From: Optimizing cost-efficiency in mean exposure assessment - cost functions reconsidered
a. (s 2 BS , s 2 BD , s 2 μWD ) = (2, 10, 10) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
 | α: | 0.50 | 0.75 | 1.00 | 1.25 | 1.50 | |||||
 |  | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ |
(π s , π d , c q ) | β |  |  |  |  |  |  |  |  |  |  |
(2, 10, 10) | 0.50 | (14, 2) | 0.86 | (14, 2) | 0.86 | (10, 3) | 0.87 | (13, 2) | 0.92 | (9, 3) | 0.96 |
 | 0.75 | (24, 1) | 0.92 | (13, 2) | 0.92 | (9, 3) | 0.96 | (12, 2) | 1.00 | (8, 3) | 1.08 |
 | 1.00 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (11, 2) | 1.09 | (10, 2) | 1.20 |
 | 1.25 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 1.50 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
(11, 5.5, 5.5) | 0.50 | (17, 3) | 0.51 | (15, 3) | 0.58 | (11, 4) | 0.64 | (7, 7) | 0.69 | (5, 10) | 0.80 |
 | 0.75 | (22, 2) | 0.55 | (14, 3) | 0.62 | (10, 4) | 0.70 | (6, 7) | 0.81 | (6, 6) | 0.89 |
 | 1.00 | (39, 1) | 0.56 | (18, 2) | 0.67 | (9, 4) | 0.78 | (8, 4) | 0.88 | (6, 5) | 1.00 |
 | 1.25 | (39, 1) | 0.56 | (32, 1) | 0.69 | (14, 2) | 0.86 | (7, 4) | 1.00 | (6, 4) | 1.17 |
 | 1.50 | (39, 1) | 0.56 | (32, 1) | 0.69 | (13, 2) | 0.92 | (6, 4) | 1.17 | (5, 4) | 1.40 |
(20, 1, 1) | 0.50 | (49, 5) | 0.12 | (27, 7) | 0.18 | (14, 12) | 0.26 | (8, 23) | 0.36 | (6, 28) | 0.45 |
 | 0.75 | (52, 4) | 0.13 | (21, 9) | 0.20 | (13, 12) | 0.28 | (8, 19) | 0.38 | (6, 23) | 0.48 |
 | 1.00 | (80, 2) | 0.15 | (26, 5) | 0.23 | (13, 9) | 0.32 | (8, 14) | 0.43 | (6, 17) | 0.53 |
 | 1.25 | (74, 2) | 0.16 | (27, 4) | 0.26 | (13, 7) | 0.37 | (8, 10) | 0.50 | (6, 12) | 0.61 |
 | 1.50 | (134, 1) | 0.16 | (29, 3) | 0.30 | (12, 6) | 0.44 | (9, 6) | 0.59 | (5, 12) | 0.73 |
b. ( s 2 BS , s 2 BD , s 2 μWD ) = (11, 5.5, 5.5) | |||||||||||
 | α: | 0.50 | 0.75 | 1.00 | 1.25 | 1.50 | |||||
 |  | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ |
(2, 10, 10) | 0.50 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 0.75 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 1.00 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 1.25 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 1.50 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
(11, 5.5, 5.5) | 0.50 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (12, 2) | 1.38 | (9, 2) | 1.83 |
 | 0.75 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (12, 2) | 1.38 | (9, 2) | 1.83 |
 | 1.00 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (9, 2) | 1.83 |
 | 1.25 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (8, 2) | 2.06 |
 | 1.50 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (8, 2) | 2.06 |
(20, 1, 1) | 0.50 | (134, 1) | 0.16 | (44, 2) | 0.38 | (19, 4) | 0.72 | (11, 6) | 1.17 | (7, 14) | 1.68 |
 | 0.75 | (134, 1) | 0.16 | (43, 2) | 0.38 | (18, 4) | 0.76 | (11, 5) | 1.20 | (7, 12) | 1.70 |
 | 1.00 | (134, 1) | 0.16 | (42, 2) | 0.39 | (19, 3) | 0.77 | (11, 4) | 1.25 | (7, 9) | 1.75 |
 | 1.25 | (134, 1) | 0.16 | (40, 2) | 0.41 | (18, 3) | 0.81 | (10, 5) | 1.32 | (7, 7) | 1.80 |
 | 1.50 | (134, 1) | 0.16 | (53, 1) | 0.42 | (20, 2) | 0.83 | (11, 3) | 1.33 | (7, 5) | 1.89 |
c. ( s 2 BS , s 2 BD , s 2 μWD ) = (20, 1, 1) | |||||||||||
 | α: | 0.50 | 0.75 | 1.00 | 1.25 | 1.50 | |||||
 |  | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ | ( n s , n d ) | s 2 μ |
(2, 10, 10) | 0.50 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 0.75 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 1.00 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 1.25 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
 | 1.50 | (24, 1) | 0.92 | (23, 1) | 0.96 | (22, 1) | 1.00 | (20, 1) | 1.10 | (17, 1) | 1.29 |
(11, 5.5, 5.5) | 0.50 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (10, 1) | 2.20 |
 | 0.75 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (10, 1) | 2.20 |
 | 1.00 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (10, 1) | 2.20 |
 | 1.25 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (10, 1) | 2.20 |
 | 1.50 | (39, 1) | 0.56 | (32, 1) | 0.69 | (22, 1) | 1.00 | (15, 1) | 1.47 | (10, 1) | 2.20 |
(20, 1, 1) | 0.50 | (134, 1) | 0.16 | (53, 1) | 0.42 | (22, 1) | 1.00 | (12, 2) | 1.75 | (8, 3) | 2.58 |
 | 0.75 | (134, 1) | 0.16 | (53, 1) | 0.42 | (22, 1) | 1.00 | (12, 2) | 1.75 | (8, 3) | 2.58 |
 | 1.00 | (134, 1) | 0.16 | (53, 1) | 0.42 | (22, 1) | 1.00 | (12, 2) | 1.75 | (8, 2) | 2.63 |
 | 1.25 | (134, 1) | 0.16 | (53, 1) | 0.42 | (22, 1) | 1.00 | (12, 2) | 1.75 | (8, 2) | 2.63 |
 | 1.50 | (134, 1) | 0.16 | (53, 1) | 0.42 | (22, 1) | 1.00 | (12, 1) | 1.83 | (8, 2) | 2.63 |