PERT
Construction durations are uncertain. The Program Evaluation and Review Technique (PERT) asks for three estimates per activity, optimistic, most likely and pessimistic, and combines them into an expected duration and a variance.
The expected duration weights the most likely value four times and assumes a beta distribution. The standard deviation is one sixth of the range between pessimistic and optimistic. Along the critical path, expected durations add, and so do variances, assuming activities are independent.
By the central limit theorem, the project duration along that path is treated as roughly normal, so the probability of finishing by a target date comes from a z-value. This is a simplification: near-critical paths can also finish late, which classic PERT ignores, so Monte Carlo schedule risk analysis is now preferred on large projects.
PERT is still a clear way to show why a single-number deadline needs a margin.
t_e = (t_o + 4 t_m + t_p) / 6σ = (t_p − t_o) / 6; variance σ²Path: T_e = Σ t_e, σ_T = √(Σ σ²); z = (T_target − T_e) / σ_T
Problem. An activity has t_o = 4, t_m = 6, t_p = 14 days. Find t_e and σ.
- t_e = (4 + 24 + 14) / 6 = 7.0 days.
- σ = (14 − 4) / 6 = 1.67 days.
Answer. t_e = 7 days, σ ≈ 1.67 days
Quick quiz
1Weight given to the most likely time?
Four.
2Do path variances or standard deviations add?
Variances.
3A weakness of classic PERT?
It ignores near-critical paths merging.
- PMI PMBOK Guide / ANSI standard for project management (USA): Framework of project management principles and practices.
Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.
References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- B. C. Punmia, K. K. Khandelwal, Project Planning and Control with PERT and CPM, Laxmi Publications, latest edition.
- J. W. Hinze, Construction Planning and Scheduling, Pearson, latest edition.
Free and official sources
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