Availability of k-out-of-n: F Secondary Subsystem with General Repair Time Distribution

In this paper we study the steady state availability of main k-out-of-n: f and secondary subsystems. when more than k units of main subsystem fail, then the main subsystem shuts off the secondary subsystem. the life time distributions of the main units and that of secondary subsystem are exponentially distributed. a repair facility having single repairman is facilitated to restore the failed unit. the repair time is assumed to be i.i.d. general distributed. the failure of the main unit shuts off the operation of secondary subsystem, but not the other way around. the steady state availability is obtained by solving the linear ordinary differential equations governing the model by using supplementary variable technique. four special cases of the repair distribution namely exponential, gamma, weibull and pareto have been examined numerically for the illustration purposes.