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Q3. Each time a machine is repaired it remains up for an exponentially distributed time with rate A. It then fails and dow

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Solution :-

For any given machine, it can have any one of the three states

State Condition

0 Machine works

1 Machine suffered faliure Type I and is being repaired

2   Machine suffered faliure Type II and is being repaired

For long term percentages we need to balance, the inflow and outflow rate for each state.

For state 0, the inflow rate is the sum of the repair rates and the outflow rate is the failure rate.

For State I, the inflow rate is the failure rate and the outflow rate is the repair rate.

State inflous rote udflora rate μ, 2

The system is in steady state, if all these rate balance.

We have the additional condition,

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