Please read through the assignment carefully. By running your simulation experiment many times, you can collect data that consists of random outcomes of your model. Statistical techniques can be applied to this "data" that’s been collected from your simulation to make decisions. You should use your rail gun model created in Arena back in Hw2 for this problem. Make sure it is working correctly (or use the solution file). We will use this basic model as the basis for the assignment, and run it in different configurations to obtain data. Call the original RailGun problem Model 1 (M1). It has one rail gun as a "server", its interarrival distribution is Exponentially distributed with mean 9 minutes, and its service time is Normally distributed with mean 6 minutes, and standard deviation of 0.5 minutes. We will use three models with difference service distributions summarized here:

Table 1: Three models for analysis.

You can do the statistical analysis for this assignment in JMP, Excel, or any other program you are comfortable with. You do not need to include your Arena files, but you should provide the data you collected at each stage, and explain what you did in the statistical software to get your answer.

Background: Confidence intervals are a great way of summarizing data. Suppose we want to find a confidence interval (CI) for the average waiting time to process a target in the rail gun problem. If we run M1 once, we get one estimate of the average waiting time based on the results in the Arena report. One estimate is not enough to calculate a confidence interval. If we run the model 10 times, we get 10 estimates, and we can calculate a CI for the mean waiting time. However, in order to use the usual confidence interval formula, we need two assumptions: independence and normality. We can get independence between the 10 estimates by using a different seed for each run of the experiment. Arena takes care of this automatically when you ask for multiple replications. We can test for normality using the input analyzer in Arena.

Question 1 : Use the Replications box in the Run Setup/Replication Parameters options to collect data for 10 replications of the experiment. You can find the waiting times for each run by looking in the Reports section of the Progress Bar at "Category by Replication" to see info for replications 1 through 10. Copy the average waiting time for each run to a separate JMP/Excel file for analysis. We know they are independent estimates because the runs are independent. Use the input analyzer to check for normality of these 10 numbers you collected. What do you find? Calculate a 95% CI for the mean waiting time from the 10 estimates, assuming normality (even if the input analyzer says otherwise). You can use software to calculate this, or do this by hand.

M1 AVERAGE WAIT TIMES (FROM SIMULATION)

Key point: You should have noticed a wide range of average waiting time values from your 10

replications. It is crucial to run any simulation model multiple times in order get a feel for what the output could be. If the variance of the output is high, then just looking at one run could give you misleading information.

Question 1A : Batched Means method and how Arena implements it automatically in the reports. In this method, you run one really long run of the simulation, and divide the data into batches to estimate a CI. Run one really long run of the Rail Gun model (50,000 minutes) and report the CI based on what Arena gives as the average and half-width for the average waiting time. How does this compare to the CI you calculated above? Why is it different?

RESULTS FROM SIMULATION (50,000 MINUTES)

AVG WAIT TIME: 5.6839

HALF-WIDTH: 0.533379839

MIN: 0

MAX : 46.9567

Question 2. T-Test. Now suppose that you want to compare two different models. Keep your data from Problem 1 handy, and return the run length to 480 (if you changed it for question 1A). Now change M1 to be M2, (the same model but with a different service distribution as defined in Table 1). Run model M2 10 times and collect the average waiting time for each run. Do a t-test (with an alpha value of 0.05) to compare the sample means of the waiting times M1 and M2. What do you find? Is there a significant difference between the two systems?

M1 AVERAGE WAIT TIMES (FROM SIMULATION)

M2 AVERAGE WAIT TIMES (FROM SIMULATION)

Question 3 . Linear Regression. Perhaps you want to see how the mean service time affects the average waiting time. Change your model to M3 with the new service distribution according to Table 1. Run this model 10 times, collect your results. Now for each model (M1, M2, and M3), take the sample mean of the 10 reps. Plot these against the mean service time for each model (6,7,8) and run a linear regression of the average waiting time for each model against the mean service time. Report your results and plot the fitted regression line. Do you see a trend? Do you think three points is enough to fit a trendline?

M1 AVERAGE WAIT TIMES (FROM SIMULATION)

M2 AVERAGE WAIT TIMES (FROM SIMULATION)

M3 AVERAGE WAIT TIMES (FROM SIMULATION)

Question 3A: Three points to fit a linear regression is not always enough. Try even more service time distributions so you can get have more data to fit the linear regression. Report your results.

RESULTS FROM SIMULATION

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Solution: The downloadable solution consists of 12 pages, 1192 words and 4 charts.
Deliverable: Word Document