7. The
cable supports two independently and normally distributed forces F1 ~ N(15,
22) Nand F2 ~ N(10, 12) N shown below. If the maximum
tension of the cable is 20 N, determine the reliability of the system.
Solution
Connector
B:
Solve
the above equations, we have
Connector
C:
Solve
it, we have
Therefore,
we can obtain the distributions of all forces
,
and
The
reliability can be determined by if the largest force is smaller than the
allowable tension, thus we have:
, where
.
Finally,
we have ANS.