One mechanic services 6 drilling machines for a steel plate manufacturer. Machin

Question

One mechanic services 6 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 6 working? days, and breakdowns tend to follow a Poisson distribution. The mechanic can handle an average of three repair jobs per day. Repairs follow a negative exponential distribution.

?a) On the? average, how many machines are waiting for? service?

The average number of machines waiting for service is _____

b) how many are in the system?

c) how many drills are running on average??

Explanation / Answer

Arrival rate, ? = 6 machines*(1/6 days per machine) = 1 job per day

Service rate, ? = 3 jobs per day

a) Number of machines waiting for service (Lq) = ?2/(?*(?-?)) = 12/(3*(3-1)) = 0.167

b) Number of machines in the system, (L) = ?/(?-?) = 1/(3-1) = 0.5

c) Machines running on average = 6 - L = 5.5 machines

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