# Poisson Distribution and Machines

The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of . = 3 per day (approximately Poisson in nature). The crew can service an average of µ = 8 machines per day, with a repair time distribution that resembles the exponential distribution.

Please help me with the following:

A) What is the utilization rate of this service system?

B) What is the average downtime for a machine that is broken?

C) How many machines are waiting to be serviced at any given time?

D) What is the probability that more than one machine is in the system? What is the probability that more than two are broken and waiting to be repaired or being serviced, as well as three and four machines?

Please put in Excel file.

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#### Solution Summary

The solution discusses Poisson distribution and determines the utilization rate, average downtime, how many and what the probability is of more than one machine in the system (see Excel document attached).