Question: A manufacturing system has five identical machines and a single repairman. The operating time until failure of a machine is exponentially distributed with parameter (rate)

A manufacturing system has five identical machines and a single repairman. The operating

time until failure of a machine is exponentially distributed with parameter (rate) 0.2 per

hour. The repair time of a failed machine is exponentially distributed with parameter (rate)

0.5 per hour. Up to five machines may be operating at any given time, their failures being

independent of one another, but at most one machine may be in repair at any time as there

is only one repairman.

a) Let N(t) be the number of machines operating at time t. Model the evolution of N(t) over

time as a continuous time Markov chain by providing the corresponding graphical

representation. Feel free to use any of the alterative characterizations discussed in class.

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