Question: A system consists of two components. Suppose each component is subject to failure at constant rate λ, independently of the other, up to when the first component fails. After that moment the remaining component is subject to additional load and to failure at constant rate 2λ.
a) Find the distribution of the time until both components have failed.
b) What are the mean and variance of this distribution?
c) Find the 90th percentile of this distribution.