Other Scheduling Methods - Construction Project Scheduling and Control - page 303

9. The completion date with at least a 90% confidence level .Goto
Table 11.1 and pick a probability value close to (but not less than)
0.9. Read the corresponding Z value. You should read 1.28. Apply
equation 11.8:

T S =σ E ∗ Z + T E = 2 . 972 ∗ 1 . 28 + 32 = 35 . 8 ≈ 36 days

Difference between “Most Likely” and “Expected” Durations

From a linguistic viewpoint, the terms most likely and expected may be thought of as
similar. However, statistically they are different. The “most likely” duration is sim-
ply the duration that we believe has more likelihood of happening than any other
duration. In our case, it is a user-defined amount; that is, we provide it along with
other durations (optimistic and pessimistic) in the equation so that we can calculate
the expected duration and the standard deviation. It does not represent the arithmetic
mean or the median.
The “expected duration” is the amount of time that we expect the project
or path duration to take, considering the different durations (optimistic and pes-
simistic), their values, and their weights. It is a computed amount. For example,
consider a case in which 6, 8, and 10 are the optimistic, most likely, and pessimistic
durations, respectively. The expected duration will be equal to 8. In this case, it is
equal to the most likely duration because the optimistic and pessimistic durations
“deviate” by the same amount from the most likely duration (6 to 8 and 10 to
8). Now, suppose that the pessimistic duration is 13 days, whereas the optimistic
and most likely durations are still the same. The expected duration is calculated
as 8.5 days by using equation 11.1. The expected duration value has increased as
a result of the increase in the skewness of the pessimistic duration. Even though
the probability of the occurrence of the pessimistic duration (or the weight) is
still the same in both examples (one-sixth), the consequences have worsened in
the second case.

Is the Longest Path Still the Most Critical?

A typical network project has tens or hundreds (perhaps even thousands) of
paths. Typically, we define the critical path as the longest path from the start
until the end of the network (see the full definition of critical path in Chapter
4). In addition to the duration, another factor must be considered in the crit-
icality of the path in PERT. This factor is the “uncertainty” of the duration of
the path, measured by the standard deviation. Let us look at example 11.2 for an
illustration.