discrete component testing

[cncjerry]

Can someone please point me at a document or site that would explain the statistical methodology for testing discrete components like resistors, for example?

Little background using resistors for simplicity:

I assume manufacturers use statistical sampling to determine the quality of a batch of resistors.  To simplify it further, ignore other parameters like TC, PPM, etc.  I was thinking about it lately and assume they don't test each resistor coming off a line as even with very high quality equipment the settling time alone would make it impractical.  So when a batch of resistors is declared to be for instance, 1%, 5%, etc, they use (I assume) a statistical algorithm and maybe only test x (10, 100) out of y (1000, 10,000 or whatever).  The x and y is what I am interested in mostly.  I was thinking they must test a certain number and determine, high, low, median and as with most components probably end up with a normal distribution curve.

This is what I am thinking: Just for grins, say you purchase qty 500, 1K, 1% resistors and take the time to measure each one.  The distribution should be a normal curve with the min at > 99% and the max at < 101%.  (probably made my first mistake right there).  Using 1% resistors and testing a given quantity one would think that the resistors near to the median resistor (can't remember the statistical term for these) should be a lower percentage closer to the ideal 1k than the outlying few.  At this point people will point out that your median could be anywhere between 99% and 101% but if you use the proper sampling method, that should not be the case.  If your median ended up at say 998 ohms, than you would have a batch of 1%, 998 ohm resistors, no?

Here's where I am going:  You drop your HP3458A 8.5 digit meter and don't have your trusted standard resistors.  Your meter is completely out of whack, off by 50% or more but from a relative perspective it is fine.  You start measuring your 500 (or whatever the number is) resistors keeping track of the values.  You know they are .005% resistors and by measuring you get values from 499.975 ohms to 500.025 ohms keeping track of every one.  You then pick out the median (the one in the middle, not the mean (average)).  This resistor has the highest propensity (assuming you have a large enough sample) to be closer to 1k than all the others.

Here's the question:  Given a sample size of x, .005% resistors and a normal distribution curve,  how closely would your meter be calibrated if you use this resistor as a standard?  Statistically, it should be closer than .005%, no?

On another somewhat related topic, I found it interesting while transfer calibrating one of my HP 3456a meters against one of my 3457a meters, that using a high quality metal film resistor for a value standard I don't have doesn't work at all.  I can watch the meter climb from what I assume is the constant current from the 3457a heating it up.  My other standards are pretty solid.

I don't mean to accomplish anything like this, just curious.  I was sorting a batch of SM resistors for a VNA, just needed two that matched closely which was more important than the absolute value, and started wondering about it.

Thanks
   

[Paul Moir]

I think you're assuming you'll get a standard distribution curve, aren't you?  But that may not be true in real life.

Say I'm a resistor manufacturer who has a problem.  I can produce fresh off the grill +-.25% resistors all day long but I know that some of them will drop by 1% for like no reason after 2 years.  So what do I do but shoot for +.5%,  and sell them as 1% resistors.  I'll hit +.75 to +.25 and after two years the bad ones will drop at most to at worst -.75%.  I can sleep at night, but it'll mess up your calibration.

Going to real life, it seems to me that with electrolytic capacitors, as they age their capacitance goes up.  New capacitors from trusted manufacturers seem to be at the low end of their capacitance tolerance spec.  If this is true, then using the average new electrolytic capacitor for calibration will set you low.

PS - I assume they use AQL rather than measure each resistor, but I'm not in the business.

[Seekonk]

They are pretty good at controlling film capacitors.  Saving a little foil really adds up.  If a cap is  10%, they will all come in at -9% if it is a high volume cap.

[matseng]

Dave has already done that - analyzing measured batches of resistors to see if they spread out on a bell-curve nor not.  (Spoiler alert - They are not...)

Have a look at Eevblog #215 & #216

- Gaussian Resistor
- Gaussian Resistor Redux

[cncjerry]

thx for the links.  I watched both videos and the distribution isn't that far off given the sample size.  You'll note the majority in that batch fell around 0% deviation.  The conclusion I can make is that yes, calibration accuracy would improve by some factor by using the median of a batch in his larger sample of like 500.

It doesn't look like you can avoid cost by going that route (e.g. purchasing a large batch of lower tolerance) and the hassle of finding the median is worth the $100 for a quality standard for home use.

I was hoping someone from the industry would chime in on their process.

Thanks again.

[Evil Lurker]

I do know that some manufacturers 100% test each and every monolithic cap that rolls off the production line at the very minimum to a voltage well over their rated working voltage as any tiny defect in their construction is enough to totally fubar one.   

In addition with some resistors it is in theory possible to test their resistance during construction itself. There are some metal film capacitors or carbon on glass where the resistance is determined by cutting a spiral around the nonconducting core material of the resistor. The more turns of the spiral, the longer the effective track, and more resistance the component has.