# Apogee: Monte Carlo

Simulate the effects of variation on your designs

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**$269**OVERVIEW | PARAMETERS | DISTRIBUTIONS | RESPONSES | MODELS | FORMULATION EDITOR | OPTIONS | VIDEOS

## OVERVIEW

Monte Carlo analysis is a powerful way to assess the magnitude and shape of response variation caused by the variation of the parameters. It approximates each response distribution by randomly generating single values for each of the input parameters, plugging these values into the model, and computing a value for each response. By then applying sample statistics a substantial amount of information can be derived about the response distribution - its location, spread and shape. Monte Carlo Analysis is the gold standard to which all other techniques are judged, and if computational expense is not a problem, then it will always be the preferred method.

### FEATURES

- Identify tolerances that are too tight or too loose
- Quantify risk of not meeting requirements
- Easy-to-use and learn interface
- Unlimited number of factors*
- Estimate number of Monte Carlo runs needed
- Random or Latin Hypercube sampling

*Constrained only by worksheet size/memory limits in MS Excel™

### BENEFITS

If the input parameters of a mathematical function have statistical variation, then the output response will also have variation. Monte Carlo analysis approximates the output distribution by randomly generating single values for each of the input parameters, plugging these values into the model, and computing a value for the response. By then applying sample statistics a substantial amount of information can be derived about the response distribution – its location, spread and shape. Monte Carlo Analysis is the gold standard to which all other techniques are judged, and if computational expense is not a problem, then it will always be the preferred method.

If the response has a defined Upper Specification Limit (USL) or Lower Specification Limit (LSL) then a confidence interval on the probability of the response falling outside of these limits will be computed using the binomial statistics. This probability is called the Probability of Non-Compliance or PNC.

Histogram plots of the responses, along with summaries of their sample statistics, will be created in a Monte Carlo report after all trials are run. Pareto plots of the contributions of each parameter to the response are also created. This can be useful for identifying which parameters have the largest impact on response standard deviation and which parameters could be changed to reduce the response PNC.

If the response has a defined Upper Specification Limit (USL) or Lower Specification Limit (LSL) then a confidence interval on the probability of the response falling outside of these limits will be computed using the binomial statistics. This probability is called the Probability of Non-Compliance or PNC.

Histogram plots of the responses, along with summaries of their sample statistics, will be created in a Monte Carlo report after all trials are run. Pareto plots of the contributions of each parameter to the response are also created. This can be useful for identifying which parameters have the largest impact on response standard deviation and which parameters could be changed to reduce the response PNC.

### REQUIREMENTS

- Microsoft Windows 7, 8, or 10
- Microsoft Excel 2007, 2010, 2013 (32 or 64 bit), or 2016 (32 or 64 bit)
- Administrator rights required to install software

## VIDEOS

This video shows Sensitivity Analysis and Monte Carlo using SDI Tools v3 in action. We will be updating this video to reflect changes to

**SDI Tools v4**soon.