7. (6 points) Determine the steady-state availability for a system consisting of one active and two standby components. All units have identical failure rates and repair rates with only a single repair crew available and no failures in standby, as implied by the following rate diagram. In state 1 the active component is on-line, in state 2 the first backup is on-line, in state 3 the second backup is on-line, and in state 4 all three components have failed. Derive the steady-state equations and determine the steady-state availability if the failure rate is 2 per week and the repair rate is 5 per week.

7. (6 points) Determine the steady-state availability for a system consisting of one active and two standby components. All units have identical failure rates and repair rates with only a single repair crew available and no failures in standby, as implied by the following rate diagram. In state the active component is on-line, in state 2 the first backup is on-line, in state 3 the second backup is on-line, and in state 4 all three components have failed. Derive the steady-state equations and determine the steady-state availability if the failure rate is 2 per week and the repair rate is 5 per week. 2 oro