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

the same setup as b but now the switch has a reliability of .97. what is the reliability?

Answer 1

Solution -

Reliability of A1 = working prob + (non working prob*backup working prob) = .98 + (.98*.02) = .9996

Reliability of A2 = working prob + (non working prob*backup working prob) = .97 + (.97*.03) = .9991

Reliability of A3 = working prob + (non working prob*backup working prob) = .98 + (.98*.02) = .9996

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

The above system in series is 99.83% reliable

2nd Condition

switch has a reliability of .97.

Reliability of A1 = working prob + (non working prob*backup working prob) = .98 + (.98*.02) = .9996

Reliability of A2 = working prob + (non working prob*backup working prob) = .97 + (.97*.03) = .9991

Reliability of A3 = working prob + (non working prob*backup working prob) = .98 + (.98*.02) = .9996

Overall reilability A* = 0.97*(.9996*.9991*.9996) = .9686

The above system in series is 96.84% reliable