Estimating with the PERT-Beta Distribution
Back in 1957, the year in which the Project Evaluation and Review Technique (PERT) was developed by the US Navy, statisticians developed a simple technique to estimate the amount of time it might take to carry out a task. To use the technique, all one needs is to be able to estimate three parameters: a = the best case duration (fastest), b = the most typical case (mode), and c = the worst case duration (slowest). Given these three parameters, estimators can employ the following formula to estimate the expected amount of time it takes to do a job:
Expected time = e(t) = (a + 4b + c)/6
The expected value of time calculated by using this formula turns out to be roughly the mean value of a PERT-Beta distribution:
The standard deviation (SD) for this estimate is roughly (c – a)/6. The standard deviation tells us that the true value of an estimate lies within the range of +/- 1 SD roughly 60-70% of the time. For example, if we usethe PERT-Beta distribution to determine that the expected value of task duration is 4.33 days and the standard deviation is 0.67 days, we can say: “Roughly 60-70% of the time, the actual task duration lies in the range of 4.33 days +/- 0.67 days.”
Note that while this approach to estimating values was originally employed in estimating durations, it can be also used to estimate costs and number of resources required to do a job.
Questions:
Company records show that the time taken to install a piece of equipment at customer facilities as follows:
What is the expected time for the installation effort?
What is the standard deviation associated with the installation effort?
What is a practical interpretation for the results reported in 1a and 1b above?