Probability of Completing a Project: Normal Distribution

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Del curso dictado por Columbia University

Construction Scheduling

757 calificaciones

Columbia University

Construction Scheduling

757 calificaciones

Curso 2 de 4 en SpecializationConstruction Management

Learners will discover the key project scheduling techniques and procedures including; how to create a network diagram, how to define the importance of the critical path in a project network, and defining project activities float. Also covered are the fundamentals of Bar Charts, Precedence Diagrams, Activity on Arrow, PERT, Range Estimating, and linear project operations and the line of balance.

De la lección

Program Evaluation & Review Technique (PERT) and Range Estimating

The Program Evaluation and Review Technique (PERT) is introduced in this module which relates to uncertainty in estimating the duration of construction activities in a project schedule. PERT helps project managers determine the probability of a project being completed in a certain number of days.

Program Evaluation and Review Technique7:53

Probability of Completing a Project: Normal Distribution5:21

PERT Probability Example12:33

PERT Example on Completing a Project10:45

PERT Calculations: Critical Activities16:12

Applying PERT: Range Estimating19:51

Conoce a los instructores

Ibrahim Odeh, Ph.D., MBA
Instructor, Department of Civil Engineering and Engineering Mechanics, Columbia University
Director of Research and Founder, Global Leaders in Construction Management

So moving forward the probability of completing

the project is calculated by assuming that the probability

distribution of the total project duration

is normal distributed with the longest path,

of te, the values, or the expected values

as a mean value of the normal distribution.

And I will explain further in details with numbers and

highlight the curves to understand this definition and

the concept of the normal distribution of the entire project.

So, the normal distribution is defined by three points here,

one is the mean value, or te or x

which is the expected value, duration of that entire project.

Second, is the standard deviation or

sigma here, and the value sigma or standard deviation,

this shows how widely about te about the mean value.

The actual observed values are spread or

distributed, and the equation for that is the following.

tb minus ta,

tb is the worst case scenario that pessimistic duration of that

activity minus the ta which is the optimistic

of that activity, optimistic duration divided by 6.

That's the standard deviation.

Now, the last one is the variance.

And the variance is that square of that standard deviation as we can see here.

We refer to it as V or the sigma squared.

And the summation of the V for all critical activities,

not all activities, just the critical activities,

you find the variance for all of them, and you sum up all of them,

and that is the variance of the entire project duration.

Which then we can also calculate the standard deviation of the entire

project from the variance of the project.

What I mean by that, that you find the variance,

which would be exactly the same equation but

at the end here in the top, you have the power 2.

After you find the values for each of these critical activities,

you sum it up and then you take the square root of that number

to give you the standard deviation of the project.

Now, and we will go through an example soon.

Now, mathematically, in normal distribution,

it can be shown that 99.7% of the values of normally distributed values or

normally distributed variables will lie in a range

defined by three standard deviations or three sigma.

Below the mean, the te or x here and

three standard deviation above the mean or

above the te or the x of the project,

and as we can see in the figure here.

So this is te and this is what we refer to as the normal distribution.

It has same distribution from the right of the mean to the left of the mean of te and

when you go one signal to the right, one signal to the left on te.

The area here, It will be equal to 68.2%.

The entire area under the curve is the 100%.

So when you go 2 sigma, to the right and to the left,

the area, here, until like the 2 sigma.

It will cover around 95.4%, and

when you go up to 3 sigma on each direction,

the area under the curve,

it will be closer to 99.7%, or to the 100%.

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