Other Scheduling Methods - Construction Project Scheduling and Control - page 296

Figure 11.1 Probability density function curve (shaded area indicates the probability that an
event will occur by a certain date)

Rewriting equation 11.7, we get

T S =σ E ⋅ Z + T E (11.8)

These calculations are clarified further in the following examples.

Graphic Explanation

The probability density function (PDF) of a normal distribution is represented by
a bell-shaped curve. The area under the curve represents the probability universe ,
where all possibilities are covered, which is 1.00, or 100%. The probability that an
event will occur by a certain date (i.e., on or before that date) is the area under the
curve to left of that date. See Figure 11.1.

Example 11.1

In a CPM network, the critical path includes five activities. Their durations are
tabulated next.

Duration (Days)

Activity Optimistic ( To ) Most Likely ( Tm ) Pessimistic ( Tp )

A 2 4 7

B 5 8 14

C 4 6 8

D 2 2 2

E 7 10 21

Compute the following nine values:

1. The probability that the project will finish by the end of day 32
2. The probability that the project will finish by the end of day 34