6.6.2 A certain type component has two states: 0 D OFF and 1 D OPERATING. In state 0, the process remains there a random length of time, which is exponentially distributed with parameter , and then moves to state 1. The time in state 1 is exponentially distributed with parameter , after which the process returns to state 0.

The system has three of these components, A;B, and C, with distinct parameters:

In order for the system to operate, component A must be operating, and at least one of components B and C must be operating. In the long run, what fraction of time does the system operate? Assume that the component stochastic processes are independent of one another.

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Component Operating Failure Rate Repair Rate A B BB c B