4803hw7s18

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University Of Georgia *

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MISC

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Statistics

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Feb 20, 2024

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pdf

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Uploaded by CaptainFireEagle41

1 ISyE 4803 — Spring 2018 Homework #7 – Due Monday, April 23, 11:55 p.m. Start with the Simio model for Problem 1 of Homework #5 (Emergency Department). To be on equal footing, use the file 4803hw5s18-p1.spfx in the homework solutions. Add the following embellishments:  Create a Tally Statistic, say TIS, that collects times-in-system for all patients.  Create a (User Defined) File Element where the observations of the Tally Statistic will be recorded.  Create an add-on Process that is triggered at the two Sinks, collects observations for the Tally Statistic, and records the data (in minutes) in the external file using a (User Defined) Write step.  Set the run length to 250,100 hours; this will result in a long run and will create a large external file with the tallied observations. Then do the following: 1. Make a single replication, with a warmup period of 100 hours, and use the Tally Statistic to compute an approximate 95% confidence interval for the mean time a patient spends in the ED in steady state. 2. Use the labatch.2 method (ABATCH algorithm) of Fishman and Yarberry (1997) with the tallied data from the external file to compute an approximate 95% CI for the mean time-in- system in steady state. Is this CI comparable with the CI from item 1 above? Write a script that reads from the external file and use the final batch size from the output tableau of the labatch.2 method to compute and plot the batch means. Comment on the potential effect of the initial transient, the independence of the batch means, and the normality of the batch means. Recall that the labatch.2 method does not eliminate transient data. 3. Use the Sequest method with the tallied data to compute approximate 95% CIs for the steady- state quantiles 𝑥 𝑝 , for 𝑝 = 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 0.99, 0.995 . In each case set the CI relative precision to 0.05 (5%). Report the outcomes in the following table using two significant decimal places: 𝑝 𝑥 ̃ 𝑝 CI Half-width CI Relative Precision (%) Warmup Length Batch Size Sample Size .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 .995

2 Write a script that reads the tallied observations and plots a histogram and the empirical CDF (cumulative histogram). In Matlab, you can read an external text file to an array using the command x = textread('filaname'); The command histogram(x,'Normalization','probability','FaceColor','none','DisplayStyle','stairs'); creates a histogram resembling the PDF (with relative counts), and the command ecdf(x); creates an empirical CDF.

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4803hw7s18

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