Which of the following statements regarding PERT analysis is NOT true?
A Project standard deviation is the sum of all critical activity standard deviations.
B Each activity has three estimates of its duration.
C Only critical activities contribute to the project variance.
D The most likely time is different from the expected activity time.
E Project variance is the sum of all critical activity variances.
The correct answer and explanation is :
The correct answer is:
A. Project standard deviation is the sum of all critical activity standard deviations.
Explanation:
Program Evaluation and Review Technique (PERT) is a project management tool used to analyze and manage the time required to complete tasks within a project. It helps in dealing with uncertainty by considering three time estimates for each activity: Optimistic (O), Pessimistic (P), and Most Likely (M).
Now, let’s analyze the statements:
- Statement A (Incorrect Statement): The project standard deviation is not the sum of all critical activity standard deviations. Instead, the project standard deviation is the square root of the sum of the variances of all critical activities. This is derived using statistical principles, where variances add up, but standard deviations do not simply sum up.
- Statement B (True): Each activity in PERT has three time estimates—Optimistic (O), Pessimistic (P), and Most Likely (M). These estimates help calculate the Expected Time (TE) using the formula:
[
TE = \frac{O + 4M + P}{6}
] - Statement C (True): Only critical activities contribute to the project variance because they directly impact the project’s duration. Non-critical activities have slack time and do not influence overall project variance.
- Statement D (True): The most likely time (M) represents the mode of the distribution, whereas the expected time (TE) is the weighted average of the three estimates, so they are generally different.
- Statement E (True): The project variance is computed as the sum of variances of all activities on the critical path, not standard deviations.
Thus, option A is incorrect, making it the right choice for the answer.
