Last Updated on 05-Feb-2021 by Charles Maxwell

**How do you estimate a project when it is complex, lengthy, novel, and it doesn’t have a precedent?**

This was the problem William (“Red”) Raborn faced during late 1955 when he became the US Navy’s Director of Special Projects at the Bureau of Weapons. He was assigned to develop the first submarine-launched ballistic missile in what was called the Polaris program. The technical challenges were immense, and the schedule was very ambitious. The Polaris program eventually involved more than 9,000 organizations working on 400 major research and development projects in most of the fields of engineering and the physical sciences.

Many of us—while not encountering as large a challenge—still confront difficulties estimating the schedule and cost of tasks or projects. This is true all along the value chain—from design to fabrication and from marketing to sales and delivery.

### PERT

A year into development, the Polaris program urgently needed an integrated planning and control system to improve scheduling and cost control. Raborn authorized the development of a planning tool and appointed the economist Willard Fazar to lead the work. Fazar assembled a team of Navy personnel and employees from Lockheed’s Missiles and Space Division and from the consulting firm Booz-Allen & Hamilton, including industrial engineer Donald Malcolm. During early 1958, the team originated a statistical method ultimately called the Program Evaluation and Review Technique (PERT).

The technique used 3 estimates to overcome the limitations of single-point estimates for cost and schedule. The 3 PERT estimates included optimistic, pessimistic, and most likely of the time and cost to complete each task. Using computers, the team then calculated the time to complete an immensely complex series of tasks and provided statistics describing the probability of completing the project on time and at various cost levels.

Although the Polaris program required manufacturing more than 250,000 parts and components, the program team achieved its goal 3 years early.

### 3-Point Estimating Method

In my own work I have used PERT to improve the quality of capital and operating cost estimates. This approach helped our team improve the speed and ease of making estimates. More important, the method provided management with higher confidence of the accuracy and precision of our work.

The method—called the 3-point estimating method—consists of making individual estimates of the best, worst, and most likely cost or time required for the many small tasks that compose a complete project. When making estimates, I have found it is often easier to first determine the worst and best cases and then select the most likely.

The technique works equally well to quantify capital and operating costs, as well as schedules.

Project managers can further enhance their estimates by using a panel of experts to make various independent 3-point estimates for the small tasks and then compiling those estimates. I have done this, and it works well. This improves objectivity and team buy-in.

### Theory and Calculations

The power of the 3-point estimating method becomes even more apparent when a few reasonable assumptions are made. These include:

- The estimates for the small tasks are statistically independent
task estimates (*Worst***A**) and theestimates (*best***B**) lie approximately 3 sigma from the mean (**μ**)- The
estimates (*most likely***M**) represent the mode (the most often encountered value) - The overall estimate (the critical path for schedule and the overall cost) is the sum of the expected values for the many tasks; and in like fashion, the overall variance is the sum of the task variances
- The aggregation of the many small task estimates is normally distributed—this is an application of the central limit theorem, which teaches that many random measurements of tasks yields an overall project result that is normally distributed

With these assumptions, it is possible to calculate such useful information as the ** expected value** or

**(**

*mean***μ**), the

**(**

*standard deviation***σ**), and the

**using the following formulas:**

*confidence limits*- Expected value = Mean = μ= (A + 4M + B)/6
- Standard deviation = Sigma = σ = (B-A)/6
- Upper 95% confidence limit = Mean + 2 Sigma = μ + 2σ
- Lower 95% confidence limit = Mean – 2 Sigma = μ – 2σ

The mean +/- 1 sigma embraces 68% of the possibilities. This is approximately 2/3, and it is for this reason that the mode (M) is weighted at 4/6 as reflected in the formula for calculating the expected value.

The mean +/- 2 sigma embraces 95% of the possibilities; thus yielding typical upper and lower confidence limits.

Applying the 3-point estimating method to project management, the project team decomposes a project into many small parts using a work breakdown structure (WBS), and then the team estimates all elements of the WBS. Once the team adds together all the estimates, they have an overall estimate that is more accurate.

### Conclusion

In summary, the 3-point method is a powerful tool for enhancing the quality of cost and schedule estimates.

- 3-point estimates are more reliable, because they are more accurate and more precise
- Those who use 3-point estimates better understand the limitations of their estimates
- Fewer surprises occur when work is performed
- The 3-point method works particularly well for bottom-up estimating approaches, where you have lots of detail

### Further Information

The following video discusses the Polaris missile program and PERT’s role in it.

This video provides a brief overview of PERT.

The following video provides a good summary of the math involved in 3-point estimating.

You can read more on 3-point estimating and PERT in the following articles:

- “Three-point estimation,” Wikipedia, https://en.wikipedia.org/wiki/Three-point_estimation
- “Program evaluation and review technique,” Wikipedia, https://en.wikipedia.org/wiki/Program_evaluation_and_review_technique
- D. G. Malcolm, J. H. Roseboom, C. E. Clark, and W. Fazar. “Application of a Technique for Research and Development Program Evaluation,”
*Operations Research*, Vol. 7, No. 5, 1959 Sep–Oct, pp. 646–669, http://mech.vub.ac.be/teaching/info/Ontwerpmethodologie/Appendix%20les%202%20PERT.pdf

### Photo Credit

Shocked female worker in workplace (perhaps after being asked to estimate the schedule and cost of a project that is complex, lengthy, novel, and unprecedented), photographer Andrea Piacquadio, Pexels, 3791129.