4. A system contains two connected links that are subject to a random force. The probabilities of failure of the links are and . Find the probability of failure of the system.

Solution

Events:

A = Fracture of link A

B = Fracture of link B

C = Fracture of the system

We don’t know . We could consider two extreme cases.

1) A and B are independent.

2) A and B are completely dependent. If one component fails, the other component will fail.

or

Therefore,