Calculating Activity Variance in PERT

In project management, specifically using the Program Evaluation and Review Technique (PERT), we often estimate activity durations based on three different time estimates: optimistic time, pessimistic time, and most likely time. These estimates help account for the uncertainty inherent in project activities.

The optimistic time ($T_o$) is the shortest possible time in which the activity can be completed, assuming everything goes perfectly. The pessimistic time ($T_p$) is the longest possible time required to complete the activity, assuming unfavorable conditions.

Based on these estimates, PERT uses formulas to calculate the expected time and the variance of the activity completion time. The variance is a measure of the uncertainty or risk associated with the activity duration. A higher variance indicates greater uncertainty.

PERT Variance Formula

The formula for calculating the standard deviation ($\sigma$) of an activity's duration in PERT is:

$$\sigma = \frac{T_p - T_o}{6}$$

The variance ($\sigma^2$) is the square of the standard deviation:

$$\sigma^2 = \left(\frac{T_p - T_o}{6}\right)^2$$

Step-by-Step Calculation

We are given the following values:

• Pessimistic time ($T_p$) = 10 days
• Optimistic time ($T_o$) = 4 days

Now, we can substitute these values into the variance formula:

$$\text{Variance} = \left(\frac{10 \text{ days} - 4 \text{ days}}{6}\right)^2$$

$$\text{Variance} = \left(\frac{6 \text{ days}}{6}\right)^2$$

$$\text{Variance} = (1)^2$$

$$\text{Variance} = 1$$

Result

The variance of the activity completion time is 1.

Comparing this result with the given options, the variance is 1.