Abstract
We analyze the long-run availability of a two-unit parallel system sustained by a cold standby unit and attended by two identical repairmen. The system satisfies the usual conditions (i.i.d. random variables, perfect repair, instantaneous and perfect switch, queueing). Each operative unit has a constant failure rate and a general repair time distribution. We use Hokstad's supplementary variable method to construct a system of simultaneous partial differential equations. We present a first-order numerical scheme and an iterative algorithm for the solution of the equations. A particular but important numerical example (Weibull repair), illustrated by computer-plotted graphs, motivates the proposed approximation.
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