All components have specification tolerances and ranges. Some examples are:-

Resistor 1%

Electrolytic capacitor 20%

Zener diode breakdown voltage 5%

Clearly it kinda indicates that the specification may vary by x% from that stated. So a 5%, 24V Zener diode may change it's breakdown voltage by 1.2V. But this is a statistical measure. So are they saying that you will never find one of these diodes with a 1.3V difference for as long as you live? Or might one in ten exceed the 5% range. It must be (somewhat normally) distributed around a mean, and the manufacturer must have measured several to arrive at a 5% figure. Similarly, is there a percentage chance that a 1% resistor may actually be out by 1.5%?

If I were manufacturing precision thingies with thousands of resistors, I would need to know the statistics to a greater degree. There must be a fair few resistors in a 12 core Xeon processor, so statistical considerations would be important. I would have thought that perhaps a mean and standard deviation might be more appropriate in a data sheet of a part intended for large scale production.

The only examples of a statistical description I've seen is like this one for a LT1007 op amp:-


Is this what Linear Technology would call 3nV/root(Hz)?

My personal interest is that I'm trying to match some Zener diodes by the greatest degree reasonable. Should I buy a 1000, or just measure the pack of 5 they came in? Others do this with valves and transistors so I'm not crazy.

  • \$\begingroup\$ "There must be a fair few resistors in a 12 core Xeon processor" Resistors on a processor are usually something like poly layer snaking around, if they are a resistor at all (most are active resistors). But this is completely different from monolithic resistors. \$\endgroup\$ – jbord39 Sep 28 '16 at 23:04
  • \$\begingroup\$ @jbord39 And are they 100.0% identical electrically? \$\endgroup\$ – Paul Uszak Sep 28 '16 at 23:06
  • \$\begingroup\$ No, not at all. They would use monte carlo analysis to determine the spread and adjust the layout as needed to achieve the desired tolerance. Depending on the application this ranges from around 0.5-5 sigma. It depends on the component and cost. if very good matching is required, they fabricate the components symmetrically and optimize the layout so that any variations apply as evenly as possible to both devices, so that they are still balanced (albeit not exactly the expected value). \$\endgroup\$ – jbord39 Sep 28 '16 at 23:09

Components are usually tested for datasheet specifications, and parts outside the specification are rejected. So the distribution may be a truncated normal distribution, or a normal distribution well within the specified limits, depending on the manufacturing process.

So you will never see a 1% resistor with a value outside the 1% specification.

Sometimes parts are binned, with the 1% resistors going into the 1% bin, and ones outside that going into (e.g.) the 5% bin. So you wouldn't see any 5% parts that were within 1%. This is less common for many parts mainly because manufacturing tolerances are much better than they used to be, so (for example) the 1% line often runs well within 1% without any outliers. (Or as a minimum the yield is so high that it's not worth binning.)

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  • \$\begingroup\$ Really? Every single component, even dumb ones like resistors are tested individually? That doesn't seem to chime with total quality management principles and continuous improvement techniques where you'd only sample test... \$\endgroup\$ – Paul Uszak Sep 28 '16 at 23:11
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    \$\begingroup\$ @PaulUszak I suppose that would depend a bit on customer expectations and likelihood of returns. I was involved in binning LEDs -- even when cut from the same wafer. Every single LED was tested and binned. Those are dumb parts, too. The customers (product development) expected them to "appear" uniform when used in an instrument together. So there really was no choice. \$\endgroup\$ – jonk Sep 28 '16 at 23:14
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    \$\begingroup\$ I haven't worked for a passive component manufacturer, but I have worked for 3 semiconductor manufacturers. In each case if there was a max or min spec on the data sheet (even for a sub 1 cent diode) it was 100% tested by ATE before shipping, with rare exceptions that were "guaranteed by design" in which case the comment above by @ThePhoton applied. At my current company we try to do 100% testing regardless of how tight the distribution is within the limits. Of course "typical" specs come from characterization and aren't guaranteed (or very useful). \$\endgroup\$ – John D Sep 29 '16 at 0:10
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    \$\begingroup\$ You're technically correct, a true normal distribution doesn't have bounds. However, in a manufacturing process you don't necessarily have a true normal distribution. What I meant was that if after you have measured or simulated over process (and voltage/temperature) to the point (like @ThePhoton said) where only parts that are 6-sigma out would fail, you might call the spec guaranteed by design. My current employer does not, and we test 100% with very few exceptions. \$\endgroup\$ – John D Sep 29 '16 at 0:25
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    \$\begingroup\$ @ThePhoton Definitely correct, we call them "test escapes". The test limits are set such that the inaccuracies and repeatability of the tester are taken into account (and the test results are not on a normal distribution, there is a definite accuracy band just like your multimeter, etc.) And also right about SPC, when a test escape happens we do an 8d report to find the root cause and implement a corrective action so that it can't happen in the future. \$\endgroup\$ – John D Sep 29 '16 at 1:24

All things are imperfect and an "ideal" is defined. e.g., an ideal resistor behaves as R = V/I.

In the manufacturing process "quality control" is essentially figuring out how to get closer to the ideal. It is a recursive feedback processes. Create->Measure->Modify->Create. This is called "learning".

The measurement process is simple. Take your device, measure it's properties and compare them to what you want(the ideal).

Of course, what really is the ideal? That is defined differently by different people. For consumer, it is different than military, etc.

Suppose your ideal includes a lifespan of, say, 1000 years. You want the device to only vary by 1% over. Well, you can measure that. If it is a variation of 1% over 1000 years, then that is 1/100% over 10 years. (We assume linearity, which we can approximately measure).

Suppose we want 1% over a temperature range of 100C. Again, same thing goes on. We set up a mock use case and do measurements.

The measurements are what tells us the behavior of our devices. After all, all devices are the same but with just radically different properties. An inductor is a resistor is a capacitor but all just have different behaviors. A capacitor is a very bad resistor, and we could, just throw all such devices away. But a capacitor has a very good uses. Any resistor that behaves like a capacitor is a capacitor. Seems nonsensical but it is how we come up with stuff. Everything is useful, it is just a matter of finding the application for it.

So, which statistics and measurement we can get a profile about how a device behaves in the "real world". We then modify our manufacturing processes to get the desired quality we need to make it affordable for our target audience.

Now, as far as the statistics is concerned, yes, there is a chance a single device may deviate quite substantially. But if the quality control is tightly regulated, one can make, say, 1 in 10 billion not have any significant differences.

Statistics only gives you an estimation. You have confidence intervals, say like 99.999% of all the resistors created by this process will be within 1%. A few will be a little outside 1% and even fewer will be further out... basically depending on the distribution, which is usually bell curved.

That could seem like a big deal, considering trillions of transistors are used in a cpu!

BUT don't forget that the user of the components also has to make the circuit robust. Almost all circuits are not so critical that a small 0.001% deviation will create a failure. If they did, most things will fail.

Most circuits are rather robust, even with significant deviations. Maybe your cpu runs a little hotter or slower or has a 0.000001% more likelihood to crash than mine, but you do not notice this, nor do I.

The people that design the components are usually smart enough to not create devices or circuits that have a high likelihood of failure. Why? Because they are responsible for the issues. Intel will rather improve their quality control rather than have to replace millions of cpu's.

This is also why most datasheets give you some idea about the quality of component and also expect you to stay within reason. Resistors, capacitors, and inductors are expected to work within reasonable usage. If you use it in an application that might cause a failure then it is probably your fault if it fails.

Life is not so cut an dry and neither is electronics or anything else. Variations happen and are all over the place. The average person generally doesn't notice simply because the variations are "within" spec. They only notice when something goes wrong, of course, but those are the extreme cases.

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