Consider two machines that are maintained by a single repairman. Machine i functions for an exponential time

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Consider two machines that are maintained by a single repairman. Machine i functions for an exponential time with rate μi before breaking down, i = 1, 2.

The repair times (for either machine) are exponential with rate μ. Can we analyze this as a birth and death process? If so, what are the parameters? If not, how can we analyze it?

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