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.