Abstract
Abstract A system with N operating units and M warm standby units having ‘r’ repair facilities is considered. Failure rates for operating and standby units are constant while the repair times are arbitrarily distributed. The system under consideration fails when there is either a common cause failure or when there are only K-1 good units. The problem is formulated using supplementary variable technique and the differential equations are solved using Lagrange's method for linear partial differential equations. Expressions for state probabilities, reliability and steady-state availability are obtained followed by special cases.
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