Datasheets and probability (2025 Update)

I doubt very much that this hasever been spelled out, but a span of two standard deviations above and below the mean would include 95% of a randomly distributed variable, which would mean that one customer in twenty might complain about getting an out-of-spec component.

I haven't done it that often, which suggests that the industry has a adopted a three standard deviation span which would include 99.5% of a randomly distributed variable.

I have bitched about duff components enough to fit that, but most of them were fine at room temperature and only fell out of spec after they'd warmed up, or to be more precise, after they'd been stuck in a box in an enclosed rack and had had time to warm up a bit.

Parameters often have a gaussian distribution, You then can expect typ values as the center of the bell curve and min/max values are cut offs. With cut off at 1 sigma, about 35 % of the part would be out of tolerance, so cut off is at a higher sigma value, but manufacturers will not tell you ar what value it is.

In the case of some TI op-amps there are different grades for parameters like offset voltage. They mark the package of the higher spec versions before testing them and then throw away any that don't meet that higher spec. I was told this by a TI applications engineer. Apparently it is cheaper to throw away a few op-amps than to have branches in the production line to cope with different grades. This does suggest that most devices are much closer to the typical values than one might expect from the limiting values. For parameters that take a long time to test the typical values may be much better than the limit values. John

It is actually a rather deep and difficult to answer question in general because for some components the answer can be "it depends".

Semiconductors I generally take it to mean ~3 sigma either side of the mean but design with a bit of extra margin so the 0.5% tail doesn't cause trouble.

But for some components like resistors and capacitors that may be obtained in 10%, 5%, 2%, 1%, 0.1% tolerances you can find that the frequency distribution of the components in the wider tolerance bins consists of values that are almost *never* inside the narrower ones. IOW you are guaranteed at least 2% error in the 5% parts.

It is a bit better today than it used to be when they made batches and then selected from the process output. These days it is all a lot more reproducible and laser trimmed for precision parts.

Nah, all parts nowadays follow their spice models exactly.

Cheers

Phil “alias Dr Tung In Chic” Hobbs

I can imagine that production test and trim create a nonsymmetric distribution of some spec, and chop off the tails. And make a hole in the middle where premium parts have been binned away to sell at a higher price.

That doesn't seem to be the pattern nowadays. We buy ultra-cheap 1% resistors by the reel, and they are really 0.1% resistors. In a production line, with laser trimming, seems like all the resistors are right on.

There's no reason to buy surface-mount resistors that are spec'd worse than 1%. It's easier to design knowing all the various Rs in stock are better than 1%.

What we pay extra for is low tempco. And thoe are usually way better than their spec. Tempco is a nuisance to test for, at the PPM level.

Caps are not usually laser trimmed so are not as good. And they have plenty of other issues that work against accuracy.

Some part data sheets have histograms, which can hint at what you'll see in real life.

Abs max voltage ratings are especially interesting. Most silicon mosfets seem to zener reliably at 1.2x abs max drain voltage. Some have gate zeners, some don't. Some fets and RF parts are reliable at

RF schotttky detector diodes can have silly ratings like 2 volts max reverse. If you need their absurdly low drop and capacitance, you've got to test them and break the rules.

Another approach that I have heard of is to test all of the parts to the tightest limits (which it would have been designed to pass), and see which grade the customers order, only have to keep one pile of stock, and then mark them with whichever grade the customers ordered and paid for. I don't know whether this actually happens much. If it does, then it would not suit the manufacturer for customers to know.

For anything that has been trimmed (whether or not you know that it has been trimmed, especially digitally trimmed), assuming that parts will have a gaussian distribution in parameters is a mistake. If the part can auto-calibrate itself in use, even more so.

Also, batch-to-batch variation often exceeds part-to-part variation within a batch. They might not know the batch-to-batch variation at the time when they are writing the datasheet, as there is probably only one batch. They can run "skew lots" where they ask the fab to deliberately adjust the process parameters of some wafers to the upper and lower limits of some parameters, but this is never exhaustive, and so the limits in the datasheet will likely be sand-bagged (overly cautious) to some degree.

Also, specs that are not a major selling point would likely be chosen to be very easy to meet, because they really do not want to be throwing away parts because of a spec that nobody cares about. For example, if you buy a low-noise amplifier, you might reasonably expect that the noise figure specification (which involves a trade-off with power and/or chip area) is chosen such that they can meet it on say 99% of the untested parts, so some of them will be only just passing by a margin equal to the uncertainly of the tester calibration. On the other hand, if there is a CMOS logic enable pin of the low-noise amplifier which typically has a leakage of a couple of femtoamps, it might be specced with a maximum leakage of 10 microamps, just because it would be stupid to throw out one of these amplifiers if the package was slightly dirty and leaked a picoamp instead of a femtoamp, and unreasonably expensive to configure the tester to be able to tell the difference.

A guy at EEVblog forum has done a lot of measurements on resistors:

Yes. Thanks, Klaus, I watched that some months ago.

And thanks to everyone for your comments. Cheers,

John S