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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")?

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  • \$\begingroup\$ I suspect the characteristic tolerances are not just summed up because those variables all fall into some physics equation somewhere, and the individual error of variables in an equation are not just summed together. When you calculate the total error of such an equation, you have to handle each variable differently depending on where it appears in the equation ( with an addition, multiplication, division, square root, exponent, etc). There are general rules you can look up but you would need that capacitor equation. Error Propagation: lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm \$\endgroup\$ – DKNguyen Apr 25 '19 at 22:19
  • \$\begingroup\$ @Obcy - this can get a little tricky... if it's something deterministic, like capacitance change over DC bias, for instance, then simply adding is the way to go. If it's something intrinsically random, like part-to-part capacitance variation, then it makes more sense to add the squares of the standard deviations to get the total standard deviation squared. \$\endgroup\$ – joribama Apr 26 '19 at 0:47
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    \$\begingroup\$ Depends on WHO SUFFERS that 0.003% of the time when all the tolerances stack up? Is this a TOY that ceases working at cold temperatures and old-discharged battery? Or is this a bit-clock-tracking phase-lock-loop, and the loop filter cap changes and the JITTER soars and the PACKET BIT ERRORS increase from 1 part per Trillion to 1part per 100/ \$\endgroup\$ – analogsystemsrf Apr 26 '19 at 4:40
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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

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MLCC and for example the classification X7R is just a classification not anything more, it's not a material group or determined structure. There for the properties varies between X7R capacitor from manufacture 1 and 2 and different models. It just says that this MLCC full files the X7R classification.

Therefor the attributes depending on temperature and voltage is different, between different models.

The easiest way to determine the total tolerance of operation for the chooses capacitor would therefor in my opinion be to go to the specific manufacturer that hopefully has enough data publicly available so you can take out the tolerances for the operations of the capacitor of your use and then the ageing deviation from there.

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I don't know that there is any such thing as "total tolerance" of a capacitor. Capacitors possess a capacitance tolerance around the nominal value but temperature coefficients, DC bias and ageing are distributions (not tolerances) that cannot be summed.

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