Three possible states - operating (1), degraded (2) and failed (3).

When operating, it fails with a failure rate of =1/day and degrades with a failure rate of =1/day. When degraded, its failure rate increases to =2/day .

Degraded state is detected with probability 0.9 (failed state with probability 1) and repair occurs in both degraded and failed states. Repair starts immediately upon detection of the failed or degraded state and restores the system to the operating state, with a MTTR of 2 hours from the degraded state and with a MTTR of 6 hours from the failed state. The system is available in the operating and the degraded states. Set up the differential equations describing the evolution of the system states in time