Unit 12: Use a PERT analysis to estimate task durations - Subjective Questions

PERT, or Program Evaluation and Review Technique, is a technique used to estimate task durations when there is uncertainty about the time required to complete project activities.

PERT uses three duration estimates:

• Optimistic duration (): The shortest reasonable duration under favorable conditions.
• Most likely duration (): The duration expected under normal working conditions.
• Pessimistic duration (): The longest reasonable duration under unfavorable conditions.

The three estimates are combined to calculate a weighted expected duration. Its purposes are to:

• Account for uncertainty in task-duration estimates.
• Produce more realistic schedules.
• Identify tasks with high estimation risk.
• Improve project planning, monitoring, and decision-making.

PERT analysis uses the following estimates:

• Optimistic estimate (): The task duration if work proceeds exceptionally well and no major difficulties occur.
• Most likely estimate (): The realistic duration under normal working conditions.
• Pessimistic estimate (): The task duration if significant, but reasonable, difficulties occur.

For example, consider a software integration task:

• Optimistic duration: days
• Most likely duration: days
• Pessimistic duration: days

Using the default PERT formula:

Thus, the expected task duration is 7.5 days.

The general weighted-average formula for a PERT duration is:

where:

• is the optimistic duration.
• is the most likely duration.
• is the pessimistic duration.
• , , and are their respective weights.

The default PERT weights are:

• Optimistic weight:
• Most likely weight:
• Pessimistic weight:

Substituting these values gives:

Therefore:

The most likely estimate receives four times the influence of either extreme estimate. This means the expected duration remains close to the normal estimate while still accounting for favorable and unfavorable conditions.

The default PERT formula is:

Substituting the estimates:

Therefore, the estimated duration is approximately 10.67 days.

Interpretation:

• The result is close to the most likely estimate because it has a weight of .
• The pessimistic estimate raises the result slightly above days.
• Depending on the scheduling tool and calendar settings, the value may be displayed or rounded to an appropriate unit.

A typical procedure for performing a default-weight PERT analysis is:

1. Prepare the task list: Create the project tasks, dependencies, calendars, and resources as required.
2. Open the PERT entry interface: Display the PERT Entry Sheet or the corresponding three-point estimation view.
3. Enter three estimates: For each task, enter the optimistic, most likely, and pessimistic durations.
4. Retain the default weights: Use for optimistic, for most likely, and for pessimistic.
5. Calculate the PERT estimate: Run the PERT calculation command.
6. Review the calculated durations: The software replaces or updates task durations with the weighted estimates.
7. Inspect the schedule: Examine start dates, finish dates, milestones, dependencies, and the critical path.
8. Validate and save: Confirm that the estimates are reasonable and save or back up the plan.

Because recalculation can change the project schedule, the original plan should be saved before applying PERT calculations.

The default PERT expected duration is:

Thus, deterministic estimation is simpler, whereas PERT is generally more informative when software activities involve technical, staffing, or requirement-related uncertainty.

In the default PERT model, the most likely estimate represents the duration expected under normal project conditions. It is therefore considered more representative than either extreme.

The default weights are in the ratio:

The weight of has the following effects:

• It keeps the calculated duration close to the most likely estimate.
• It prevents rare best-case or worst-case outcomes from dominating the result.
• It still allows the optimistic and pessimistic values to influence the schedule.
• It provides a balanced estimate when the uncertainty is approximately symmetrical.

However, if a project has unusually high risk or strong evidence of favorable conditions, the project manager may change the weights.

The expected duration is:

The conventional PERT standard deviation is:

The variance is:

Therefore:

• Expected duration: hours
• Standard deviation: hours
• Variance: hours squared

The relatively broad range from to hours indicates meaningful uncertainty even though the expected duration is hours.

PERT weights are numerical factors that determine the relative influence of optimistic, most likely, and pessimistic estimates on the calculated duration.

The generalized formula is:

Effects of changing weights include:

• Increasing moves the result toward the optimistic estimate.
• Increasing moves the result toward the most likely estimate.
• Increasing moves the result toward the pessimistic estimate.
• Equal weights produce a simple average of all three values.

Many project management tools use the default ratio . When the software requires the conventional total of , the project manager should choose weights whose sum is . Weight changes should reflect project evidence and risk policy rather than an arbitrary desire to shorten or lengthen the schedule.

(a) Default weights

(b) Risk-averse weights

Comparison:

• Default-weight duration: 10.17 days
• Risk-averse duration: 13.83 days
• Increase: days

The risk-averse calculation gives greater importance to the pessimistic estimate, producing a longer and more conservative schedule.

The general procedure is:

1. Open the project containing the task estimates.
2. Display the PERT analysis controls, settings, or three-point estimation feature.
3. Select the command for setting or modifying PERT weights.
4. Enter new weights for:
   • Optimistic duration
   • Most likely duration
   • Pessimistic duration
5. Verify that the values meet the software's requirements. In conventional implementations, the weights commonly total .
6. Confirm the settings.
7. Recalculate the PERT durations.
8. Review the resulting task durations and schedule changes.

For example, changing the ratio from to gives more influence to pessimistic estimates. Before recalculating, the original project file or baseline should be preserved so that the effect can be compared and reversed if necessary.

For estimates , , and , the weighted result is:

An optimistic strategy may create an aggressive schedule but increase the chance of delay. A pessimistic strategy provides more protection against adverse events but may produce a longer schedule. The balanced strategy is appropriate when neither extreme deserves extra influence.

Saving a backup or baseline is important because PERT calculation can modify task durations and consequently alter the entire schedule.

Possible changes include:

• New task start and finish dates.
• Changes to milestone dates.
• Movement of the project's completion date.
• Changes to the critical path and total slack.
• Resource allocation changes caused by shifted tasks.
• Altered cost estimates if resources are time-based.

A backup preserves the original three-point estimates and schedule. A baseline provides a reference against which the recalculated schedule can be measured. This supports comparison, variance analysis, auditing, stakeholder communication, and restoration if the new calculation is unsuitable.

The estimates should be based on realistic assumptions and relevant project evidence.

Factors to consider include:

• Historical data from similar software projects.
• Experience and skill of the assigned team members.
• Complexity and novelty of the technology.
• Stability and clarity of requirements.
• Availability of tools, test environments, and infrastructure.
• Integration and external dependency risks.
• Probability of defects and rework.
• Resource availability, leave, and competing assignments.
• Review, approval, and communication delays.
• The project calendar and nonworking time.

The assumptions behind , , and should be documented. The pessimistic estimate should represent a credible adverse scenario rather than an impossible catastrophe, while the optimistic estimate should remain realistically achievable.

For each task, use:

Task A:

Task B:

Task C:

Because the tasks are sequential, their durations are added:

Therefore, the expected duration of this task sequence is approximately 11.67 working days, subject to calendar and rounding settings.

The critical path is the longest-duration path through the project's dependency network. Tasks on this path generally have zero or very little total slack.

When PERT-calculated durations replace single-point durations:

• The length of individual activities may increase or decrease.
• Total slack may change.
• A previously noncritical path may become the longest path.
• A previously critical task may gain slack.
• Milestone and completion dates may move.

For example, giving greater weight to pessimistic estimates can lengthen high-risk tasks. If those tasks lie on, or create, the longest dependency path, the project's forecast completion date will become later. Therefore, the critical path should always be recalculated and reviewed after applying PERT durations or changing PERT weights.

Changing duration estimates modifies the possible task outcomes themselves:

• , , or is revised.
• It reflects new information about task scope, resources, complexity, or risk.
• It can change both the estimated center and the range of uncertainty.

Changing PERT weights modifies the relative influence of the existing outcomes:

• The values of , , and remain unchanged.
• Only , , and are revised.
• It reflects a different planning attitude or confidence level.

The relationship is:

Estimates should be changed when task evidence changes. Weights should be changed when the organization intentionally wants to emphasize a particular scenario, such as pessimistic outcomes in a high-risk project.

Advantages:

• Represents uncertainty through three estimates.
• Produces a more balanced duration than a single guess.
• Encourages discussion among developers, testers, and managers.
• Highlights tasks with a wide optimistic-to-pessimistic range.
• Supports risk-aware scheduling and contingency planning.
• Allows alternative weighting strategies.

Limitations:

• The estimates may still be subjective or politically biased.
• The default weighting may not suit every task.
• Poor historical data can lead to unreliable estimates.
• Dependencies, resource constraints, and correlated risks may not be fully captured by task-level calculations.
• Calculated precision can create false confidence.
• Replacing durations without review can unexpectedly alter the schedule.

PERT should therefore support, rather than replace, expert judgment, historical analysis, risk management, and continuous schedule updating.

A large difference between and indicates high uncertainty in the task.

The conventional standard deviation is:

Therefore, a larger range produces a larger standard deviation and variance.

Possible causes include:

• Unclear or changing requirements.
• Use of unfamiliar technology.
• External system dependencies.
• Uncertain resource availability.
• High probability of defects or rework.
• Lack of comparable historical information.

The manager should investigate the assumptions, divide the task into smaller activities, create prototypes, reduce dependencies, assign experienced staff, and maintain contingency plans. The range should not simply be hidden by calculating an average because it contains important risk information.

A complete workflow can be organized as follows:

1. Define the work: Create a work breakdown structure and identify measurable tasks.
2. Consult responsible personnel: Obtain estimates from developers, testers, analysts, and technical specialists.
3. Record three estimates: Enter realistic optimistic, most likely, and pessimistic durations for each uncertain task.
4. Document assumptions: Record resource, technology, requirement, dependency, and calendar assumptions.
5. Select weights: Begin with the default ratio unless project evidence supports another strategy.
6. Calculate durations: Apply

7. Recalculate the schedule: Update dependencies, start and finish dates, slack, milestones, and the critical path.
8. Validate results: Compare calculated values with historical data, expert judgment, and organizational standards.
9. Analyze uncertainty: Review tasks with large values of and prepare risk responses.
10. Save a baseline: Preserve the approved expected schedule for later comparison.
11. Monitor actual performance: Compare actual and remaining durations with the PERT estimate.
12. Update responsibly: Revise estimates when scope, resources, risks, or technical information changes.

This workflow integrates PERT calculations with practical software project control instead of treating the result as a one-time mathematical answer.