An operator is in charge of FIVE machines. After each machine completes a job, t

Question

An operator is in charge of FIVE machines. After each machine completes a job, the operator must reset it before a new job is started. In other words, the operator’s task is to set up each machine when a job is completed. The time to complete a job on any machine is negative exponential with mean 45 minutes. The time to set up any machine is also negative exponential with mean 8 minutes.

(1) Determine the average number of machines that are awaiting set up or are being set up.

(2)Determine the average time a machine is awaiting set up or are being set up.

(3) What is the probability that all machines are working?

Explanation / Answer

It is given that there are five machines , each machine requires 8 minutes to get set

This means the arrival rate A= 5 machines

The service rate S= 60 minutes/8 Minutes= 7.5

1)Determine the average number of machines that are awaiting set up or are being set up = Average number of Machines in the Queue = A2/S(S-A) = 52/7.5(7.5-5) = 25/7.5*2 = 1.66 Machines

2) Determine the average time a machine is awaiting set up or are being set up.= Average time in the Queue

= A/S(S-A) = 5/7.5(7.5-5) = 5/15 hour = 1/3 Hour = 20 Minutes

3)What is the probability that all machines are working?= The probability that there is 5 machines =

(A/S)5 *(1-A/S) = (5/7.5)5 * (1-5/7.5) =0.131687 *0.2857 = 0.03762

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