RESEARCH ARTICLES | RISK + CRYSTAL BALL + ANALYTICS

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?

 

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.

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:

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.

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.

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