A system has two components C1 and C2 , which work in series (i.e., when one component fails, the system fails). Suppose that components fail at rates i , and can be repaired at rates μi , i = 1, 2. When one of the components fail, the other is not in use and therefore cannot fail until the system is functioning again.

Assume now that the machines are not serially connected, and if one of them fails, the other continues to function, and therefore may also fail while the first machine is being repaired.

(a) Develop the diagram for this Markov chain.

(b) Write down the time-dependent ordinary differential equations for this Markov chain.

(c) Construct the steady-state equations.