Consider a system consisting of three components (labeled 1, 2, 3) that operate simultaneously. The system is able to function satisfactorily as long as any two of the three components are still functioning satisfactorily. The goal is for the system to function satisfactorily for a length of time t, so the system’s reliability, R(t), is the probability that this will occur. The times until failure of the individual components are independently (but not identically) distributed, where pi is the probability that the time until failure of component i exceeds t, for i = 1, 2, 3.
(a) Is this a k out of n system? If so, what are k and n?
(b) Draw a network representation of this system.
(c) Develop an explicit expression for the structure function of this system.
(d) Find R(t) as a function of the pi’s.