91Ó°ÊÓ

Consider a structure in which the minimal path sets are \(\\{1,2,3\\}\) and \(\\{3,4,5\\}\). (a) What are the minimal cut sets? (b) If the component lifetimes are independent uniform \((0,1)\) random variables, determine the probability that the system life will be less than \(\frac{1}{2}\).

Find the mean lifetime of a series system of two components when the component lifetimes are respectively uniform on \((0,1)\) and uniform on \((0,2) .\) Repeat for a parallel system.