# 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:

a b ! c (! = highest point of arch between b and c

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:

1)Company records show that the time taken to install a piece of equipment at customer facilities as follows:

a)What is the expected time for the installation effort?

b)What is the standard deviation associated with the installation effort?

c)What is a practical interpretation for the results reported in 1a and 1b above?

2)Marsha is in charge of planning a large software development project. She is trying to estimate the cost of the design phase. She works with a group of five experienced designers and asks them to estimate the lowest cost, highest cost, and most typical cost possibilities. After an hour of spirited discussion, the group provides the following estimates:

Lowest cost $30,000

Highest cost $50,000

Most likely cost $45,000

a)Using the PERT-Beta formula, what is the expected cost of the design effort?

b) What is anticipated standard deviation for the design effort?

c)What is a practical interpretation for the results reported in 2a and 2b above?

3)Build-It-Quick house construction company has turned house-building into a science. The standard plan for framing the Excelsior Model house is to execute this effort in 10 working days. Depending on the details of site conditions, the number of carpenters needed to do the job varies slightly from job to job. as shown below:

Fewest number of needed carpenters3Carpenters

Largest number 10Carpenters

Most likely number 5Carpenters

a)Using the PERT-Beta formula, what is the expected number of needed carpenters?

b)What is anticipated standard deviation for the number of needed carpenters?

c)What is a practical interpretation for the results reported in 3a and 3b above?

4)What are some dangers you see in relying on this estimating technique?

5)Using your imagination and/or experience, describe another way to estimate task duration, cost, or manpower requirements.

6)Note that good estimates can be made by guessing the values of only three parameters (best case, worst case, most likely case). Why is this a tremendous advantage?

**Category**: Management