 | 50 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 895.873 | 1.686 |
Optimal np | 12 | 0.12 | 4 | 531.253 | ||||||||||||||
11 | 0.01 | 0.040 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 3 | Traditional np | 50 | 1 | 3 | 4.822 | 1.290 |
Optimal np | 123 | 2.46 | 4 | 3.737 | ||||||||||||||
12 | 0.01 | 0.024 | 300 | 100 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 100 | 1 | 5 | 6.967 | 1.863 |
Optimal np | 99 | 0.99 | 4 | 3.741 | ||||||||||||||
13 | 0.01 | 0.040 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 206.367 | 1.243 |
Optimal np | 39 | 0.39 | 3 | 165.966 | ||||||||||||||
14 | 0.01 | 0.040 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.01 | 0.025 | 1 | Traditional np | 100 | 1 | 5 | 38.977 | 1.312 |
Optimal np | 131 | 1.31 | 5 | 29.706 | ||||||||||||||
15 | 0.05 | 0.117 | 600 | 50 | 1 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 8 | 53.867 | 1.097 |
Optimal np | 33 | 0.66 | 6 | 49.106 | ||||||||||||||
16 | 0.01 | 0.040 | 300 | 50 | 1 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 4.053 | 1.375 |
Optimal np | 123 | 2.46 | 4 | 2.949 | ||||||||||||||
17 | 0.01 | 0.023 | 300 | 100 | 0.5 | 0.09 | 1000 | 300 | 500 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 8.202 | 1.561 |
Optimal np | 50 | 0.5 | 3 | 5.254 | ||||||||||||||
18 | 0.05 | 0.202 | 300 | 50 | 0.5 | 0.09 | 1000 | 300 | 500 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 7 | 8.362 | 1.008 |
Optimal np | 38 | 0.76 | 6 | 8.294 | ||||||||||||||
19 | 0.01 | 0.023 | 600 | 100 | 1 | 0.01 | 10,000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 158.184 | 1.130 |
Optimal np | 80 | 0.8 | 4 | 139.960 | ||||||||||||||
20 | 0.05 | 0.117 | 300 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 7 | 447.019 | 1.039 |
Optimal np | 38 | 0.76 | 6 | 430.034 | ||||||||||||||
21 | 0.05 | 0.117 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 50 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 575.798 | 1.167 |
Optimal np | 29 | 0.29 | 6 | 493.330 | ||||||||||||||
22 | 0.01 | 0.023 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 5.958 | 1.382 |
Optimal np | 108 | 2.16 | 4 | 4.311 | ||||||||||||||
23 | 0.01 | 0.023 | 600 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 6.499 | 1.208 |
Optimal np | 99 | 1.98 | 4 | 5.382 | ||||||||||||||
24 | 0.01 | 0.023 | 600 | 100 | 1 | 0.09 | 1000 | 300 | 100 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 5 | 8.211 | 1.297 |
Optimal np | 80 | 0.8 | 4 | 6.332 | ||||||||||||||
25 | 0.01 | 0.023 | 300 | 50 | 0.5 | 0.01 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 6.405 | 1.644 |
Optimal np | 123 | 2.46 | 4 | 3.896 | ||||||||||||||
26 | 0.05 | 0.117 | 300 | 50 | 1 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.125 | 1 | Traditional np | 50 | 1 | 7 | 142.729 | 1.032 |
Optimal np | 38 | 0.76 | 6 | 138.243 | ||||||||||||||
27 | 0.01 | 0.023 | 300 | 50 | 1 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 6.511 | 1.630 |
Optimal np | 123 | 2.46 | 4 | 3.995 | ||||||||||||||
28 | 0.01 | 0.202 | 600 | 50 | 1 | 0.01 | 10,000 | 50 | 500 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 8 | 704.151 | 1.255 |
Optimal np | 14 | 0.28 | 4 | 561.154 | ||||||||||||||
29 | 0.01 | 0.040 | 600 | 100 | 0.5 | 0.01 | 10,000 | 50 | 100 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 5 | 138.669 | 1.121 |
Optimal np | 80 | 0.8 | 4 | 123.662 | ||||||||||||||
30 | 0.01 | 0.040 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 4.171 | 1.367 |
Optimal np | 123 | 2.46 | 4 | 3.052 | ||||||||||||||
31 | 0.01 | 0.023 | 600 | 50 | 0.5 | 0.09 | 10,000 | 50 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 140.097 | 1.118 |
Optimal np | 99 | 1.98 | 4 | 125.292 | ||||||||||||||
32 | 0.01 | 0.023 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 100 | 1 | 5 | 139.267 | 1.262 |
Optimal np | 131 | 1.31 | 5 | 110.331 | ||||||||||||||
33 | 0.05 | 0.202 | 300 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 897.269 | 1.805 |
Optimal np | 14 | 0.14 | 4 | 497.233 | ||||||||||||||
34 | 0.05 | 0.202 | 300 | 50 | 0.5 | 0.01 | 10,000 | 300 | 100 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 7 | 677.842 | 1.275 |
Optimal np | 16 | 0.32 | 4 | 531.480 | ||||||||||||||
35 | 0.05 | 0.117 | 300 | 50 | 1 | 0.01 | 10,000 | 50 | 100 | 0.01 | 0.125 | 3 | Traditional np | 50 | 1 | 7 | 160.205 | 1.028 |
Optimal np | 38 | 0.76 | 6 | 155.898 | ||||||||||||||
36 | 0.05 | 0.117 | 300 | 50 | 0.5 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.125 | 1 | Traditional np | 50 | 1 | 7 | 14.533 | 1.030 |
Optimal np | 38 | 0.76 | 6 | 14.105 | ||||||||||||||
37 | 0.05 | 0.202 | 600 | 50 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 8 | 705.787 | 1.254 |
Optimal np | 0.14 | 0.28 | 4 | 562.970 | ||||||||||||||
38 | 0.01 | 0.023 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 6.499 | 1.629 |
Optimal np | 123 | 2.46 | 4 | 3.990 | ||||||||||||||
39 | 0.05 | 0.117 | 600 | 100 | 1 | 0.09 | 10,000 | 300 | 100 | 0.01 | 0.025 | 1 | Traditional np | 100 | 1 | 12 | 93.055 | 1.034 |
Optimal np | 115 | 1.15 | 13 | 89.968 | ||||||||||||||
40 | 0.01 | 0.117 | 300 | 50 | 1 | 0.09 | 10,000 | 300 | 500 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 7 | 95.339 | 1.137 |
Optimal np | 106 | 2.12 | 11 | 83.831 | ||||||||||||||
41 | 0.05 | 0.202 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 466.191 | 1.142 |
Optimal np | 39 | 0.39 | 7 | 408.124 | ||||||||||||||
42 | 0.01 | 0.023 | 300 | 50 | 1 | 0.01 | 1000 | 300 | 500 | 0.05 | 0.025 | 3 | Traditional np | 50 | 1 | 3 | 14.605 | 1.263 |
Optimal np | 123 | 2.46 | 4 | 11.561 | ||||||||||||||
43 | 0.05 | 0.202 | 600 | 100 | 0.5 | 0.01 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 897.169 | 1.686 |
Optimal np | 12 | 0.12 | 4 | 532.268 | ||||||||||||||
44 | 0.01 | 0.023 | 300 | 50 | 0.5 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.025 | 1 | Traditional np | 50 | 1 | 3 | 63.832 | 1.647 |
Optimal np | 123 | 2.46 | 4 | 38.761 | ||||||||||||||
45 | 0.01 | 0.040 | 600 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.01 | 0.025 | 3 | Traditional np | 50 | 1 | 3 | 46.302 | 1.137 |
Optimal np | 99 | 1.98 | 4 | 40.725 | ||||||||||||||
46 | 0.05 | 0.202 | 600 | 50 | 0.5 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.025 | 1 | Traditional np | 50 | 1 | 8 | 33.642 | 1.077 |
Optimal np | 44 | 0.88 | 7 | 31.239 | ||||||||||||||
47 | 0.05 | 0.202 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 500 | 0.01 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 281.441 | 1.884 |
Optimal np | 20 | 0.2 | 5 | 149.379 | ||||||||||||||
48 | 0.05 | 0.202 | 300 | 50 | 0.5 | 0.09 | 1000 | 50 | 100 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 7 | 68.942 | 1.265 |
Optimal np | 16 | 0.32 | 4 | 54.510 | ||||||||||||||
49 | 0.05 | 0.202 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 100 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 897.204 | 1.683 |
Optimal np | 12 | 0.12 | 4 | 533.016 | ||||||||||||||
50 | 0.05 | 0.202 | 600 | 100 | 1 | 0.09 | 10,000 | 300 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 12 | 898.879 | 1.681 |
Optimal np | 12 | 0.12 | 4 | 534.716 | ||||||||||||||
51 | 0.05 | 0.117 | 300 | 100 | 1 | 0.09 | 10,000 | 50 | 100 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 12 | 184.819 | 1.457 |
Optimal np | 33 | 0.33 | 6 | 126.838 | ||||||||||||||
52 | 0.05 | 0.202 | 600 | 100 | 1 | 0.01 | 1000 | 300 | 100 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 12.195 | 1.097 |
Optimal np | 50 | 0.50 | 8 | 11.112 | ||||||||||||||
53 | 0.05 | 0.202 | 600 | 100 | 1 | 0.09 | 1000 | 300 | 500 | 0.01 | 0.125 | 1 | Traditional np | 100 | 1 | 12 | 27.672 | 1.876 |
Optimal np | 20 | 0.20 | 5 | 14.754 | ||||||||||||||
54 | 0.01 | 0.023 | 300 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 3 | 150.252 | 1.119 |
Optimal np | 65 | 1.3 | 3 | 134.227 | ||||||||||||||
55 | 0.01 | 0.040 | 300 | 50 | 1 | 0.01 | 1000 | 50 | 100 | 0.05 | 0.125 | 3 | Traditional np | 50 | 1 | 3 | 18.107 | 1.130 |
Optimal np | 23 | 0.46 | 2 | 16.029 | ||||||||||||||
56 | 0.01 | 0.040 | 300 | 100 | 1 | 0.01 | 1000 | 50 | 500 | 0.01 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 7.589 | 1.500 |
Optimal np | 16 | 0.16 | 2 | 5.059 | ||||||||||||||
57 | 0.05 | 0.202 | 300 | 100 | 1 | 0.01 | 1000 | 300 | 100 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 49.083 | 1.175 |
Optimal np | 33 | 0.33 | 6 | 41.756 | ||||||||||||||
58 | 0.01 | 0.040 | 600 | 100 | 1 | 0.09 | 1000 | 50 | 100 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 5 | 4.955 | 1.224 |
Optimal np | 133 | 1.31 | 5 | 4.049 | ||||||||||||||
59 | 0.05 | 0.202 | 600 | 50 | 1 | 0.09 | 10,000 | 300 | 100 | 0.01 | 0.125 | 1 | Traditional np | 50 | 1 | 8 | 174.064 | 1.375 |
Optimal np | 23 | 0.46 | 5 | 126.571 | ||||||||||||||
60 | 0.05 | 0.117 | 600 | 100 | 0.5 | 0.09 | 10,000 | 300 | 500 | 0.01 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 112.815 | 1.027 |
Optimal np | 115 | 1.15 | 3 | 109.819 | ||||||||||||||
61 | 0.01 | 0.023 | 600 | 100 | 1 | 0.01 | 10,000 | 300 | 100 | 0.01 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 81.563 | 1.292 |
Optimal np | 80 | 0.80 | 4 | 63.112 | ||||||||||||||
62 | 0.05 | 0.117 | 600 | 100 | 0.5 | 0.09 | 1000 | 50 | 500 | 0.05 | 0.025 | 3 | Traditional np | 100 | 1 | 12 | 37.429 | 1.010 |
Optimal np | 88 | 0.88 | 11 | 37.049 | ||||||||||||||
63 | 0.01 | 0.023 | 300 | 50 | 0.5 | 0.01 | 1000 | 50 | 100 | 0.05 | 0.125 | 1 | Traditional np | 50 | 1 | 3 | 15.045 | 1.119 |
Optimal np | 65 | 1.3 | 3 | 13.444 | ||||||||||||||
64 | 0.01 | 0.023 | 600 | 100 | 0.5 | 0.09 | 1000 | 50 | 500 | 0.05 | 0.125 | 3 | Traditional np | 100 | 1 | 5 | 16.341 | 1.115 |
Optimal np | 80 | 0.80 | 4 | 14.651 | ||||||||||||||
