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* D-eff (%)
G-eff (%)
5 21 BBD
D536
(5,2,4)
(5,3,6)
40+6
40+6
2
2
0.9974
0.9911
95.08
89.84
83.00
43.48
6 28 BBD
D636
(6,3,3)
(6,3,6)
48+6
48+6
2
2
0.9905
0.9959
91.11
93.75
62.22
70.71
7 36 BBD
D736
(7,3,3)
(7,3,6)
56+6
56+6
2
2
1.0000
1.0000
96.38
96.38
92.90
92.90
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
97.29
96.38
95.15
96.69
85.52
69.43
71.01
90.50
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
91.86
95.60
86.24
95.93
78.11
87.53
16.81
65.93
10 66 BBD
D1048
(10,4,4)
(10,4,8)
160+10
160+10
2
2
0.9928
0.9982
91.26
95.94
65.39
76.39
11 78 BBD
D1148
(11,5,5)
(11,4,8)
176+12
176+12
1
2
0.9996
0.9977
96.46
94.80
76.60
77.20
12 91 BBD
D1248
(12,4,4)
(12,4,8)
192+12
192+12
2
2
0.9962
0.9980
94.20
95.30
84.80
84.80
13 105 D1344 (13,4,4) 208+12 2 0.9990 96.23
90.25
16 153 BBD
D1645
(16,4,6)
(16,4,5)
384+12
320+10
12
10
0.9935
0.9974
92.53
96.17
82.88
88.84

*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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