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System Modeling and Simulation Homework 2 a ll of the following changes: 1. Modify Model 3-1 in ARENA Book Samples folder with all

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 the same 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 5 minutes to carry out and has an 80% chance of a passing result; queueing is possible at inspection, and the queue is first-in, first-out. 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. Configure them as needed. Run the simulation for 480 minutes instead of 20 minutes Points (15)

Solution: See Arena Model uploaded on mytsu

From the final values of the counters next n ext to the Dispose modules in the animation, 66 passed and 23 failed. At the Inspection center (for example): Avg. Max Time in queue 2.1083 8.44387 Queue length 0.4062 3 Utilization 0.8363 2. A production process manufactures alternators for outboard engines used in recreational boating. On the average, 1% of the alternators will not perform up to the required required standards when tested at the engine assembly plant. When a large shipment of alternators is received at the plant, 100 are tested, and, if more than two are nonconforming, the shipment is returned to the alternator manufacturer. What is probability of returning a shipment? Points (5)

3. The Hawks are currently winning 0.55 of their games. There are 5 games in the next two weeks. What is the probability that they will win more games than they lose? Points (5)

4. Joe Coolidge is the third string quarterback for Tennessee State University. The probability that Joe gets into any game is 0.40. Points (5) a) What is the probability that the first game Joe enters is the fourth game of the season? b) What is the probability that Joe plays in no more than two of the first five games?

5. The number of hurricanes hitting the coast of Florida annually has a Poisson distribution with a mean of 0.8. Points (5)

a) What is the probability that more than two hurricanes will hit the Florida coast in a year? b) What is the probability that exactly one hurricane will hit the coast of Florida in a year?

6. A tool crib has exponential interarrival and service times, and it serves a very large group of mechanics. The mean time between arrivals is 4 minutes. It takes 3 minutes on the average for a tool-crib attendant to service a mechanic. The attendant is paid $10 per hour and the mechanic is paid $15 per hour. Would it be advisable to have a second tool-crib attendant? Points (5)

7. A machine shop repairs small electric motors, which arrive according to a Poisson process at the rate of 12 per week (5-day, 40-hour workweek). An analysis of past data indicates that engines can be repaired, on the average in 2.5 hours, with a variance of 1 hour 2. How many working hours should a customer expect to leave a motor at the repair shop (not knowing the state of the system)? If the variance of the repair time could be controlled, what variance would reduce the expected waiting time to 6.5 hours? Points (5)

8. Classic Car Care has one worker who washes cars in a four-step method – soap, rinse, dry, vacuum. The time to complete each step is exponentially distributed with a mean of 9 minutes. Every car goes through every step before another car begins the process. On the average, one car every 45 minutes arrives for a wash job, according to a Poisson process. What is the average time a car waits to begin the wash job? What is the average number of cars in the car wash system? What is the average time required to wash a car? Points (5) The service process can be thought of as the convolution (that is the sum of) 4

independent exponential random variables (each with the same mean). The mean is 1/4. The variance of each exponential is 1/4 22. Thus variance of their sum is 4/422 = 1/42.

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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 the same 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 5 minutes to carry out and has an 80% chance of a passing result; queueing is possible at inspection, and the queue is first-in, first-out. 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. Configure them as needed. Run the simulation for 480 minutes instead of 20 minutes Points (15)

Solution: See Arena Model uploaded on mytsu

From the final values of the counters next n ext to the Dispose modules in the animation, 66 passed and 23 failed. At the Inspection center (for example): Avg. Max Time in queue 2.1083 8.44387 Queue length 0.4062 3 Utilization 0.8363 2. A production process manufactures alternators for outboard engines used in recreational boating. On the average, 1% of the alternators will not perform up to the required required standards when tested at the engine assembly plant. When a large shipment of alternators is received at the plant, 100 are tested, and, if more than two are nonconforming, the shipment is returned to the alternator manufacturer. What is probability of returning a shipment? Points (5)

3. The Hawks are currently winning 0.55 of their games. There are 5 games in the next two weeks. What is the probability that they will win more games than they lose? Points (5)

4. Joe Coolidge is the third string quarterback for Tennessee State University. The probability that Joe gets into any game is 0.40. Points (5) a) What is the probability that the first game Joe enters is the fourth game of the season? b) What is the probability that Joe plays in no more than two of the first five games?

5. The number of hurricanes hitting the coast of Florida annually has a Poisson distribution with a mean of 0.8. Points (5)

a) What is the probability that more than two hurricanes will hit the Florida coast in a year? b) What is the probability that exactly one hurricane will hit the coast of Florida in a year?

6. A tool crib has exponential interarrival and service times, and it serves a very large group of mechanics. The mean time between arrivals is 4 minutes. It takes 3 minutes on the average for a tool-crib attendant to service a mechanic. The attendant is paid $10 per hour and the mechanic is paid $15 per hour. Would it be advisable to have a second tool-crib attendant? Points (5)

7. A machine shop repairs small electric motors, which arrive according to a Poisson process at the rate of 12 per week (5-day, 40-hour workweek). An analysis of past data indicates that engines can be repaired, on the average in 2.5 hours, with a variance of 1 hour 2. How many working hours should a customer expect to leave a motor at the repair shop (not knowing the state of the system)? If the variance of the repair time could be controlled, what variance would reduce the expected waiting time to 6.5 hours? Points (5)

8. Classic Car Care has one worker who washes cars in a four-step method – soap, rinse, dry, vacuum. The time to complete each step is exponentially distributed with a mean of 9 minutes. Every car goes through every step before another car begins the process. On the average, one car every 45 minutes arrives for a wash job, according to a Poisson process. What is the average time a car waits to begin the wash job? What is the average number of cars in the car wash system? What is the average time required to wash a car? Points (5) The service process can be thought of as the convolution (that is the sum of) 4

independent exponential random variables (each with the same mean). The mean is 1/4. The variance of each exponential is 1/4 22. Thus variance of their sum is 4/422 = 1/42.

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