Box-Behnken Designs vs new 3-level Second-Order Designs*

m p Design IBD of size
(v,k,r)
n+n0 # of orthogonal
blocks
Q* |M| G-eff
5 21 BBD
D536
(5,2,4)
(5,3,6)
40+6
40+6
2
2
0.9974
0.9911
1.54E-27
4.68E-28
0.8300
0.4348
6 28 BBD
D636
(6,3,3)
(6,3,6)
48+6
48+6
2
2
0.9905
0.9959
2.67E-41
5.95E-41
0.6222
0.7071
7 36 BBD
D736
(7,3,3)
(7,3,6)
56+6
56+6
2
2
1.0000
1.0000
7.98E-57
7.98E-57
0.9290
0.9290
8 45 D8312
D848
BBD
D8318
(8,3,12)
(8,4,8)
(8,3,9)
(8,3,18)
128+8
128+8
192+16
192+16
1
2
2
1
0.9983
0.9974
0.9974
0.9993
5.64E-76
3.71E-76
2.07E-76
4.26E-76
0.9108
0.6943
0.7101
0.9050
9 55 BBD
D934
BBD
D948
(9,3,5)
(9,3,4)
(9,4,4)
(9,4,8)
120+10
96+8
144+10
144+10
10
8
2
2
0.9924
0.9985
0.9927
0.9982
7.25E-100
6.50E-99
2.24e-101
7.84e-99
0.7811
0.8753
0.1681
0.6593
10 66 BBD
D1048
(10,4,4)
(10,4,8)
160+10
160+10
2
2
0.9928
0.9982
3.64E-126
9.87E-125
0.6539
0.7639
11 78 BBD
D1148
(11,5,5)
(11,4,8)
176+12
176+12
1
2
0.9996
0.9977
7.48E-154
1.93E-154
0.7660
0.7720
12 91 BBD
D1248
(12,4,4)
(12,4,8)
192+12
192+12
2
2
0.9962
0.9980
1.51E-187
4.38E-187
0.8480
0.8480
13 105 D1344 (13,4,4) 208+12 2 0.9990 5.10E-223 0.9025
16 153 BBD
D1645
(16,4,6)
(16,4,5)
384+12
320+10
12
10
0.9935
0.9974
1.80E-356
6.54E-354
0.8288
0.8884

*Nguyen N-K & J. J. Borkowski (2008) New 3-level response surface designs constructed
from incomplete block designs. J. of Statistical Planning & Inference 138, 294-305.pdf

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