# Monte Carlo Simulation

## Monte Carlo Integration

This video shows how definite integrals can be estimated using Monte Carlo simulation.  A triple integral is estimated using Simulation Master. Other Resources Blog article on Monte Carlo integration. Tutorial on using the Simulation Master integration tool.   For more videos, visit our YouTube channel. Excel is a registered trademark of Microsoft Corporation.  Used with permission …

## Correlation Matrix Definiteness

When simulating a model, some random variable inputs may be correlated.  One way to introduce this correlation into the simulation is by rank order correlation.  In this method a correlation matrix is used to define the correlation structure.  The correlation matrix definiteness is important. A correlation matrix must be either positive definite (PD) or positive …

## Decision Tree Simulation – An Example

Traditional decision trees are characterized by discrete outcomes.  However, Monte Carlo simulation can be combined with a decision tree to have a more rich data set to identify risk.  We will show an example of decision tree simulation for an R&D project to see how this works. To simulate a tree, a node’s value (cost …

## Presenting Simulation Results

Presenting the results of a Monte Carlo simulation can be challenging when your audience isn’t inclined to receive probabilistic information.  Decision makers often want a single number for net present value, project completion date, or profit. How do we as the modeler/analyst present this information so it is understood and appreciated for the extra information …

## Comparing Simulations with a Box Plot

A box plot, aka box and whisker chart, is a simple way to show the results of a Monte Carlo simulation.  It’s also a useful way to visualize the differences between several simulations in one plot. Typically the results of a single simulation is shown as a histogram.  This a good tool for visualizing outcomes, …

## Modeling Tip: Sum Random Variables

An easy to make mistake when modeling identically distributed random variables is to use a single variable to model several identically distributed values.  We could easily assume that several random variables that have the same probability distribution could be modeled by sampling a single variable and multiplying by the total number of variables.  This is …

## Simulating a Cost Estimate

Simulating a cost estimate can be used to get an understanding of the potential range of outcomes. Cost estimates by their nature contain uncertainty and lend themselves well to simulation.  In this article we’ll look at how to simulate an estimate and some items that need to be considered. Estimating costs for simulation comes in …

## Sampling from an Empirical Distribution

When data is available, an empirical distribution can be used in a Monte Carlo simulation.  In this article we’ll cover the basics of the empirical distribution and how to use it in your models. Empirical vs. Parametric Distributions Before we get into details, let’s look at the big picture for a minute.  A parametric probability …

## Optimizing a Design with Monte Carlo Simulation

Performance and cost trade-offs are a constant in engineering design.  Optimizing a design to balance these competing forces can be challenging to quantify and we often have to resort to experience or intuition.  One of the traditional cost drivers is specifying tolerances.  Part dimensions are naturally random variables since each part manufactured will not be …

## Monte Carlo Simulation for Business

Monte Carlo simulation for business purposes is a great tool to have in your toolbox.  If you’re a business owner or a product line owner in a larger enterprise, chances are you’ve created a spreadsheet to model a business case or something similar.  Anytime you have a spreadsheet that contains estimates that are inputs to …