Question: 6.2. A certain type component has two states: 0 = OFF and 1 = OPERATING. In state 0, the process remains there a random length

6.2. A certain type component has two states: 0 = OFF and 1 =

OPERATING. In state 0, the process remains there a random length of time, which is exponentially distributed with parameter

a, and then moves to state 1. The time in state 1 is exponentially distributed with parameter J3, after which the process returns to state 0.

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

Component Operating Failure Rate ABC BA K Bc BB Repair Rate B

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.

Component Operating Failure Rate ABC BA K Bc BB Repair Rate B

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