16. A
shaft undergoes a reversing nomial stress 
with the number of cycles 
. The ultimate strength and
edurance limit are 
and 
, respectively. The fatigure
strenghth fraction is determined as 
. If 
and 
are independent, estimate the
probability of failure using the First Order Second Moment Method.
Solution
The number of cycles to failure is
where
So
the limit-state function is the actual number of cycles subtracted from the
number of cycles to failure. Failure occurs when
.
where
.
Using FOSM, we have
The probability of failure is then given by
