## The Monte Carlo Process

The Monte Carlo process, as applied to risk management, is an attempt to create a series of probability distributions for potential risk items, randomly sample these distributions, and then transform these numbers into useful information that reflects quantification of the potential risks of a real-world situation. While often used in technical applications (e.g., integrated circuit performance, structural response to an earthquake), Monte Carlo simulations have been used to estimate risk in the design of service centers; time to complete key milestones in a project; the cost of developing, fabricating, and maintaining an item; inventory management; and thousands of other applications.

The structure of cost estimating simulations is often additive—meaning that the cost sums across WBS elements regardless of the estimating approach used for a particular WBS element. The structure of schedule simulations is generally based on a schedule network, which encompasses milestones or durations for known activities that are linked in a predefined configuration. Performance models can take on a variety of different structures, which are often unique to the item being simulated, and thus do not follow a simple pattern.

A summary of the steps used in performing a Monte Carlo simulation for cost and schedule follows. Although the details of implementing the Monte Carlo simulation will vary between applications, many cases use a procedure similar to this.

1. Identify the lowest WBS or activity level for which probability distributions will be constructed. The level selected will depend on the program phase—often lower levels will be selected as the project matures.

2. Develop the reference point estimate (e.g., cost or schedule duration) for each WBS element or activity contained within the model.

3. Identify which WBS elements or activities contain estimating uncertainty and/or risk. (For example, technical risk can be present in some cost estimate WBS elements and schedule activities.)

4. Develop suitable probability distributions for each WBS element or activity with estimating uncertainty and/or risk.

5. Aggregate the WBS element or activity probability distributions functions using a Monte Carlo simulation program. When performed for cost, the results of this step will typically be a WBS Level 1 cost estimate at completion and a cumulative distribution function (CDF) of cost versus probability. These outputs are then analyzed to determine the level of cost risk and to identify the specific cost drivers. When performed for schedule, the results of this step will be a schedule at the desired (WBS) level and CDFs of schedule versus probability. The CDFs will typically represent duration or finish date at the desired activity level, but can include other variables as well. These outputs are then analyzed to determine the level of schedule risk and to identify the specific schedule drivers.

Note: It should be recognized that the quality of Monte Carlo simulation results are only as good as the structure of the model, the quality of the reference point estimates, and the selection of probability distributions used in the simulation [the types of distributions (e.g., normal, triangle), the number of distributions per element, and the specific critical values that