When running a Monte Carlo Analysis, each parameter that has a set tolerance will be assigned a value randomly in accordance with a statistical distribution over the range of possible values. There are 4 different types of statistical models you can use to define the distributions: normal, uniform, parabolic, or user defined. The normal statistics is a Gaussian distribution with a default width of four standard deviations between the minimum and maximum allowable values. A uniform distribution will select any value within the acceptable range with equal probability. The parabolic statistical distribution models the possible values with a parabola, thus favoring the ends of the range rather than the center like a Gaussian. And finally, a user defined statistical distribution is very flexible and can use measured statistical data, feature multiple peaks, show a skewed distribution, etc.

In the Monte Carlo tab of the Tolerancing window, you can change the type of statistics that are used during the tolerancing analysis, or you can set a different type of statistics for each tolerancing operand in the Tolerance Data Editor using the STAT command.

In the end, the type of statistics you should use depends on your design and how strictly you are tolerancing it. A normal distribution is the default setting and is optimistic that most of the manufactured parts will be closer to the nominal design. Using the uniform distribution or a parabolic distribution will give increasingly pessimistic results as the weight on the possible values shifts closer to the extremes, highlighting some of the more sensitive tolerances. However, because it expects parts to be further from the nominal values, using parabolic statistics may lead to a more rigorous design with a higher yield when the lenses is commercially produced. And finally, user defined statistics might be appropriate for a system where you are trying to mimic a specific production process in your tolerancing analysis. So while the default setting of a normal distribution may work for most projects, exploring your design with the other statistics may be insightful depending on how appropriate conservative tolerances are for your lens.

Hey Sarah, I htink it's useful to point out that the control in the UI is only used if you do not provide more specific guidance in the Tolerance Data Editor. The STAT operand can be used in the TDE to change the statistics used, right down to a tolerance-by-tolerance basis if needed. 

In general, things like radii tolerances might be Gaussianly distributed, whereas thickness tolerances might be clustered more towards the limits of their manufacture. Aslo, STAT supports user-defined distributions, so the more detailed information you have about what a particular machine or process produces, the more detailed your production simulation can be.

It's OK to do a quick first-pass with one set of statistics for the whole system, but detailed analysis means to need to get as much detail into the tolerance model as possible, and STAT is fantastic at that.  

Great notes all around! Just to add a bit more info here in the thread, as both Sarah and Mark mentioned, STAT is very helpful getting the nuances of your manufacturing process defined in the simulation. A nice detail that I think is overlooked sometimes is that the STAT operand can also customize your normal distribution of tolerances as well. As Sarah noted, the default is a distribution with a width of four standard deviations, but this can be adjusted with the STAT operand. The following is directly from our Help Files at 'The Tolerance Tab > Tolerancing Group > Tolerance Data Editor > Tolerance Control Operands > STAT: Define Statistics':

Just in case anyone wanted to know! :)

~ Angel

These are all good points! Personally, I found “a width of n standard deviations” confusing at first, so I thought I’d just add this graphic from the Help Files into the mix. In this normal distribution, the standard deviation is defined as half of the range of the tolerance, divided by n. This means that the larger the value of n, the more likely the value chosen will be close to the mean, while a smaller n will approach a shape like a uniform distribution.