# 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 areVariance = [(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.

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