Example 3
The position of a slider-block linkage is required to be m when
. A failure occurs
if the actual position
is outside the tolerance range
m. The design variables are
independent and follow normal distributions of
,
. Since uncertainty exists in the
measurement of
,
the angle also follows a normal distribution with
. The measurement
uncertainty is independent of that in the mechanism dimensions. Use the First Order
Second Moment (FOSM) method to calculate the probability of failure.
Solution:
The vector of random
variables is .
The actual position of the slider is given by
Since the tolerance range is , failure occurs
when
or
. Let
, and
. Then, the
probability of failure of the mechanism is given by
Since the ransom variables are
independent and follow normal distributions, according to the FOSM method, the
mean and standard deviation of are calculated by
Thus, we have
Similarly, the mean and standard deviation of are calculated by
We have
The probability of failure of this mechanism is then given by
Ans.