1. A generator system consists of a primary and a standby unit. The primary fails at a constant failure rate of 2 per month, and the standby unit fails only when on-line at a constant rate of 4 per month. Repair can begin only when both units have failed. Both units are repaired at the same time with an MTTR of 20 days. Derive the steady state equations for the state probabilities and solve for the system availability.
2. An emergency backup generator experiences standby (dormant) failures at a constant rate of 0.00314 per day. It takes 6 hr to inspect and test the generator. If it is found to be inoperative, it takes 24 hour to repair it. Determine an inspection interval that will maximize the availability of generator.
3. A radar unit consists of two primary components: a power supply and a transceiver. The power supply has a constant failure rate of 0.0031 failures per operating hour and takes an average of 5 hr (mean) to repair (constant repair rate). The transceiver fails an average (mean) of every 100 operating hours (constant failure rate) and takes 3 hr to repair (constant repair rate). What is the point availability of the radar unit after 10 hr use? How much does this differ from the steady state availability? If two radar units are operating in parallel (high-level active redundancy), what are the point, interval (after 10 hr), and steady state availability?
4. Derive steady-state availability solution to the two-component active redundant system (constant failure rate) when repair can be accomplished as shown in eth following diagram.