4 ms·

> 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 com

by nomel 2y ago

> 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 2y ago
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.
deleted 2y ago
[deleted]
jjmarr 2y ago
> 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%.
- Dylan16807 2y ago
  > 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_ 2y ago
    >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.
- nomel 2y ago
  > 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 2y ago
If you're going to say "Complete nonsense." you shouldn't get the calculation wrong in your next sentence.
- nomel 2y ago
  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 2y ago
    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 2y ago
      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 2y ago
        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.

by nomel 2y ago

tempestn 2y ago

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.

deleted 2y ago

[deleted]

jjmarr 2y ago

> 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%.

Dylan16807 2y ago
> 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_ 2y ago
  >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.
nomel 2y ago
> 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 2y ago

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

nomel 2y ago
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 2y ago
  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 2y ago
    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 2y ago
      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.