The time to failure in years of a type of computer has the P

The time to failure in years of a type of computer has the PDF f(t)=1/(t+1)².

A. If three of these computers are placed in parallel, what is the system reliability for the first six months of operation?

Solution

We integrate given function from 0 to 0.5 to get probability that a component lasts 6 months = 1/3

Since components are paralell, all 3 fails and the system will fail, thus probability of failing is (1/3)^3 , and reliability = 1 -(1/3)^3=0.963 (correct)