A device has three states, i.e. good (State 1), degraded (State 2) and failed (State 3). Initially, the device is good. The transition rates from good to degraded and failed states are ?12 = 0.3/hr and ?13 = 0.2/hr, respectively. The degraded state is not detected. The unit can also go from State 2 to State 3 with ?23 = 0.2/hr. Repair starts immediately upon device failure and restores the device to State 1. The MTTR (mean time to repair) is 1 hour.
a) What is the repair rate ?
b) Show the state transition diagram for the device.
c) If the unit can perform its function either in State 1 or 2, find the steady-state availability A for the device.