50% Confidence
z ¼ 0
S 1 ¼ 37.62
S 2 ¼ 28.91
S 3 ¼ 34.97
85% Confidence
z ¼ 1.037
S 1 ¼ 37.62 À (1.037 Â 2.944) ¼ 34.56
S 2 ¼ 28.91 À (1.037 Â 1.835) ¼ 27.01
S 3 ¼ 34.97 À (1.037 Â 0.56) ¼ 34.38
99% Confidence
z ¼ 2.327
S 1 ¼ 37.62 À (2.327 Â 2.944) ¼ 30.77
S 2 ¼ 28.91 À (2.327 Â 1.835) ¼ 24.64
S 3 ¼ 34.97 À (2.327 Â 0.56) ¼ 33.66
What can be seen is that while the expected values indicate that S l is approximately 10% better than S 3 (37.62 > 34.97), their scores are practically the same at
85% confidence level (34.56 % 34.38). At 99%, S 3 outperforms S l by 10%
(33.66 > 30.77).
Table 15.10 Standard normal distribution data
z
Probability
z
Probability
z
Probability
z
Probability
0
0.50
À0.45
0.6736
À0.90
0.8159
À1.60
0.9452
À0.05
0.5199
À0.50
0.6915
À1.00
0.8413
À1.70
0.9554
À0.10
0.5398
À0.55
0.7088
À1.05
0.8531
À1.80
0.9641
À0.15
0.5596
À0.60
0.7257
À1.10
0.8643
À1.90
0.9713
À0.20
0.5793
À0.65
0.7422
À1.15
0.8749
À2.00
0.9772
À0.25
0.5987
À0.70
0.7580
À1.20
0.8849
À2.10
0.9821
À0.30
0.6179
À0.75
0.7734
À1.30
0.9032
À2.20
0.9861
À0.35
0.6368
À0.80
0.7881
À1.40
0.9192
À2.30
0.9893
À0.40
0.6554
À0.85
0.8023
À1.50
0.9332
À2.40
0.9918
Table 15.11 Option scores for different confidence levels
Statistical data
Confidence level
Variance
Standard deviation
50%
85%
99%
z ¼ 0
z¼ 1.04
z ¼ 2.33
S 1
8.669
2.994
37.62
34.56
30.77
S 2
3.367
1.835
28.91
27.01
24.64
S 3
0.31
0.560
34.97
34.38
33.66
426
15 Multi Objective Evaluation Criteria for Infrastructure