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PERT – Program Evaluation & Review Technique Module: 03-04 PERT Modified: February 20, 2003 1 CVEN 349 - Maxwell 3/20/2003 Purpose: 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. 2 CVEN 349 - Maxwell 3/20/2003 Learning Objectives: 3 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. 4 CVEN 349 - Maxwell 3/20/2003 Basic Statistical Ideas Mean = X-bar = (Lo + 4*ML + Hi)/6 S.D. = sigma = (Hi – Lo)/6 5 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 9 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. 10 CVEN 349 - Maxwell 3/20/2003 4. Find Expected Duration 11 CVEN 349 - Maxwell 3/20/2003 5. Make Statistical Inferences 13 CVEN 349 - Maxwell 3/20/2003 … … The application to construction should be obvious. 14 CVEN 349 - Maxwell 3/20/2003 Class Assessment Take out a piece of paper and write 1 sentence on the least clear topic of the day … Pass it forward. 19 CVEN 349 - Maxwell 3/20/2003