Example 1
The position of a slider-crank mechanism is required to be mm when
. If the actual
position
is
outside the tolerance range
mm, it is considered that a failure occurs. The design variables
are independent and follow normal distributions of
,
, and
. 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 design variables are
independent and follow normal distributions, and
also follow normal distributions with
and
, respectively.
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.