Reliability, MTTF and steady-state availability analysis of systems with exponential lifetimes

Our analysis focuses mainly on coherent systems and series connection of k-out-of-n standby subsystems with exponentially distributed component lifetimes. We analyze system reliability, mean time to failure, and steady-state availability as a function of the component failure rates. Our primary objective is provide explicit expressions for these performance measures and obtain various characterizations on their mathematical structures. This primarily involves difference of convex functions which are known to be very useful in the context of optimization problems.