Pert Analysis and Time Estimates

In PERT (Program Evaluation and Review Technique) analysis, the time estimates of activities are represented by probability distributions. These distributions are used to model the uncertainty and variability in the time it takes to complete each activity in a project. The most commonly used distribution in PERT analysis is the Beta distribution, which is represented by the Greek letter β.

Beta Distribution

The Beta distribution is a continuous probability distribution defined on the interval [0, 1]. It is commonly used in PERT analysis to represent activity durations because it allows for a wide range of possible values and can account for both optimistic and pessimistic estimates. The Beta distribution has two shape parameters, α (alpha) and β (beta), which determine the shape of the distribution curve.

Shape of the Beta Distribution Curve

The shape of the Beta distribution curve can vary depending on the values of the shape parameters α and β. When both α and β are equal to 1, the Beta distribution reduces to a uniform distribution, where all values between 0 and 1 are equally likely. As the values of α and β increase, the distribution becomes more peaked and concentrated around the mean.

Interpretation in PERT Analysis

In PERT analysis, the time estimates for each activity are usually provided in the form of three values: optimistic (a), most likely (m), and pessimistic (b). These values are used to calculate the shape parameters α and β of the Beta distribution.

The most likely estimate (m) is used as the mode of the distribution, while the optimistic estimate (a) and pessimistic estimate (b) are used to calculate the standard deviation of the distribution. The mean of the distribution is calculated using the formula:

mean = (a + 4m + b) / 6

The shape parameters α and β can then be calculated using the formulas:

α = ((mean - a) / (b - a)) * ((mean - a) / (b - a)) * ((mean - a) / (b - a))

β = ((b - mean) / (b - a)) * ((b - mean) / (b - a)) * ((b - mean) / (b - a))

Conclusion

In PERT analysis, the time estimates of activities follow a Beta distribution curve. This distribution allows for a range of possible values and can model the uncertainty and variability in activity durations. The shape of the Beta distribution curve is determined by the shape parameters α and β, which are calculated using the optimistic, most likely, and pessimistic estimates provided for each activity.