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Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values—a probability distribution—for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions.

Engineering Ethics - Responsibility for Safety

Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values.


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By using probability distributions, variables can have different probabilities of different outcomes occurring. Probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis. Values in the middle near the mean are most likely to occur. Examples of variables described by normal distributions include inflation rates and energy prices.

Values are positively skewed, not symmetric like a normal distribution. Examples of variables described by lognormal distributions include real estate property values, stock prices, and oil reserves. All values have an equal chance of occurring, and the user simply defines the minimum and maximum.


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Examples of variables that could be uniformly distributed include manufacturing costs or future sales revenues for a new product. The user defines the minimum, most likely, and maximum values. Values around the most likely are more likely to occur. Variables that could be described by a triangular distribution include past sales history per unit of time and inventory levels.

An Introduction for Engineers

The user defines the minimum, most likely, and maximum values, just like the triangular distribution. However values between the most likely and extremes are more likely to occur than the triangular; that is, the extremes are not as emphasized. An example of the use of a PERT distribution is to describe the duration of a task in a project management model. Where the content of the eBook requires a specific layout, or contains maths or other special characters, the eBook will be available in PDF PBK format, which cannot be reflowed. For both formats the functionality available will depend on how you access the ebook via Bookshelf Online in your browser or via the Bookshelf app on your PC or mobile device.

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Stay on CRCPress. Preview this Book. Add to Wish List. Close Preview. Toggle navigation Additional Book Information. Summary A Training Tool for the Environmental Risk Professional Environmental Risk Analysis: Probability Distribution Calculations defines the role that probability distributions play in risk analysis, and gives direction on how to measure and compare the magnitude of risk more efficiently. Includes a complete overview of environmental risk and covers environmental risk-related topics Presents a simplified approach to the industrial application of environmental risk analysis and probability distributions Offers a practical understanding of environmental risk analysis calculations involving probability distributions Environmental Risk Analysis: Probability Distribution Calculations provides a working knowledge of the principles and applications needed to solve real-world problems relevant to environmental risk analysis and probability distributions.

Acceptability of Risk

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What is Monte Carlo Simulation?

Shopping Cart Summary. As part of the risk assessment, risk dependencies, interdependencies, and the timeframe of the potential impact near-, mid-, or far-term need to be identified. For additional details, see the Risk Management Tools article in this Guide. When assessing risk, it is important to match the assessment impact to the decision framework. For program management, risks are typically assessed against cost, schedule, and technical performance targets.

Risk and How to use a Risk Matrix

Some programs may also include oversight and compliance, or political impacts. Garvey [2] provides an extensive set of rating scales for making these multicriteria assessments, as well as ways to combine them into an overall measure of impact or consequence. These scales provide a consistent basis for determining risk impact levels across cost, schedule, performance, and other criteria considered important to the project. In addition, the Risk Matrix tool can help evaluate these risks to particular programs see the Risk Management Tools article.

For more details on these analyses, see the Tools to Enable a Comprehensive Viewpoint article in the Comprehensive Viewpoint topic of the Enterprise Engineering section. For some programs or projects, the impacts of risk on enterprise or organizational goals and objectives are more meaningful to the managing organization.

Risks are assessed against the potential negative impact on enterprise goals.


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Using risk management tools for the enterprise and its components can help with the consistency of risk determination. This consistency is similar to the scale example shown below, except that the assessment would be done at the enterprise level. Depending on the criticality of a component to enterprise success e. One way management plans for engineering an enterprise is to create capability portfolios of technology programs and initiatives that, when synchronized, will deliver time-phased capabilities that advance enterprise goals and mission outcomes.

A capability portfolio is a time-dynamic organizing construct to deliver capabilities across specified epochs; a capability can be defined as the ability to achieve an effect to a standard under specified conditions using multiple combinations of means and ways to perform a set of tasks [2].

These factors are generally applicable to the government acquisition environment see the Guide article Portfolio Management in the Enterprise Engineering section. For portfolio risk assessment, investment decision, or analysis of alternatives tasks, using categories of risk area scales may be the most appropriate way to ensure each alternative or option has considered all areas of risk. Risk areas may include advocacy, funding, resources, schedule and cost estimate confidence, technical maturity, ability to meet technical performance, operational deployability, integration and interoperability, and complexity.

Scales are determined for each risk area, and each alternative is assessed against all categories.

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Probability and Risk Analysis - An Introduction for Engineers | Igor Rychlik | Springer

Risk assessment may also include operational consideration of threat and vulnerability. For cost-risk analysis, the determination of uncertainty bounds is the risk assessment. When determining the appropriate risk assessment approach, it is important to consider the information need. There are no technical or performance expectations identified that will have any impact on achieving the stated outcome objectives expected from the alternative. Limited technical or performance expectations identified that will have a minor impact on achieving the stated outcome objectives expected from the alternative.

Key technologies are not ready and mature and require moderate effort to implement the alternative.