A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is
9
PERT Network Standard Deviation
In project management, the Program Evaluation and Review Technique (PERT) is a valuable tool used for planning, scheduling, and controlling complex projects. A key component of a PERT network is the critical path, which represents the longest sequence of activities in the project. This path determines the minimum time required to complete the entire project.
Critical Path Variability
Each activity in a PERT network has an associated duration, which can be uncertain. This uncertainty is often quantified using statistical measures like standard deviation and variance. When dealing with the critical path, understanding its overall variability is crucial for risk assessment and accurate project completion time estimation.
For activities on the critical path, the standard deviation of the path is calculated based on the standard deviations of the individual activities. The fundamental principle is that the variance of the entire critical path is the sum of the variances of the individual activities that lie on that path. The standard deviation of the path is then the square root of this total variance.
Activity Variance Calculation
Given in this problem, we have a PERT network where:
- The number of activities on the critical path is 9.
- The standard deviation of each activity on the critical path is 3.
First, we need to calculate the variance for a single activity. The variance ($\sigma^2$) is simply the square of the standard deviation ($\sigma$).
$Var_{activity} = (\text{Standard Deviation of one activity})^2$
$Var_{activity} = (3)^2$
$Var_{activity} = 9$
Critical Path Standard Deviation Determination
To find the standard deviation of the entire critical path, we follow these steps:
- Calculate Individual Activity Variances: As determined above, the variance for each activity is 9.
- Sum of Variances: The variance of the entire critical path is the sum of the variances of all activities on that path. Since there are 9 activities and each has a variance of 9, the total variance of the critical path is:
$Var_{critical\_path} = \text{Sum of variances of all activities on critical path}$
$Var_{critical\_path} = 9 \times Var_{activity}$
$Var_{critical\_path} = 9 \times 9$
$Var_{critical\_path} = 81$
- Calculate Critical Path Standard Deviation: The standard deviation of the critical path is the square root of its total variance.
$\sigma_{critical\_path} = \sqrt{Var_{critical\_path}}$
$\sigma_{critical\_path} = \sqrt{81}$
$\sigma_{critical\_path} = 9$
PERT Path Calculation Summary
Here's a quick summary of the values:
| Description | Value |
|---|---|
| Number of activities on critical path (n) | 9 |
| Standard deviation of each activity ($\sigma_{activity}$) | 3 |
| Variance of each activity ($Var_{activity} = \sigma_{activity}^2$) | 9 |
| Total Variance of critical path ($Var_{critical\_path} = n \times Var_{activity}$) | 81 |
| Standard deviation of critical path ($\sigma_{critical\_path} = \sqrt{Var_{critical\_path}}$) | 9 |
Therefore, the standard deviation of the critical path is 9.
Important Questions from PERT and CPM
Which one of the following distributions provides information regarding the uncertainty of duration time estimates is PERT described network?
Which of the following distribution represents the time estimates in PERT ?
Negative slack occurs when -
In PERT analysis, the possible number of time estimates for activities linking up two events are -
The amount of time by which an activity can be delayed without affecting project completion time is
