# RESEARCH ARTICLES | RISK + CRYSTAL BALL + ANALYTICS

## Tolerance Analysis using Monte Carlo (Part 11 / 13)

How do Monte Carlo analysis results differ from those derived via WCA or RSS methodologies? Let us return to the one-way clutch example and provide a practical comparison in terms of a non-linear response. From the previous posts, we recall that there are two system outputs of interest: stop angle and spring gap. These outputs are described mathematically with response equations, as transfer functions of the inputs.

## Introduction to Monte Carlo Analysis (Part 10 / 13)

In past blogs, I have waxed eloquent about two traditional methods of performing Tolerance Analysis, the Worst Case Analysis and the Root Sum Squares. With the advent of ever-more-powerful processors and the increasing importance engineering organizations place on transfer functions, the next logical step is to use these resources and predict system variation with Monte Carlo Analysis.

## Root Sum Squares Explained Graphically, continued (Part 9 / 13)

The other RSS equation, that of predicted output mean, has a term dependent on 2nd derivatives that is initially non-intuitive:

Why is that second term there?

## Root Sum Squares Explained Graphically (Part 8 / 13)

A few posts ago, I explained the nature of transfer functions and response surfaces and how they impact variational studies when non-linearities are concerned. Now that we have the context of the RSS equations in hand, let us examine the behavior of transfer functions more thoroughly.

## Tolerance Analysis using Root Sum Squares Approach, continued (Part 7 / 13)

As stated before, the first derivative of the transfer function with respect to a particular input quantifies how sensitive the output is to that input. However, it is important to recognize that Sensitivity does not equal Sensitivity Contribution. To assign a percentage variation contribution from any one input, one must look towards the RSS output variance (σY2) equation: