Module 5 - E-Courses

Reliability Engineering Prof. G. L. Sivakumar Babu
Figure
8 - Algorithm for finding βHL
Indian Institute of Science Bangalore
Note: A number in parentheses indicates iteration numbers
Consider a limit state function g(X1, X2, . . . , Xn) where the random variables Xi are all
uncorrelated. (If the variables are correlated, then a transformation can be used to obtain
uncorrelated variables. See Example 5.15.) The limit state function is rewritten in terms
of the standard form of the variables (reduced variables) using
Z
i
=
X i
− µ
σ
X i
X i
As before, the Hasofer-Lind reliablity index is defined as the shortest distance from the
origin
of the reduced variable space to the limit state function g = 0.
Thus far nothing has changed from the previous presentation of the reliability index. In
fact, if the limit state function is linear, then the reliability index is still calculated as in
Eq 5.18
a
β =
0
+
n
∑
i=
1
n
∑
i=
1
i
a µ
i
X i
X i
( a σ )
2
-------------------------------- (26)
22