Total Tolerance of an Electonic Circuit

I am trying to evaluate a circuit with a lot of parts given their associated tolerances and I'm really struggling.

For the electronic parts with 2% tolerance I am guessing the values are to specification by about 5 $\sigma$ spread, for 1% perhaps 4 $\sigma$ and 0.05% parts perhaps 3 $\sigma$.

What can I do to to arrive at a unified value representing 3 $\sigma$ spread overall? Would I adjust the tolerance value according to some function and re-run the max-min calculation or do I need to evaluate each item separately with the other parts set to nominal values (0% tolerance)?

• My own approach is to assume (incorrectly, but probably good enough) that tolerances are worst case values, and make sure that my design will function if worst cases stack up. I can't put an sd on such an approach. – Scott Seidman Mar 25 '16 at 14:40

These assumptions on standard deviation are only true if the spread of values is purely statistical. In many real-world cases, distribution of actual values is far from gaussian. Several reasons for that:

• In many manufacturing processes the difference between two components produced in the same run is rather low, but the run-to-run spread is large. Thus, components from the same reel will have a small spread, but identical components bought a week later might be at the other edge of the allowed values.

• Especially more expensive items might be tested one-by-one and every one that doesn't meet the specification is discarded (or sold in a lower grade bin).

• This leads to the fact that in lower grade bins it is unlikely to find a component with a precise value (as this would sell in the higher grade bin) but rather many that are off from the nominal value but still in the specs.

I have no idea how you derive at the relation between tolerance and s.d. (significant digits?? sigma deviation??).

If you want to know the possible values of a certain quantity in your circuit you'll have to calculate it twice, once with all tolerances 'working towards' the maximum value, and once in the opposite direction. If the circuit is linear one calculation might be sufficient. For funny circuits it might be non-obvious which component values (or combinations of values!) work towards the highest and lowets values of your quantity.

If you are aiming for reliability intervals, remember that you can't assume that component values follow a normal distribution. A uniform (rectangle) distribution might a better bet, or even a rectangle with the middle part cut away because those were sold as higher-precision components.