Consider a system consisting of three independent components. Suppose the lifeti
ID: 3174766 • Letter: C
Question
Consider a system consisting of three independent components. Suppose the lifetimes of these components follow an Exponential distribution with mean 200 hours, 360 hours, and 400 hours, respectively.
b. Suppose that the system works only if at least one component is functional (e.g., parallel connection). Find the probability that the system still works after 335 hours. That is, find the probability that at least one component still work after 335 hours. Round your answer to 4 decimal places.
"Hint": P(X1 > 335 hours OR X2 > 335 hours OR X3 > 335 hours).
Explanation / Answer
probability that at least one component will work =1-P(none of the component works)
=1-(1-e-335/200)*(1-e-335/360)*(1-e-335/400) =1-0.2792=0.7208