PERT Three-Point Estimates: Expected Duration, Standard Deviation, and Confidence

Combining Tasks in Sequence

For tasks done one after another, expected durations add: 5 + 5 + 7 = 17 days. Variances (SD squared) also add: 2.78 + 0.44 + 2.78 = 6.0, so the path's SD is √6 = 2.45 days. Note that you add variances, not standard deviations; adding the SDs (4.0) would overstate the spread. Uncertainty adds less than linearly because delays in one task tend to be offset by early finishes in another (assuming independence).

A normal approximation gives schedule probabilities: the chance of finishing within 17 days is about 50%, within 19.4 days (17 + 1 SD) about 84%, within 21.0 days (17 + 1.645 SD) about 95%, and within 24.3 days (17 + 3 SD) about 99.7%.

Setting a Commitment

Quote a date at the confidence you need: 17 days if you accept a coin-flip chance of delay, 19.5 days for about 84%, 21 days for 95%. Compare this with the sum of the most likely values (4 + 5 + 6 = 15 days), which is optimistic: there is only about a 20% chance of finishing in 15 days. Because the pessimistic estimates are skewed, the expected value (17) exceeds the sum of the most likely (15). That is a common source of overrun when only the most likely values are used.

Parallel Paths and Limits

For a project with parallel paths, the critical path (the longest) drives the schedule, but the chance of finishing on time is lower than for any single path, because any of them might be late. Estimates are subjective and often biased toward optimism; gather estimates from the people doing the work and review them against past projects. The beta distribution assumed by PERT is an approximation, and for large projects, simulation provides a better picture.