Pert Calculator

PERT Task Duration Calculator

The shortest possible time to complete the task (best-case scenario).

The most realistic time to complete the task (normal conditions).

The longest possible time to complete the task (worst-case scenario).

Results:

Estimated Duration (Te):

Standard Deviation (SD):

function calculatePERT() { var optimisticTime = parseFloat(document.getElementById('optimisticTime').value); var mostLikelyTime = parseFloat(document.getElementById('mostLikelyTime').value); var pessimisticTime = parseFloat(document.getElementById('pessimisticTime').value); var estimatedDurationOutput = document.getElementById('estimatedDurationOutput'); var standardDeviationOutput = document.getElementById('standardDeviationOutput'); if (isNaN(optimisticTime) || isNaN(mostLikelyTime) || isNaN(pessimisticTime) || optimisticTime < 0 || mostLikelyTime < 0 || pessimisticTime < 0) { estimatedDurationOutput.innerHTML = 'Estimated Duration (Te): Please enter valid positive numbers for all time estimates.'; standardDeviationOutput.innerHTML = 'Standard Deviation (SD):'; return; } if (optimisticTime > mostLikelyTime || mostLikelyTime > pessimisticTime) { estimatedDurationOutput.innerHTML = 'Estimated Duration (Te): Optimistic time must be ≤ Most Likely time ≤ Pessimistic time.'; standardDeviationOutput.innerHTML = 'Standard Deviation (SD):'; return; } // PERT Estimated Duration (Te) = (O + 4M + P) / 6 var estimatedDuration = (optimisticTime + 4 * mostLikelyTime + pessimisticTime) / 6; // PERT Standard Deviation (SD) = (P – O) / 6 var standardDeviation = (pessimisticTime – optimisticTime) / 6; estimatedDurationOutput.innerHTML = 'Estimated Duration (Te): ' + estimatedDuration.toFixed(2) + ' units of time'; standardDeviationOutput.innerHTML = 'Standard Deviation (SD): ' + standardDeviation.toFixed(2) + ' units of time'; }

Understanding the PERT Calculator

The Program Evaluation and Review Technique (PERT) is a project management tool used to analyze and represent the tasks involved in completing a project. It's particularly useful when task durations are uncertain, providing a more realistic estimate than a single-point estimate.

How PERT Works

PERT uses a weighted average of three time estimates to determine a more probable task duration:

1. Optimistic Time (O): This is the shortest possible time in which an activity can be completed, assuming everything goes perfectly. There are no unforeseen problems or delays.
2. Most Likely Time (M): This is the most realistic time an activity is expected to take, assuming normal conditions and typical problems. This is the time that would occur most often if the activity were repeated many times.
3. Pessimistic Time (P): This is the longest possible time an activity might take, assuming everything goes wrong (e.g., major delays, unexpected issues, resource unavailability).

The PERT Formulas

The calculator uses the following formulas:

• PERT Estimated Duration (Te): This is the weighted average of the three estimates, giving more weight to the "Most Likely" time.
  Te = (Optimistic Time + 4 × Most Likely Time + Pessimistic Time) / 6
• Standard Deviation (SD): This measures the variability or uncertainty in the task duration. A larger standard deviation indicates greater uncertainty.
  SD = (Pessimistic Time - Optimistic Time) / 6

Interpreting the Results

The Estimated Duration (Te) provides a single, more reliable estimate for the task's completion time, taking into account potential best and worst-case scenarios. This is often used for scheduling and resource planning.

The Standard Deviation (SD) helps project managers understand the risk associated with the task. A higher standard deviation suggests that the actual completion time could vary significantly from the estimated duration, indicating a need for closer monitoring or contingency planning. For example, if the estimated duration is 10 days and the standard deviation is 2 days, the task is likely to be completed between 8 and 12 days (Te ± SD) about 68% of the time, assuming a normal distribution.

Example Usage

Imagine a software development task:

• Optimistic Time (O): 5 days (if the code is clean and no bugs are found)
• Most Likely Time (M): 8 days (typical development time with minor debugging)
• Pessimistic Time (P): 15 days (if major refactoring is needed and complex bugs arise)

Using the calculator with these values:

• Estimated Duration (Te): (5 + 4*8 + 15) / 6 = (5 + 32 + 15) / 6 = 52 / 6 ≈ 8.67 days
• Standard Deviation (SD): (15 – 5) / 6 = 10 / 6 ≈ 1.67 days

This suggests the task is most likely to take around 8.67 days, but there's a variability of about 1.67 days, indicating that it could reasonably range from approximately 7 to 10.34 days.