Transcript PERT – Program Evaluation & Review Technique

PERT – Program
Evaluation & Review
Technique
Module: 03-04 PERT
Modified: February 20, 2003
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CVEN 349 - Maxwell
3/20/2003
Purpose:
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Introduce the ideas that:
Construction is a variable process. –
there are few constants.
 These variations cause risk in
estimating any outcome. And
 There are ways to deal with that risk.
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CVEN 349 - Maxwell
3/20/2003
Learning Objectives:
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Assuming a normal distribution, be
able to make statistical inferences
about estimated completion times,
based on variable task times.
CVEN 349 - Maxwell
3/20/2003
PERT – Basic Concept
First used by NASA to Flow-Chart and
Schedule their projects.
 Approach is used for projects where
the activity durations and costs are
largely “guess work” – that is,
SWAGs.
 Works surprising well on large
projects because of the math and
statistics.
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CVEN 349 - Maxwell
3/20/2003
Basic Statistical Ideas
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Mean = X-bar = (Lo + 4*ML + Hi)/6
S.D. = sigma = (Hi – Lo)/6
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Lo = Estimate for Minimum Value
ML = Estimate for Most Likely Value
Hi = Estimate for Maximum Value
Use the Delphi Technique or some other
systematic process to get estimates for Lo,
ML, Hi
Central Limit Theorem (CTL) forces
Normality
CVEN 349 - Maxwell
3/20/2003
1. Take a “standard” process activity flow diagram.
2. Add Time Estimates from Delphi or other technique.
3. Apply to Activity Diagram and Find Critical Path
Central Limit Theorem
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Given N samples of size M drawn from the same
population of unknown distribution.
The Mean of the distribution of the sample means
(DSM) is an unbiased estimator of the population
mean.
The Variance of the DSM is an unbiased estimator of
the Variance of the population divided by the sample
size M. Standard Deviation = SQRT of the Variance
The DSM approaches normal as M approaches infinity.
M = 30 is generally OK.
CVEN 349 - Maxwell
3/20/2003
The Problem is the “Shape of the
Curve” – What Distribution?
We assume Normal for ease of use
but the “tails are too thin” causing an
underestimation of extreme cases.
 A Triangular is easier to use but the
“tails are too fat” causing overestimation of extreme cases.
 A gamma distribution appears a best
fit to most unsymmetrical cases.
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CVEN 349 - Maxwell
3/20/2003
4. Find Expected Duration
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CVEN 349 - Maxwell
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5. Make Statistical
Inferences
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CVEN 349 - Maxwell
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… … The application to
construction should be obvious.
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CVEN 349 - Maxwell
3/20/2003
Class Assessment
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Take out a piece of paper and write 1
sentence on the least clear topic of
the day …
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Pass it forward.
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CVEN 349 - Maxwell
3/20/2003