Question

There is a system that has the following reliabilities for 3 components: 0.98, 0.97, and 0.98. Each component has a back-up with the same reliability and a switch with a reliability of 1.0. What is the reliability?

Answer 1

Assuming that - no specific configuration is given in the ques, so we assume them to be connected in series to each other.

Let 3 components be - C1, C2, C3

Reliability of C1 = working prob + (non working prob*backup working prob) = .98 + (.98*.02) = .9996

Reliability of C2 = working prob + (non working prob*backup working prob) = .97 + (.97*.03) = .9991

Reliability of C3 = working prob + (non working prob*backup working prob) = .98 + (.98*.02) = .9996

Overall reilability = 1.0*(.9996*.9991*.9996) = .9983

The system in series is 99.83% reliable