## Modelling and Simulation

HW5
1) Modify Model 3-1: A Simple Processing System with all of the following changes:
• Add a second machine to which all parts go immediately after exiting the first machine for a separate kind of processing (for example, the first machine is drilling and the second machine is washing). Processing times at the second machine are independent of those from the first machine but drawn from the same probability as for the first machine. Gather all the statistics as before, plus the time in queue, queue length, and utilization at the second machine.
• Immediately after the second machine there’ s a pass/fail inspection that takes a constant 4.5 minutes to carry out and has an 75% chance of passing results; queueing is possible for the single inspector, and the queue is FIFO. All parts exit the system regardless of whether they pass the test. Count the number that fail and the number that pass, and gather statistics on the time in queue, queue length, and utilization at the inspection center. (Hint: Try the Decide flowchart module.)
• Include plots to track the queue length and number busy at all three stations; put all queue lengths together in the same plot, and put all numbers busy in the same plot (you’ll need to turn on the plot Legends to identify the three curves). Configure them as needed.
• Run the simulation for 480 minutes instead of 20 minutes. (Provide 4 decimal accuracy.)
Performance Measures
Total Production=
Average Total Time in System=
Maximum Total Time in System=
Drill Press Statistics
Average Waiting Time in Queue=
Maximum Waiting Time in Queue=
Time Average Number of Parts in Queue=
Max. Number of Parts in Queue=
Utilization=
Second Machine (Washer) Statistics
Average Waiting Time in Queue=
Maximum Waiting Time in Queue=
Time Average Number of Parts in Queue=
Max. Number of Parts in Queue=
Utilization=
Inspection Center Statistics
Number of Parts Fail the Inspection=
Number of Parts Pass the Inspection=
Average Waiting Time in Queue=
Maximum Waiting Time in Queue=
Time Average Number of Parts in Queue=
Max. Number of Parts in Queue=
Utilization=
2) Five identical machines operate independently in a small shop. Each machine is up 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. 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.)
Performance Measures
Time Average Number of Machines that are Down=
Utilization=

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