A unit has three modes, i.e. good (State 1), degraded (State 2) and failed (State 3). The unit can still function in the degraded state. The transition rate from the good to the degraded state is λ 12=0.3/hr and the transition rate from degraded to failed state is λ23=0.2/hr. There is no repair.
a) Write down the differential equations which describe the probabilistic behavior of the unit in time as a Markov process.
b) Find the reliability function for the unit.
c) Find the probability that the unit fails during the first 10 hr of operation.