Maximum Typical and minimum into datasheets. What is the distribution?

Question

What is the probability of having a component with the minimum and maximum specified value into the datasheet ?

I suppose this follow a normal law and the typical value is the mean :

Have a nice day !

Answer 1

As you can see beautifully from your figure, it's the integral over your probability density function of the parameter you're considering.

Your figure shows something that looks quite a bit like a normal distribution. So, the cumulative density function \$\Phi(x)\$ of your normalized parameter would answer your question.

Generally, very few things in life are actually normally distributed (it's just that it's often a good approximation, if the extreme values that don't make physical sense are sufficiently rare). So, you'll need to study what the distribution of the parameter you care about is. Unless something or someone specifically says what the distribution is, you can't assume anything, and you can't answer your question. It's as simple as that!

Answer 2

One important thing to add is that if you have a 1% resistor, it is not going to be normally distributed around for example, 100ohm.

In fact, you are almost guaranteed that it will not be 100.0 ohm as those are often binned out and sold as a higher tolerance.

It it not as simple as that though; supply/demand might persuade factories to supply 0,1% resistors into the 1% resistor supply chain, etc.

So to answer your question; You don't know the distribution, and you should always assume the worst.

Answer 3

Speaking as an application engineer with 20+ years at an analog semiconductor manufacturer...

What is the probability of having a component with the minimum and maximum specified value into the datasheet ?

For a shipping IC? Must be 100%. Even for a passive component it's 100%. (As a customer: if I buy a 1k 5% resistor that turns out to be 800 ohms, I'll demand a refund and never buy from that vendor again.) That's not to say that 100% of the manufactured products are good, just saying that the whole point of the Min/Max limits is that those limits are what defines 100% of the shippable product.

In your graph, you highlighted a normal distribution curve with test limits set at +/- 2 sigma (standard deviations), which gives a yield loss of about 5%. When you're manufacturing hundreds of thousands of parts, a yield loss of 5% is really a big problem. It's better for the vendor to just set the Min/Max limits to where 99.9..% parts meet the specification. Different manufacturers have different policies, but the industry norm is somewhere between +/- 3 sigma and +/- 6 sigma.

Min/Max limits are not arbitrarily selected. They are contract limits. If vendor ships product that provably does not meet published Min / Max specifications, vendor is liable for damages. Even without a formal lawsuit, this is a situation vendors try to avoid -- nobody wants to buy from an unreliable vendor.

Typical numbers are the only "not guaranteed" numbers in the datasheet, since typical values are measured on a representative sample of the initial production material.

Test and measurement equipment always has some level of measurement uncertainty, so there is a "guard band" between the published Min/Max values and the true test limits. We must not ship a bad part just because a piece of test equipment was near the edge of its calibration spec one day.

Yield loss is bad. Any product material that went through fabrication but did not pass final test, is waste that cannot be sold for profit. So manufacturers use Statistical Process Control to try to avoid manufacturing bad material in the first place.

Statistical Process Control (SPC) is generally about minding how accurately the fabrication is working, especially the mean and standard deviation trends. Every wafer includes multiple "test chip" coupons that are used to measure in detail the parameters of that particular wafer (strong N / weak P, oxide capacitance, sheet resistance, etc.). The precise measurement of the parameters of the most recently fabricated wafers are tracked as corrective feedback to keep the manufacturing process on-target. So there is an active effort to minimize the standard deviation of the manufactured product, to try to avoid manufacturing material that cannot be sold.

Even for a passive component like a resistor or capacitor, where the production testing is more straightforward, there will be emphasis on using Statistical Process Control to try to minimize production line variance. Since the cost of physically handling each component is going to be a significant part of the test cost for such a simple test, it's likely that a resistor manufacturer could test a representative sample of their end production units to confirm that the lot is within spec, instead of testing 100% of the units as we do with ICs.