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📊 Planning & Project Controls Notice

Planning estimates for scheduling and controls purposes; actual outcomes depend on project execution and management judgment. Aligned with PMI PMBOK & AACE 10S-90 standards.

PERT Three-Point Duration Estimator

Calculate expected weighted duration te = (O + 4M + P)/6, standard deviation σ, variance σ², and target completion probabilities per AACE 10S-90.

Three-Point Estimate Inputs

PERT Weighted Duration Results

te = 6.0 days
Expected Duration (te)
6.0 days
68% Confidence: 5.3 to 6.7 days (±1σ)
Standard Deviation (σ): 0.67 days
Variance (σ²): 0.44 days²
Target Completion Probability: 93.3% (Target = 7 days)

PERT Beta Distribution Curve

Frequently Asked Questions (FAQ)

What is the PERT 3-point estimation formula?

PERT expected duration is te = (O + 4M + P) / 6, where O is Optimistic, M is Most Likely, and P is Pessimistic duration.

How is PERT standard deviation calculated?

Standard deviation is sigma = (P - O) / 6, representing task uncertainty.

How is PERT variance calculated?

Task variance is sigma² = ((P - O) / 6)². Project variance equals the sum of variances of critical path activities.

What is Triangular distribution vs Beta distribution?

PERT uses a Beta distribution giving 4x weight to Most Likely M. Triangular distribution uses simple average (O + M + P) / 3.

What confidence levels correspond to 1, 2, and 3 standard deviations?

In a normal distribution, te +/- 1 sigma covers 68.27%, te +/- 2 sigma covers 95.45%, and te +/- 3 sigma covers 99.73% confidence.

How is probability of meeting a target date calculated?

Z-score z = (Target Date - te) / sigma. The cumulative normal distribution function N(z) yields the probability of completing by the target date.

Why is PERT preferred over single-point duration estimates?

Single-point estimates ignore task uncertainty. PERT incorporates optimistic and pessimistic extremes to account for risk.

How do AACE 10S-90 and PMI PMBOK view PERT?

Both AACE International and PMI PMBOK recommend 3-point estimation to improve accuracy during early project planning stages.

What is the PERT weighted average duration formula?

Expected Duration (Te) = (Optimistic + 4 × Most Likely + Pessimistic) / 6.

What is the formula for task standard deviation (σ) in PERT?

Task Standard Deviation (σ) = (Pessimistic Duration - Optimistic Duration) / 6.

How is PERT task variance (σ²) calculated?

Task Variance is the square of standard deviation: σ² = [(Pessimistic - Optimistic) / 6]².

How do you calculate total project variance on a PERT critical path?

Total Project Variance = Sum of variances (σ²) of all activities lying on the critical path.

How do you calculate the probability of completing a project by a target date?

Compute Z-score: Z = (Target Date - Total Expected Duration) / √(Total Project Variance), then look up Z in a standard normal distribution table.

Why does PERT use a beta distribution weighting of 4 for the Most Likely estimate?

The beta distribution assumes the Most Likely duration occurs most frequently, giving it 4 times the weight of extreme optimistic and pessimistic boundaries.

What is the difference between PERT and CPM?

PERT handles uncertain task durations using three-point probabilistic estimates, whereas CPM uses deterministic single-duration estimates.

What is Triangular distribution in 3-point estimating vs PERT Beta?

Triangular estimation uses Te = (Optimistic + Most Likely + Pessimistic) / 3, assigning equal weight to all three points when historical data is lacking.

How does PERT handle optimistic bias in construction estimation?

By explicitly requiring estimators to define a worst-case pessimistic scenario (95th percentile delay), PERT counteracts optimistic bias.

What confidence level corresponds to +1, +2, and +3 standard deviations in PERT?

In a normal curve: ±1σ = 68.3% probability, ±2σ = 95.4% probability, and ±3σ = 99.7% probability of completing within the time range.

Sources & Governing Codes

  1. Wikipedia Program Evaluation and Review Technique (PERT): Wikipedia Program Evaluation and Review Technique (PERT) View Standard
  2. Wikipedia Three-Point Estimation Methodology: Wikipedia Three-Point Estimation Methodology View Standard