## Estimating Activity Time

Determining the elapsed time between events requires that responsible functional managers evaluate the situation and submit their best estimates. The calculations for critical paths and slack times in the previous sections were based on these best estimates.

In this ideal situation, the functional manager would have at his disposal a large volume of historical data from which to make his estimates. Obviously, the more historical data available, the more reliable the estimate. Many programs, however, include events and activities that are nonrepetitive. In this case, the functional managers must submit their estimates using three possible completion assumptions:

• Most optimistic completion time. This time assumes that everything will go according to plan and with a minimal amount of difficulties. This should occur approximately 1 percent of the time.

• Most pessimistic completion time. This time assumes that everything will not go according to plan and that the maximum potential difficulties will develop. This should also occur approximately 1 percent of the time.

• Most likely completion time. This is the time that, in the mind of the functional manager, would most often occur should this effort be reported over and over again.7

Before these three times can be combined into a single expression for expected time, two assumptions must be made. The first assumption is that the standard deviation, s, is one-sixth of the time requirement range. This assumption stems from probability theory, where the end points of a curve are three standard deviations from the mean. The second assumption requires that the probability distribution of time required for an activity be expressible as a beta distribution.8

The expected time between events can be found from the expression:

where te = expected time, a = most optimistic time, b = most pessimistic time, and m = most likely time.

As an example, if a = 3, b = 7, and m = 5 weeks, then the expected time, te, would be 5 weeks. This value for te would then be used as the activity time between two events in the construction of a PERT chart. This method for obtaining best estimates contains a large degree of uncertainty. If we change the variable times to a = 2, b = 12, and m = 4 weeks, then te will still be 5 weeks. The latter case, however, has a much higher degree of uncertainty because of the wider spread between the optimistic and pessimistic times. Care must be taken in the evaluation of risks in the expected times.