For the sake of this question (as an example only) lets consider MLCC X7R ceramic capacitor. Such a component among others is characterized by a number of tolerances. Temperature dependeant tolerance, DC bias voltage tolerance or aging tolerance as a few of them might be listed. Ommitting the problem of determining tolerances themselves (assuming knowledge of particular tolerances values), how to calculate total tolerance of a capacitor?

Is it just a sum of all tolerances or it is more complicated (e.g. there exists some sort of tolerance "propagation")?

## Best Answer

For a first order worst case analysis (WCA), you can assume that all tolerances are summed (stacked). The real complication occurs when you have multiple components. Since it often isn't obvious if positive or negative tolerance is worst case for each component, 10 components would require 1024 different analyses. Some automated simulations can be setup to calculate all possibilities. If absolute worst case doesn't pass, and redesigning is expensive, there are other techniques that assume that all parts won't have worst case errors at the same time. RSS (Root Sum Square) and Monte Carlo are 2 methods. Certainly for errors caused by temperature, parts on the same PWB will have similar temperatures, so it is unfair to assume that all will have worst case errors at the same time.

https://pdnotebook.com/statistical-tolerance-analysis-basics-root-sum-square-rss-632f2eb274ba