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The PERT approach
CPM vs PERT ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
PERT ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A-M-B time estimate
Beta distribution
Expected time and variance
Characteristics of a Normal  Probability Distribution ,[object Object],[object Object]
Characteristics of a Normal  Probability Distribution ,[object Object],[object Object]
Characteristics of a Normal Distribution Mean, median, and mode are equal Normal curve is symmetrical Theoretically, curve extends to infinity a - 5 0 . 4 0 . 3 0 . 2 0 . 1 . 0 x f ( x r a l i t r b u i o n :  = 0 ,   = 1
The Standard Normal  Probability Distribution ,[object Object],[object Object],[object Object]
EXAMPLE 1 ,[object Object]
EXAMPLE 1  continued ,[object Object],[object Object]
Areas Under the Normal Curve ,[object Object],[object Object],[object Object]
Areas Under the Normal Curve - 5 0 . 4 0 . 3 0 . 2 0 . 1 . 0 x f ( x r a l i t r b u i o n :  = 0 ,   = 1
EXAMPLE 2 ,[object Object],[object Object]
EXAMPLE 3 ,[object Object]
Example 3  continued ,[object Object],[object Object],[object Object]
-4  -3  -2  -1  0  1  2  3  4 P(0 <z<. 8) =.2881 EXAMPLE 3 0 <x<. 8 - 5 0 . 4 0 . 3 0 . 2 0 . 1 . 0 x f ( x r a l i t r b u i o n :  = 0 ,
EXAMPLE 3   continued ,[object Object]
Example 3  continued ,[object Object],[object Object],[object Object],[object Object]
Calculating Probabilistic Activity Times ,[object Object],[object Object],[object Object],[object Object]
The Statistical Distribution of all Possible Times for an Activity
Activity Expected Time and Variance
95 Percent Level ,[object Object],[object Object]
90 Percent Level ,[object Object],[object Object]
95 Percent Level (Alternative Interpretation) ,[object Object]
90 Percent Level (Alternative Interpretation) ,[object Object]
An AON Network
An MSP Version of a Sample Problem Network
A Pert/CPM Network for the Day Care Project
An MSP Calendar for the Day Care Project, 4/16/00 to 5/27/00
The Probability of Completing the Project on Time =NORMDIST( D ,  ,   ,TRUE)
The Statistical Distribution of Completion Times of the Path  a-b-d-g-h
Selecting Risk and Finding D NORMINV(probability,  ,   ,TRUE)
SIMULATION
Traditional Statistics Versus Simulation ,[object Object],[object Object],[object Object],[object Object]
EXTENSIONS TO PERT/CPM
Precedence Diagramming ,[object Object],[object Object],[object Object],[object Object]
Figure 5-27 Precedence Diagramming Conventions
Other Methods ,[object Object],[object Object],[object Object]
3 2 1 6, 7 Inspection and testing 8 11 4 3 4, 5 Install air pollution device 7 9 2 1 3 Install control system 6 7 4 1 3 Build high-temperature burner 5 6 4 2 2 Pour concrete and install frame 4 3 2 1 1 Construct collection stack 3 4 3 2 none Modify roof and floor 2 3 2 1 none Build internal components 1 Pessimistic Duration Most Likely Duration Optimistic Duration Prerequisites Task Description Task ID
 

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3 pert