KEVOS® MAKEOS · Projects

PERT Schedule Check (Three-Point Estimates, Expected Duration, Chance of Meeting the Deadline)

With optimistic, most likely and pessimistic durations for the activities on the critical path, what is the expected completion time, how likely is it to meet the deadline, and what duration can I promise at my confidence level?

PERT analysis of up to five activities in sequence on a critical path: the expected duration and variance of each activity from its three-point estimate, the expected path duration and standard deviation, the probability of finishing by the deadline from the normal distribution, and the duration to promise at the confidence you require, against that confidence.

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How this tool works

Inputs, units and where to find them

InputUnitTypical source
Activity 1
Activity 1 optimisticdaysShortest realistic duration of activity 1 if everything goes well.
Activity 1 most likelydaysMost likely duration of activity 1.
Activity 1 pessimisticdaysLongest realistic duration of activity 1 if things go badly (not a disaster case).
Activity 2
Activity 2 optimisticdaysShortest realistic duration of activity 2 if everything goes well.
Activity 2 most likelydaysMost likely duration of activity 2.
Activity 2 pessimisticdaysLongest realistic duration of activity 2 if things go badly (not a disaster case).
Activity 3
Activity 3 optimisticdaysShortest realistic duration of activity 3 if everything goes well.
Activity 3 most likelydaysMost likely duration of activity 3.
Activity 3 pessimisticdaysLongest realistic duration of activity 3 if things go badly (not a disaster case).
Activity 4
Activity 4 optimisticdaysShortest realistic duration of activity 4 if everything goes well.
Activity 4 most likelydaysMost likely duration of activity 4.
Activity 4 pessimisticdaysLongest realistic duration of activity 4 if things go badly (not a disaster case).
Activity 5 (0, 0, 0 to leave out)
Activity 5 optimisticdaysShortest realistic duration of activity 5 if everything goes well.
Activity 5 most likelydaysMost likely duration of activity 5.
Activity 5 pessimisticdaysLongest realistic duration of activity 5 if things go badly (not a disaster case).
Target
Deadline (from the start)daysWorking days from the start to the deadline or shutdown end.
Confidence required%Probability of finishing on time that you need to be able to promise.

What each input means

Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.

Activity 1

What this means: Activity 1 optimistic
Illustration: Activity 1 optimisticA timeline from a start mark to an end mark; Activity 1 optimistic is the time between them.startenda1Example: 5 daysActivity 1 optimistic
What it is
The shortest time activity 1 on the critical path could realistically take if everything goes well, the optimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 5 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Lowers the expected duration slightly and, by widening the range to the pessimistic value, raises the variance.
Get it right
Ask the people doing activity 1; an optimistic value that could never happen narrows the spread falsely.
What this means: Activity 1 most likely
Illustration: Activity 1 most likelyA timeline from a start mark to an end mark; Activity 1 most likely is the time between them.startendm1Example: 8 daysActivity 1 most likely
What it is
The duration of activity 1 that is most likely to happen, the peak of its three-point estimate, weighted four times in the expected value.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 8 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Moves the expected duration by two-thirds of any change; it does not change the variance.
Get it right
It must lie between the optimistic and pessimistic values for activity 1.
What this means: Activity 1 pessimistic
Illustration: Activity 1 pessimisticA timeline from a start mark to an end mark; Activity 1 pessimistic is the time between them.startendb1Example: 14 daysActivity 1 pessimistic
What it is
The longest time activity 1 could realistically take if things go badly, short of a disaster, the pessimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 14 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Raises the expected duration and, with the square of the range, the variance of the path.
Get it right
Use a credible bad case for activity 1; enter 0 for all three values of activity 5 to leave it out.

Activity 2

What this means: Activity 2 optimistic
Illustration: Activity 2 optimisticA timeline from a start mark to an end mark; Activity 2 optimistic is the time between them.startenda2Example: 10 daysActivity 2 optimistic
What it is
The shortest time activity 2 on the critical path could realistically take if everything goes well, the optimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 10 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Lowers the expected duration slightly and, by widening the range to the pessimistic value, raises the variance.
Get it right
Ask the people doing activity 2; an optimistic value that could never happen narrows the spread falsely.
What this means: Activity 2 most likely
Illustration: Activity 2 most likelyA timeline from a start mark to an end mark; Activity 2 most likely is the time between them.startendm2Example: 12 daysActivity 2 most likely
What it is
The duration of activity 2 that is most likely to happen, the peak of its three-point estimate, weighted four times in the expected value.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 12 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Moves the expected duration by two-thirds of any change; it does not change the variance.
Get it right
It must lie between the optimistic and pessimistic values for activity 2.
What this means: Activity 2 pessimistic
Illustration: Activity 2 pessimisticA timeline from a start mark to an end mark; Activity 2 pessimistic is the time between them.startendb2Example: 20 daysActivity 2 pessimistic
What it is
The longest time activity 2 could realistically take if things go badly, short of a disaster, the pessimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 20 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Raises the expected duration and, with the square of the range, the variance of the path.
Get it right
Use a credible bad case for activity 2; enter 0 for all three values of activity 5 to leave it out.

Activity 3

What this means: Activity 3 optimistic
Illustration: Activity 3 optimisticA timeline from a start mark to an end mark; Activity 3 optimistic is the time between them.startenda3Example: 3 daysActivity 3 optimistic
What it is
The shortest time activity 3 on the critical path could realistically take if everything goes well, the optimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 3 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Lowers the expected duration slightly and, by widening the range to the pessimistic value, raises the variance.
Get it right
Ask the people doing activity 3; an optimistic value that could never happen narrows the spread falsely.
What this means: Activity 3 most likely
Illustration: Activity 3 most likelyA timeline from a start mark to an end mark; Activity 3 most likely is the time between them.startendm3Example: 5 daysActivity 3 most likely
What it is
The duration of activity 3 that is most likely to happen, the peak of its three-point estimate, weighted four times in the expected value.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 5 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Moves the expected duration by two-thirds of any change; it does not change the variance.
Get it right
It must lie between the optimistic and pessimistic values for activity 3.
What this means: Activity 3 pessimistic
Illustration: Activity 3 pessimisticA timeline from a start mark to an end mark; Activity 3 pessimistic is the time between them.startendb3Example: 9 daysActivity 3 pessimistic
What it is
The longest time activity 3 could realistically take if things go badly, short of a disaster, the pessimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 9 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Raises the expected duration and, with the square of the range, the variance of the path.
Get it right
Use a credible bad case for activity 3; enter 0 for all three values of activity 5 to leave it out.

Activity 4

What this means: Activity 4 optimistic
Illustration: Activity 4 optimisticA timeline from a start mark to an end mark; Activity 4 optimistic is the time between them.startenda4Example: 6 daysActivity 4 optimistic
What it is
The shortest time activity 4 on the critical path could realistically take if everything goes well, the optimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 6 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Lowers the expected duration slightly and, by widening the range to the pessimistic value, raises the variance.
Get it right
Ask the people doing activity 4; an optimistic value that could never happen narrows the spread falsely.
What this means: Activity 4 most likely
Illustration: Activity 4 most likelyA timeline from a start mark to an end mark; Activity 4 most likely is the time between them.startendm4Example: 9 daysActivity 4 most likely
What it is
The duration of activity 4 that is most likely to happen, the peak of its three-point estimate, weighted four times in the expected value.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 9 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Moves the expected duration by two-thirds of any change; it does not change the variance.
Get it right
It must lie between the optimistic and pessimistic values for activity 4.
What this means: Activity 4 pessimistic
Illustration: Activity 4 pessimisticA timeline from a start mark to an end mark; Activity 4 pessimistic is the time between them.startendb4Example: 15 daysActivity 4 pessimistic
What it is
The longest time activity 4 could realistically take if things go badly, short of a disaster, the pessimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 15 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Raises the expected duration and, with the square of the range, the variance of the path.
Get it right
Use a credible bad case for activity 4; enter 0 for all three values of activity 5 to leave it out.

Activity 5 (0, 0, 0 to leave out)

What this means: Activity 5 optimistic
Illustration: Activity 5 optimisticA timeline from a start mark to an end mark; Activity 5 optimistic is the time between them.startenda5Example: 0 daysActivity 5 optimistic
What it is
The shortest time activity 5 on the critical path could realistically take if everything goes well, the optimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Lowers the expected duration slightly and, by widening the range to the pessimistic value, raises the variance.
Get it right
Ask the people doing activity 5; an optimistic value that could never happen narrows the spread falsely.
What this means: Activity 5 most likely
Illustration: Activity 5 most likelyA timeline from a start mark to an end mark; Activity 5 most likely is the time between them.startendm5Example: 0 daysActivity 5 most likely
What it is
The duration of activity 5 that is most likely to happen, the peak of its three-point estimate, weighted four times in the expected value.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Moves the expected duration by two-thirds of any change; it does not change the variance.
Get it right
It must lie between the optimistic and pessimistic values for activity 5.
What this means: Activity 5 pessimistic
Illustration: Activity 5 pessimisticA timeline from a start mark to an end mark; Activity 5 pessimistic is the time between them.startendb5Example: 0 daysActivity 5 pessimistic
What it is
The longest time activity 5 could realistically take if things go badly, short of a disaster, the pessimistic end of its three-point estimate.
Units and format
Enter a number in days: days. The form accepts 0 days to 100000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Raises the expected duration and, with the square of the range, the variance of the path.
Get it right
Use a credible bad case for activity 5; enter 0 for all three values of activity 5 to leave it out.

Target

What this means: Deadline (from the start)
Illustration: Deadline (from the start)A timeline from a start mark to an end mark; Deadline (from the start) is the time between them.startendtExample: 40 daysDeadline (from the start)
What it is
The number of working days from the start of the path to the deadline, such as the end of a shutdown or a delivery date.
Units and format
Enter a number in days: days. The form accepts 0.000001 days to 1000000 days. Required: the tool does not calculate until every input is valid.
Example
The form opens with 40 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A later deadline raises the chance of finishing on time.
Get it right
Count in the same day units as the activity estimates, working days or calendar days.
What this means: Confidence required
Illustration: Confidence requiredA bar of 100 parts with the share marked; Confidence required is that share out of 100. The bar follows the value you type.0 %100 %Example: 85%Confidence required
What it is
The probability of finishing on time that you need before promising a date, used to find the duration to promise.
Units and format
Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 99.9%. Required: the tool does not calculate until every input is valid.
Example
The form opens with 85% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Raises the duration to promise and the bar the deadline must clear.
Get it right
Higher confidence needs a longer promise; 50 % is simply the expected duration.

Method and formulas

  1. Each activity: expected duration t_e = (a + 4m + b) ÷ 6 and variance σ² = ((b − a) ÷ 6)² (PERT, Malcolm et al. 1959).
  2. Path: T = Σ t_e and σ_T = √(Σ σ²), activities treated as independent.
  3. Probability of finishing by the deadline = Φ((deadline − T) ÷ σ_T); duration at confidence c = T + z_c σ_T, with the normal distribution.
  4. Example: expected 36.333 days (σ 2.8771); a 89.874 % chance of finishing within 40 days.

Limitations

  • Covers one path: a near-critical parallel path can finish later and makes the real chance of meeting the deadline lower (merge bias); check every path that could become critical.
  • Assumes independent activities and a normal path total; common causes (weather, one supplier) make delays move together and widen the real spread.
  • Example values are illustrations. Replace them with values for your actual task.

Typical uses

  • Set a realistic delivery date for a machine build
  • Check the chance of meeting a shutdown window
  • Decide how much schedule buffer to hold

Who it is for

  • Project managers
  • Planners and schedulers
  • Engineering managers

What you get

  • Expected duration and variance of each activity
  • Expected path duration and standard deviation
  • Probability of meeting the deadline
  • Duration to promise at your confidence

Interpreting the result

  • Each activity’s spread adds as variance, so one activity with a long pessimistic tail can dominate the path’s uncertainty: tighten that estimate first.

References

  • Malcolm D. G., Roseboom J. H., Clark C. E. and Fazar W., Application of a Technique for Research and Development Program Evaluation, Operations Research 7 (5), 646–669 (1959).
  • Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.

Learn the Concepts Behind This Tool

These KEVOS® Library readings explain the method this tool uses, with worked examples.

KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.

Open the PERT Schedule Check (Three-Point Estimates, Expected Duration, Chance of Meeting the Deadline) calculator

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