Probability distribution in PERT analysis

Introduction:
PERT (Program Evaluation and Review Technique) is a project management method used to analyze and represent the uncertainties associated with the completion time of a project. In PERT analysis, the completion time is represented by a probability distribution rather than a single value. This distribution takes into account the three estimated time values for each activity: optimistic time (to), most likely time (tm), and pessimistic time (tp).

Probability distribution:
The probability distribution used to represent the completion time in PERT analysis is the Beta distribution. The Beta distribution is a continuous probability distribution defined on the interval [0, 1]. It is commonly used to model random variables that represent proportions or probabilities.

Reasons for using the Beta distribution:
There are several reasons why the Beta distribution is suitable for representing completion time in PERT analysis:

1. Flexibility: The Beta distribution allows for a wide range of shapes, making it adaptable to various types of projects and uncertainties.

2. Skewed distribution: The completion time in PERT analysis is often skewed, as it is influenced by both optimistic and pessimistic estimates. The Beta distribution can accommodate skewed distributions, making it a good choice for representing completion time.

3. Defined bounds: The completion time cannot be negative or go beyond a certain upper limit. The Beta distribution can be scaled and shifted to fit within these bounds, providing a realistic representation of completion time.

4. Incorporating expert opinions: PERT analysis involves obtaining input from experts who provide their estimates for the completion time. The Beta distribution allows for the incorporation of expert opinions by specifying the shape of the distribution based on the expert's knowledge and experience.

5. Easy calculation of expected value and variance: The expected value and variance of the Beta distribution can be easily calculated using the estimated time values (to, tm, tp) for each activity. These values are important for project scheduling and risk analysis.

Conclusion:
In PERT analysis, the completion time is represented by a probability distribution, and the most suitable distribution for this purpose is the Beta distribution. The Beta distribution offers flexibility, accommodates skewed distributions, has defined bounds, allows for the incorporation of expert opinions, and facilitates easy calculation of expected value and variance.