[nomel]

> tolerance should actually go down since the errors help cancel each other out.

Complete nonsense. The tolerance doesn't go down, it's now +/- 2x, because component tolerance is the allowed variability, by definition, worst case, not some distribution you have to rely on luck for.

Why do they use allowed variability? Because determinism is the whole point of engineering, and no EE will rely on luck for their design to work or not. They'll understand that, during a production run, they will see the combinations of the worst case value, and they will make sure their design can tolerate it, regardless.

Statistically you're correct, but statistics don't come into play for individual devices, which need to work, or they cost more to debug than produce.

[tempestn]

The total tolerance is not +/- 2x, because the denominator of the calculation also increases. You can add as many 5% resistors in series as you want and the worst case tolerance will remain 5%. (Though the likely result will improve due to errors canceling.)

For example, say you're adding two 10k resistors in series to get 20k, and both are in fact 5% over, so 10,500 each. The sum is then 21000, which is 5% over 20k.

[jjmarr]

> Statistically you're correct,

The Central Limit Theorem (which says if we add a bunch of random numbers together they'll converge on a bell curve) only guarantees that you'll get a normal distribution. It doesn't say where the mean of the distribution will be.

Correct me if I'm wrong, but if your resistor factory has a constant skew making all the resistances higher than their nominal value, a bunch of 6.8K + 6.8K resistors will not on average approximate a 13.6K resistor. It will start converging on something much higher than that.

Tolerances don't guarantee any properties of the statistical distribution of parts. As others have said, oftentimes it can even be a bimodal distribution because of product binning; one production line can be made to make different tolerances of resistors. An exactly 6.8K resistor gets sold as 1% tolerance while a 7K gets sold as 5%.

[nomel]

> Tolerances don't guarantee any properties of the statistical distribution of parts.

That's incorrect. They, by definition, guarantee the maximum deviation from nominal. That is a property of the distribution. Zero "good" parts will be outside of the tolerance.

> It will start converging on something much higher than that.

Yes' and that's why tolerance is used, and manufacturer distributions are ignored. Nobody designs circuits around a distribution, which requires luck. You guarantee functionality by a tolerance, worst case, not a part distribution.

[Dylan16807]

> The Central Limit Theorem (which says if we add a bunch of random numbers together they'll converge on a bell curve) only guarantees that you'll get a normal distribution. It doesn't say where the mean of the distribution will be.

That's kind of overstating and understating the issue at the same time. If you have a skewed distribution you might not be able to use the central limit theorem at all.

[_dain_]

>If you have a skewed distribution you might not be able to use the central limit theorem at all.

The CLT only requires finite variance. Skew can be infinite and you still get convergence to normality ... eventually. Finite skew gives you 1/sqrt(N) convergence.

[Dylan16807]

If you're going to say "Complete nonsense." you shouldn't get the calculation wrong in your next sentence.

[nomel]

Very true, I was writing as absolute value, not % (magnitude is where my day job is). My point still stands: it is complete nonsense that tolerance goes down.

[Dylan16807]

They said it "should" go down, but that another comment saying the worst case is the same is "also correct".

I do not see any "complete nonsense" here. I suppose they should have used a different word from "tolerance" for the expected value, but that's pretty nitpicky!

[nomel]

I'm sorry, but it's incorrect, as stated. It's a false statement that has no relation to reality, with the context provided.

Staying the same, as a percentage, is not "going down". If you add two things with error together, the absolute tolerance adds. The relative tolerance (percentage) may stay the same, or even reduce if you mix in a better tolerance part, but, as stated, it's incorrect.

It's a common misunderstanding, and misapplication of statistics, as some of the other comments show. You can't use population statistics for low sample sizes with any meaning, which is why tolerance exists: the statistics are not useful, only the absolutes are, when selecting components in a deterministic application. In my career, I’ve seen this exact misunderstanding cause many millions of dollars in loss, in single production runs.

[Dylan16807]

It only stays the same if you have the worst luck.

> You can't use population statistics for low sample sizes with any meaning

Yes you can. I can say a die roll should not be 2, but at the same time I had better not depend on that. Or more practically, I can make plans that depend on a dry day as long as I properly consider the chance of rain.

> In my career, I’ve seen this exact misunderstanding cause many millions of dollars in loss, in single production runs.

Sounds like they calculated the probabilities incorrectly. Especially because more precise electrical components are cheap. Pretending probability doesn't exist is one way to avoid that mistake, but it's not more correct like you seem to think.

[nomel]

I've repeatedly used a certain words in what I wrote, since it has incredible meaning in the manufacturing and engineering world, which is the context we're seeking within. It's a word that determines the feasibility of a design in mass production, and a metric for if an engineer is competent or not: determinism. That is the goal of a good design.

> It only stays the same if you have the worst luck.

And, you will get that "worst luck" thousands of times in production, so you must accommodate it. Worst off, as others have said, the distributions are not normal. Most of the << 5% devices are removed from the population, and sold at a premium. There's a good chance your components will be close to +5% or -5%

> Yes you can. I can say a die roll should...

No you cannot. Not in the context we're discussing. If you make an intentional decision to rely on luck, you're intentionally deciding to burn some money by scrapping a certain percentage of your product. Which is why nobody makes that decision. It would be ridiculous because you know the worst case, so you can accommodate it in your design. You don't build something within the failure point (population statistics). You don't build something at the failure point (tolerance), you make the result of the tolerance negligible in your design.

> Sounds like they calculated the probabilities incorrectly.

Or, you could look at it as being a poorly engineered system that couldn't accommodate the components they selected, where changing the values of some same-priced periphery components would have eliminated it completed.

Relying on luck for a device to operate is almost never a compromise made. If that is a concern, then there's IQC or early testing to filter out those parts/modules, to make sure the final device is working with a known tolerance that the design was intentionally made around.

Your perspective is very foreign to the engineering/manufacturing world, where determinism is the goal, since non-determinism is so expensive.