Using Minitab Exec files allows users to perform Monte Carlo simulations with larger sample sizes by automating replications. Exec files record Minitab commands from an initial simulation run and then repeat those commands as many times as specified by the user. This stacks the results from each replication into a single column for analysis. The document provides an example of using an Exec file to estimate the probability mass function of the distance between random points, allowing for thousands more replications than could be done manually in Minitab.

1. Using Minitab Exec Files
Prof. Tom Willemain
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2. Why Use Exec Files?
• You can do many Monte Carlo simulations
without Exec files.
• Usually, this means putting each simulation
replication in one row of the Data Window.
• But you soon run out of space for both data
and results, so you can only do relatively small
problems.
• Exec files free you to do bigger problems and
use more of the features of Minitab.
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3. Typical Simulation using Exec files
• Put (possibly lots of) data in columns, not
rows.
• Compute a statistic using Calc>Column
Statistics or Calc>Calculator.
• Store the statistic in an (invisible) location
called a “constant” (e.g., K1, K2,…)
• “Stack” the results, moving them from the
constant into a single column holding results.
• Analyze the results column.
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4. How It’s Done: Creating an Exec
1. Create the first simulation replication manually. All your
menu choices and dialog box inputs are recorded in the
form of Minitab commands in the History folder of the
Project Management window.
2. Compute the result statistic from the simulation using
Calc>Column Statistics and store it in constant K1.
3. Open the Notepad using Tools>Notepad.
4. Open the History folder, highlight the commands you
want to repeat, and copy/paste them into the Notepad.
5. Manually add one more line in the Notepad to Stack the
result statistics in a column of the data window.
6. Save the Exec file from the Notepad to your hard drive
using File>Save As>All Files. Save it as an xxx.mtb file.
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5. How It’s Done: Running an Exec
• In Minitab, select File>Other Files>Run an Exec
• In the Run an Exec dialog box, enter the number of
additional replications you want. (It’s safer to first ask
for just 2 replications to see that everything is working
ok. Then you can add more replications.)
• In response to the prompt, select the Exec file you
want to run. Exec files have names like foo.mtb.
• Minitab will run the Exec file the desired number of
times and stack the results into the column you
selected.
• Finish the problem by analyzing the column of results.
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6. Example: Inter-point Distances
• The next slide show how to estimate the
distribution of the distance between two points
whose X and Y coordinates have unit exponential
distributions.
• Note that you need 5 columns: 4 coordinates and
one distance. Without an Exec file, and with a
10,000 number limit in the Minitab Student 14
Edition, you could do a maximum of 2,000
replications (2,000 = 10,000/5).
• But with an Exec file, you can do as many as
9,995 replications.
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9. Example: A Matching Problem
• A class has 20 students, who take a quiz.
• The professor collects the quizzes, shuffles
them well, and hands them back to students
to grade.
• Some students may get their own quiz back to
grade. The number of such “matches” is a
discrete random variable ranging from 0 to 20.
• Estimate the p.m.f. using an Exec file.
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10. One Trial of the Matching Simulation
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1. List the 20 students by number.
2. Create a set of 20 random
numbers.
3. Create a list of 20 graders and
sort it by the random numbers.
4. Compute a binary variable = 1 if
there is a match or else = 0.

11. The Exec File
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This last line is added to Notepad manually.

12. The Estimated P.M.F.
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13. Comment
• We have estimated the p.m.f. by Monte Carlo simulation.
• It is possible, though quite complicated, to work out the
answer analytically. This is always preferable, if possible.
• Theory tells us that, asymptotically (as the # of cases
increases), the p.m.f. is Poisson with mean = 1.
• The simulation suggests this, since the sample mean and
sample variance are both near 1.0. Sometimes simulation
and analysis alternate in the search for knowledge: they
are complementary approaches.
– Theory first: Use simulation to check the correctness of your
theory.
– Theory second: Use simulation to suggest a theoretical
approach.
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