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Table 2 Optimal sampling strategies (n s , n d ) and the resulting mean exposure variance s 2 μ (cf. equation (3)) at different combinations of variance components (s 2 BS ,s 2 BD ,s 2 μWD ; sections a-c), unit costs (π s , π d , c q ), and exponents α and β describing the shape of the relationship between costs and number of measurements (cf. equation (4))

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
  1. In all cases, the available budget R was set at 500. The determination of the boldface strategy in section a was illustrated in figure 4.