How to Compute PERT Estimation

In project management and manufacturing process analysis, PERT estimation is a tool that yields an expected value for the duration of a project. PERT is an acronym for Program Evaluation Review Technique, a method that is used in conjunction with the Critical Path Method (CPM). PERT is most often applied to individual tasks, while CPM is a more powerful method for estimating the length of time required to complete a set of interconnected tasks.

You can easily compute the estimated time to complete a project or process if you know the optimistic, pessimistic, and most likely estimates of the duration or cost. The PERT equation for expected time is

E = (O + 4M + P)/6,

where O is the optimistic value, M is the most likely value, and P is the pessimistic value. This equation is a weighted average where the most likely estimate is weighted 4 times more heavily than the optimistic and pessimistic estimates. The prevents the PERT number from being too heavily skewed in one direction.

Example: Suppose a project manager estimates that the most likely time to complete a project is 12 days--assuming predictable delays and ignoring unlikely scenarios that will either decrease or increase the time. Her optimistic prediction for the project is 7 days--assuming that there are none of the usual delays. Her pessimistic prediction for the project is 29 days--assuming that all possible delays occur. The PERT estimate for the duration of the project is

(7 + 4(12) + 29)/6 = 14 days, or two weeks.

Variance and Standard Deviation

You can also compute the standard deviation and variance of the PERT estimate by adapting the usual formula for statistical variance. Explicitly, the equations are

Variance = [(O-E)² + 4(M-E)² + (P-E)²]/6

S. D. = √ [(O-E)² + 4(M-E)² + (P-E)²]/6 

For the example above, the standard deviation is 6.95 days, or about one week.

A simplified, but less accurate method of computing the standard deviation is often used instead:

S.D. = (E - O)/6,

That is, you subtract the optimistic value from the PERT value and divide by 6. Using this formula and the example above, we get a standard deviation of (14-7)/6 = 1.17 days for the project duration.

© Had2Know 2010