Approximate Markov Modeling of High-Reliability Telecommunications Systems

The reliability model of a system with redundancy but only a single repairman is Markov only if the component failure rates and the repair rate are constants. This paper introduces a method with which a reliability analyst can formulate an approximate (time-homogeneous) Markov model for a system with 1-out-of-2 redundancy when repair is nonexponential (repair rate is time-dependent). This approximate model yields accurate steady-state predictions of system reliability when time-to-repair is orders of magnitude smaller than timeto-component-failure, as is typical in high-reliability telecommunications systems. Transition rates and error bounds for the approximate model are given based on the first three moments of the repair time distribution. An application of the method is shown for the system in which repair time is composed of a "next day" parts delivery phase followed by an on-site repair phase.