Question

A system consists of four components in parallel. Their reliabilities are 0.40, 0.60, 0.50, and 0.40. The system reliability is \(\underline{\hspace{1cm}}\). (round off to 3 decimal places)

Hint:

Parallel systems reduce failure risk because the system works if at least one component works.

Answer 1

Correct Answer: 0.918

For components in parallel, system reliability is:
\[ R_s = 1 - \prod (1 - R_i) \] Failure probabilities:
\[ 1-0.40=0.60, 1-0.60=0.40, 1-0.50=0.50, 1-0.40=0.60 \] Multiply:
\[ 0.60 \times 0.40 \times 0.50 \times 0.60 = 0.072 \] Thus:
\[ R_s = 1 - 0.072 = 0.928 \] \[ \boxed{0.928} \]