Statistical
PERT three-point estimates and a fixed path’s duration uncertainty
Convert Optimistic, Most Likely, and Pessimistic estimates into PERT Weighted Mean (O + 4M + P)/6, Task SD (P - O)/6, and Quadrature Path Risk.
Distinguish an estimate from a simulated project schedule
The conventional PERT weighted estimate is (O+4M+P)/6 and its standard-deviation heuristic is (P-O)/6. These are modeling approximations based on ordered estimates O<=M<=P, not measured guarantees or the exact variance of every beta distribution.
For independent sequential task durations on a fixed path, variances add. Task standard deviations of 3 and 4 give path SD sqrt(9+16)=5. Correlated tasks also require covariance terms.
This example neither runs Monte Carlo simulation nor finds a critical path. Multiple competing paths and dependencies can change the project completion distribution; normal probability bounds need additional assumptions.
| PERT Risk Formula | Calculation | Result |
|---|---|---|
| PERT Expected Duration (6, 10, 20) | =(6 + 4*10 + 20) / 6 | 11.00 days |
| Single-Task PERT SD | =(20 - 6) / 6 | 2.3333 days |
| Critical Path SD (Task SDs 3d & 4d) | =SQRT(SUM({3;4}^2)) | 5.00 days under independence |
PERT 3-point expected value and Critical Path SD formulas
Weights Optimistic (1/6), Most Likely (4/6), and Pessimistic (1/6).
=ROUND((A2 + 4 * B2 + C2) / 6, 4)Combined Critical Path Standard Deviation across independent tasks
Root-sum-of-squares SQRT(SUM(E2:E3 ^ 2)) adds variances properly.
=ROUND(SQRT(SUM(E2:E3 ^ 2)), 4)Single-task standard-deviation estimate
Use the same time unit for all three inputs.
=ROUND((C2-A2)/6,4)Try the example
Use the original values or change them to test your understanding.