Component Tolerance Probability

Question

This is more of a manufacturing question than anything else. What is the probability distribution of component tolerances?

For example, let's say I ordered a 100 ohm, 5% resistor, and I order 100 parts. Are the odds of getting a 95 ohm resistor the same as getting a 100 ohm resistor (uniform distribution), or is it a normal distribution with a 95 ohm resistor being a certain standard deviation away?

The example is not tied to reality. It's not like 95 ohms would be unacceptable and I should move to a smaller tolerance or anything like that.

Answer 1

In ancient times, with carbon composition resistors, there was generally a reasonable spread of values - for "precision" circuits you might get instructions like "pick through your 100 ohm resistors to find one of 95 ohm" (at that time 10% resistors were common, and 20% might be available).

Now, with carbon or metal film resistors, the resistors are trimmed to value after manufacture, so even 5% resistors are likely to be within 1% of the marked value.

I once measured 50 or so Philips metal and carbon film 5% resistors and found the spread in values to be under 1%.

Answer 2

The problem is, nobody knows. Each manufacturer may work differently.

You might ask a specific manufacturer about a specific series of resistors how they are binned, but why would they reveal that information, as you can buy existing parts with whatever precision you need and they can guarantee it.

You might get a gaussian distribution that is centered at 100 ohms. Or an uniform distribution from 95 to 105 ohms.

Or, depending on the manufacturer, they might have already removed all resistors that are 1% accurate and 2% accurate and sold them as 1% and 2% resistors, so you might be left with only resistors that are at least 2% above or 2% below 100 ohms, but still within 5% of 100 ohms. Or maybe removed only some resistors because it might not make much sense to bin them all into 1%, 2% and 5% categories. Or maybe they are binned anyway, and they sell whatever people need and thus much of the 1% and 2% resistors are sold cheaper along with the 5% resistors.

Answer 3

Most modern resistors are trimmed to value, and roughly speaking and in my experience, they are typically within about 1/3 of their tolerance. There may be a bias (the average may lie on one side of nominal) due to the way their equipment is set up and calibrated.

The reason I investigated this at all was to decide whether to use a more sophisticated adjustment method for interacting analog adjustments. Since the typical parts were fairly close it made sense add parts in order to null out the interaction typically (to within a fraction of the resistor worst-case tolerance) in order to reduce the adjustment time in manufacturing. Made quite a difference, typically 1-2 iterations rather than 5 or so.

Answer 4

The only guarantee you have is that the value is within tolerance at 25C, and that there's a certain tempco. What exact value you get is not specified, and you can find normal distributions with standard deviation of about 10% the tolerance limit, multimodal distributions, or even values so close together that cheap multimeters fail to measure any difference between adjacent parts on the tape.

If you want to make any other assumptions in your design that do not depend on specifications given in the data sheet, you have to qualify the parts, and potentially do 100% incoming test or select parts. In other words, depending on the resistor value being anything in particular is a fool's errand. In any simulations, you'll want to use the nominal value as well as both endpoints of the tolerance range. If the circuit behavior is not monotonic with respect to the resistance value, you'll need to use more intermediate values.

Answer 5

I haven't seen a 5 % resistor that would be outside +- 5 % from the nominal or a datasheet stating that the tolerance would be something else than a "hard limit" acceptance criteria. But you are correct for some items 5 % mark might mean for example the 3 sigma point of normal distribution.

What shape the distribution is depends on the part and it is usually not revealed by the manufacturer, but one scenario is that they manufacture a batch aiming for 100 ohm, measure eatch one or a selected batch size and then divide them into 0.5 %, 1 % and 5 % bins. So buying a 5 % resistor would have a symmetric distribution of 1-5 % more or less from the nominal value, but "never" within 1 %.

For E96 etc series precision resistors it surely makes more sense to trim the values. But with 100 ohm resistors you might just pick the lucky ones that fall within 0.5 % or so and you'd be able to sell them all anyway.

Other scenario with 5 % resistors could be that they are not individually checked and trimmed, but in practice the process is stable enough to hit the mark if every 1000th resistor is within certain limit.

Answer 6

The distribution of a certain value of an element is sometimes quite a complex curve, especially if higher-accuracy elements are binned from the lower-accuracy production.

E.g. one may get a concave curve because the elements with better values are binned in the more expensive bin.

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The other interesting part of the distribution is that the elements are guaranteed within 10%, 5% or 1% of their nominal value when operated in some (quite wide) temperature interval.

There is some distribution of the temperature coefficients as well, so the distribution of the values may get different when elements are cooled or heated.

Answer 7

If you test enough resistors (millions) spread across different production batches, you'll end up with something close to a normal distribution centered around the nominal value. Resistors from the same batch are likely to have a fixed offset, i.e. the mean value will not be exactly 100 Ohm.

A 95 Ohm resistor is borderline faulty if you market it as a 100 Ohm +/- 5%. With modern quality standards something like a 5-sigma quality is common, which would mean that the chance of finding a resistor with a value of <95 Ohm or >105 Ohm is less than 1 in 3 million, and 68% of resistors will be within +/- 1 Ohm away from the nominal value.