Application of Probability to Mechanical Design
f(a) and f(A) are Gaussian or normal functions [2.18]
£(a) - --exp - ~ -L
57
(2.32)
(2.33)
The range for these evaluations is from minus to plus infinity for a and A.
The reliability or probability that capacity is greater than the load is shown
in the following equation
A - a > 0
(2.34)
and letting
~ = A - a
(2.35)
then from Eq. (2.17)
PC = #A - #a
(2.36)
~ I,~
2 _L ,~211/2
(2.37)
= L~A I ~a]
Thenf(~) =f(A)-f(a) is a normal distribution which can also be verified by
computer with two normal distribution inputs. Then
1 [ 1 (~- ~¢~21
(2.38)
’~ f(A).
Figure 2.6 Distribution of capacity and load with resulting failure.