From Simulation wtih Arena By: Kelton 3-14 Five identical machines operate indep

Question

From Simulation wtih Arena By: Kelton

3-14 Five identical machines operate independently in a small shop. Each machine is up (i.e., works) for between 7 and 10 hours (uniformly distributed) and then breaks down. There are two repair technicians available, and it takes one technician between 1 and 4 hours (uniformly distributed) to fix a machine; only one technician can be assigned to work on a broken machine even if the other technician is idle. If more than two machines are broken down at a given time, they form a (virtual) FIFO “repair” queue and wait for the first available technician. A technician works on a broken machine until it is fixed, regardless of what else is happening in the system. All uptimes and downtimes are independent of each other. Starting with all machines at the beginning of an “up” time, simulate this for 160 hours and observe the time-average number of machines that are down (in repair or in queue for repair), as well as the utilization of the repair technicians as a group; put your results in a Text box in your model. Animate the machines when they’re either undergoing repair or in queue for a repair technician, and plot the total number of machines down (in repair plus in queue) over time. (HINT: Think of the machines as “customers” and the repair technicians as “servers” and note that there are always five machines floating around in the model and they never leave.)

Explanation / Answer

Solution:

Add a second machine to which all the parts go immediately. For the second machine processing times are independent from the first machine. Gather all the statistics plus time in the queue, the length of the queue and the second machine utilization.

Immediately after this take a constant inspection to carry along and May has a 75% of positive chance. Queue is possible for only single inspector and it is FIFO that means first in first out. All parts exit the system without knowing whether they pass or fail. Similarly make a count of all positive and the fail number and gather statistics on the time in queue, the length of the queue and the second machine utilization.

You can use plots to track the queue length and put all the number busy in plot. Run the simulation for longer than the usual.

Suppose those parts that fail in inspection are send back and re used again instead of leaving and have the same probability of leaving. Run this model under the same condition. Of course now there is no need to count the part who fails or succeed, because they all eventually pass.

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