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gives a good representation of how an increase in number of trials improves the level of
confidence.
Probabililty of failure (P(f) %) versus number of trials
2.5
P(f) %
2
1.5
1
0.5
0
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
Number of trials
Figure 8.15: Probability of failure versus number of trials
The GEO-SLOPE Stability Modelling document (2008) developed an equation to calculate
the number of trials required. The method is dependent on the desired level of confidence and
the number of random variables.
𝑚
𝑑2
𝑁=�
�
4(1 − 𝜀)2
where:
N
= number of trials
𝜀
= the desired level of confidence (0 to 100%) expressed as a decimal
m
= the number of variables
d
= the normal standard deviation corresponding to the level of confidence
8.6
Table 8.7: Normal standard deviate values for levels of confidence (Abramson, 2002)
𝜀%
80
d
1.282
90
1.645
95
1.960
99
2.576
107