Consider the system shown below where the reliability of com

Consider the system shown below where the reliability of component 1 is 0.93, the reliability of component 2 is 0.9, the reliability of component 3 is 0.92, the reliability of component 4 is 0.78 and the reliability of component 5 is 0.78.

What is the reliability of the entire system?   
Give your answer to 4 decimal places.

Solution

Here,

Reliability = P[(1 and 2 and 3) U (4 U 5)]

= P(1 and 2 and 3) + P(4 or 5) - P(1 and 2 and 3 and (4 or 5))

= [P(1) P(2) P(3)] + [P(4) + P(5) - P(4 and 5)] - [P(1) P(2) P(3) P(4 or 5)]

= [P(1) P(2) P(3)] + [P(4) + P(5) - P(4) P(5)] - {P(1) P(2) P(3) [P(4) + P(5) - P(4) P(5)]}

Plugging in our values,

Reliability = (0.93*0.9*0.92) + (0.78 + 0.78 - 0.78*0.78) - ((0.93*0.9*0.92)*(0.78+0.78-0.78*0.78))

= 0.988869936 = 0.9889 [ANSWER]