# RESEARCH ARTICLES | RISK + CRYSTAL BALL + ANALYTICS

## Tolerance Analysis using Root Sum Squares Approach (Part 6 / 13)

Root Sum Squares (RSS) approach to Tolerance Analysis has solid a foundation in capturing the effects of variation. In the days of the golden abacus, there were no super-fast processors willing to calculate the multiple output possibilities in a matter of seconds (as can be done with Monte Carlo simulators on our laptops). It has its merits and faults but is generally a good approach to predicting output variation when the responses are fairly linear and input variation approaches normality. That is the case for plenty of Tolerance Analysis dimensional responses so we will utilize this method on our non-linear case of the one-way clutch.

## Using the CB.GetForeStatFN function in your Crystal Ball Models.

Crystal Ball utlizes several powerful functions and features to extract information and descriptive statistics. We are going to review these techniques and present the CB.GetForeStatFN in full detail, including Six Sigma Capability Metrics.

## Using the CB.GetForeStatFN function in your Crystal Ball Models.

Crystal Ball utlizes several powerful functions and features to extract information and descriptive statistics. We are going to review these techniques and present the CB.GetForeStatFN in full detail, including Six Sigma Capability Metrics.

## Transfer Functions & Response Surfaces in Tolerance Analysis (Part 5 / 13)

Transfer Functions (or Response Equations) are useful to understand the "wherefores" of your system outputs. The danger with a good many is that they are not accurate. ("All models are wrong, some are useful.") Thankfully, the very nature of Tolerance Analysis variables (dimensions) makes the models considered here concrete and accurate enough. We can tinker with their input values (both nominals and variance) and determine what quality levels may be achieved with our system when judged against spec limits. That is some powerful stuff!

## Probability Distributions in Tolerance Analysis (Part 4 / 13)

With uncertainty and risk lurking around every corner, it is incumbent on us to account for it in our forward business projections, whether those predictions are financially-based or engineering-centric. For the design engineer, he may be expressing dimensional variance in terms of a tolerance around his nominal dimensions. But what does this mean? Does a simple range between upper and lower values accurately describe the variation?