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MIE360 Computer Modeling and Simulation
Lecture Notes
Daniel Frances © 2010
1
Lecture 21 – Too Many Comparisons!
Earlier we mentioned that to consider 4 different types of additional resources in a model, two possible
levels for each resource, you need to simulate 2
4
= 16 scenarios.
Using the multiple comparison approach we need to perform
120
2
16
=
comparisons. Based on n
Bonferroni’s inequality we derived that the level of confidence required for the pairwise comparisons is
the overall required level of confidence divided by the number of comparisons. Thus if we require 90%
confidence, i.e.
α
=.1, then for each of 10 pairwise comparisons we need
α
= .01, i.e. 99% confidence.
As the number of comparisons grows this approach becomes impractical.
The subject of Design of Experiments (DE) tries to deal both with the problem of “too many
comparisons” as well as “too many alternatives”. The material covered here, Factorial Design, addresses
both problems. It provides an alternate approach for deciding on the appropriate followup to a set o f
simulation t r ia ls fo r all possible scenarios. More advanced topics in DE such as Fractional Factorial
Design try to reduce the number of scenarios that need to be simulated.
It turns out this problem is very similar to that faced by scientists having to perform experiments to learn
how various factors affect responses. Statisticians have then stepped into the breach to help them Design
their Experiments.
In our case the
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 Fall '10
 D.Frances

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