PERT Activity Time Estimates, Variance & Standard Deviation Calculation | Query Point Official

PERT Activity Time Estimates: Expected Time, Variance & Standard Deviation

The time estimates for the activities of a PERT (Project Evaluation and Review Technique) diagram are given below. We will calculate expected time (Te), standard deviation (S.D.), and variance for each activity using the standard PERT formulas:

Formulas:

• Expected time (Te) = (to + 4 × tm + tp) / 6
• Standard deviation (S.D.) = (tp - to) / 6
• Variance = (S.D.)² = ((tp - to)/6)²

Where:
to = Optimistic time, tm = Most likely time, tp = Pessimistic time

Solution Table

Activity	to	tm	tp	Expected Time (Te)	Standard Deviation (S.D.)	Variance
1-2	1	2	3	2	1/3	1/9
2-3	8	10	12	10	2/3	4/9
2-4	2	4	6	4	2/3	4/9
2-5	3	5	7	5	2/3	4/9
3-6	4	5	6	5	1/3	1/9
4-6	7	8	9	8	1/3	1/9
5-7	6	8	10	8	2/3	4/9
6-7	1	4	7	4	1	1

Explanation

1. Expected Time (Te): Weighted average that emphasizes the most likely duration.
2. Standard Deviation (S.D.): Measures uncertainty in the activity duration.
3. Variance: Represents the spread or risk associated with each activity’s time estimate.
These calculations help project managers determine the critical path and estimate project completion time more accurately.

Frequently Asked Questions (FAQs)

Q1: Why do we use three time estimates in PERT?

Using optimistic, most likely, and pessimistic times accounts for uncertainty and variability in project activity durations.

Q2: How is expected time different from the simple average?

Expected time gives more weight to the most likely duration, unlike a simple average which treats all values equally.

Q3: Why is variance important in PERT?

Variance quantifies the uncertainty of an activity and helps in calculating the probability of completing a project within a given time frame.

Explore more about OPERATIONS RESEARCH in Mathematics Notes & MCQs.