I'm working on a problem where I'm aggregating centers of gravity and the inertia tensor for multiple elements – each element has it’s own mean and uncertainty.

What I’ve been doing is using a Monte Carlo method to generate aggregate statistics for various assembly levels and it works quite well, but is incredibly time consuming. When an element is changed, it necessitates rerunning the MonteCarlo for each assembly which includes it.

What I would like to do is implement a mathematical process which will allow me to update the current value for mean & standard deviation (SD) for that element and recalculate the aggregated values.

I’ve set up a spreadsheet to help me and what I have is the results of a MonteCarlo for an aggregated system. I then broke out several sub-components and retrieved their individual mean and SDs. So far I’ve been unsuccessful for the more complex properties. When I try to combine the SDs for the various elements, I can’t always figure out how to combine them to get something close to the total values from the MonteCarlo. Things such as the calculated total weight & SD come out easily since the total weight is just the sum of the elemental weights and the aggregate weight SD is just the RSS of the elemental SDs and my calculations using RSS SD are close enough to the aggregate SD from the MonteCarlo to call it a success. Where I hit a brick wall is trying to figure out the aggregate center of gravity SD – and I haven’t even attempted the inertia tensor yet. The equation for the aggregate CG is the (SUM of each element Weight * element CG) divided by the Total Weight. The mean is relatively easy to calculate, but for the life of me I can not get the SDs to equate. Any ideas???