I worked for Admiral Television back in the 70's. I heard a story from one of one of the engineers. He was doing some kind of a hobby job after hours, and needed some 'high precision' resistors--5%. The standard at the time for cheap resistors was 20% carbon comp. So he got a batch of them to pick out a few that were 5%. None were. In fact, the distribution was bimodal. Either 10-20% high, or 10-20% low. It seems their resistor process made 20% resistors, and they selected 5 and 10 from that, so _none_ of them were in the 5 or 10% limits. This had an effect on the design process later. We had a CAD program that did monte carlo analysis on circuit designs, but predictions were poor when we used standard distributions. We had to modify the code to use the bimodal distribution to get realistic results.

That's a fun little statistical analysis. It would be interesting to plot a histogram of the batch. You have enough samples to make a reasonable plot. You could also run it through R and create a QQ Plot to verify if the samples follow a normal distribution or something else.

Part of that drift is the grinding wheel used to remove material to get to the value is wearing, they might not measure each resistor during grind, as that means slowing down the machine to the multimeter speed, but instead ground every 10000 to that speed, and then the grinder is going to repeat the grind 10000 times, as the coating would likely be very even on the batch once it is running. Thus the rising trend, and the outlier was the one where the grinder either did a compensation for wheel wear, or one that was ground wrong, possibly due to a bit of old material hitting the wheel and lifting it up. Of course the resistors on the reel are not actually sequential, they all are close to sequential, but are generally ground, then washed, dried and then coated, then get measured again to get the actual value, and then are sorted into 1%, 2% and 5% bins, with any that are outside the 10% value getting discarded as waste. Your 1% get the blue coat, same as the 2%, but the rest get the pale coat, and then get banded, and bandoliered. So there will be a hole around 3%, from the sorting, and thus 5% resistors are guaranteed never to be the marked value, but always a little off.

I've read about "lot variation" many times in my life, but to see real numbers drives it home - a picture is worth 1000 words ... and of course, the same effect would apply when comparing one batch to the next. Thanks for helping us clearly realize what is obvious ... even if it first has to be said (and shown) to be obvious!

You are seeing this effect due to binning. If the factory finds one that is 1K perfect (minding the tolerance) they will bin that one under a new (higher priced) series. There was a paper about it, explaining the process but I can't find it now.

You, sir, are obsessed with LEDs. Even when you try hard, you still call a resistor and LED 😅😊👍🏻🤝🏻🇳🇱

For some reason I just knew you were going to say "and here's my 10k resistors". You caught me with a curve ball, 1k resistors this time.

A reel of 5000 1K resistors! They really are your favorite!

I've always wanted to build a machine that could bin a whole reel of parts with a temperature sensor to make sure all of the readings are consistent.

Seems like an automation exercise waiting to happen. Need a take-up reel, stepper motor, some 3D printing, and your HPIB Python code. Could measure all 5000 parts pretty quickly. (not counting the weeks worth of building and programming 🙂 ).

Not to mention binning! You may end up with a lot of 5% that does not contain any 1% and the distribution curve can have a "notch" in it at the actual target!

That is fascinating.

Funny youake this video now. I've just done something similar with Vbe on a load of 2N3904 NPN transistors and ended up with an almost perfect normal distribution of values. Also, it does look like that graph begins to curve exponentially towards each end. Maybe lowering the resolution to the nearest ohm (+-0.1%) and plotting the distribution would help show that better.

I’ve done this with my B&K LCR meter. It would be good to compute the median value as well. If you wanted to compare variation around a mean, you could compute a one-sample t-test against the reputed value (i.e., 1K here) with a “large” sample. Your 100 units meet that criterion, for sure. This would provide an explicit QC test against the reputed value they present first sale. Nice video!

One of the harder classes I took in EE was "measurement theory". No actual measurements were done there, no lab exercises, only theory. We learned about value distributions, relative error calculations, 3-5-5 wire meausrements, internal workings of many measurement devices, measuring voltages, currents, impedance, time, frequency, workings of AD/DA converters, etc. The exams were not easy at all, but were nothing compared to the lab exercises later (that we hated mostly because the incoherent design.

Man, that reminds me on the swaps down here in SoCal with all the aerospace runoff. The real deal was these and the surplus gear like Tek scopes, HP stuff, etc. Got two HP 3400A, and dig gens for dirt.

Interesting thought(s) in my mind… First I pondered how much of the settling of the measurement indeed could be thermal. The 3458 meter has quite some amount of filtering and it sees Open Circuit (= full scale) between each measurement. The settling of the results downwards is likely to be due the meter. HOWEVER, limiting the results to just 2 decimal places mitigates some of the least digits drift on the statistics. So we can basically ignore the drift for the final conclusion. Then some old memory. I once designed a Unijunction Transistor and SCR based controller board. I had a choice of low cost 2N2646 or high price 2N2647. We purchased a few of the latter ones and 100 or 200 of the 2N2646 version parts. The more expensive ones were nicely at the specification window. The 2N2646 on the other hand seemed to miss entirely the nominal values or anything near the nominal. I put together a test setup and measured 100 (or 200?) units with our then new HP5245 counter that had a digital volt meter plug-in. Then I plotted the “trip” voltage - called intrinsic ratio - spread on graph paper. Very clear bimodal distribution appeared. We complained to the vendor, who contacted the manufacturer - who on their part denied any chance of having picked the “better ones” out and selling the bimodal remainders to us. My guess is the communication took place only between sales men……

The settling time may be a problem with the autozero function of the keithley. At least, for my keithley 2790, after disabling autozero it settles much faster (SYST:AZERO:STATE OFF).

very interesting, thanks for the effort!

If I'm making voltage divider I always measure them, even the 1%ers. Generally I'm not that fussy, but when I need a good degree of accuracy out comes a 22000 count DMM

It's funny, just yesterday I was measuring a load of resistors (although not quite as many as 5000) trying to find that "one golden one"... and then this video pops up in my suggestions.

Keep in mind all components have tolerances and the interaction of the components can greatly affect the desired output. Some of the tool that are used are Six Sigma design, Monte Carlo circuit simulation and Cpk studies all help to design and maintain products. Incorrect component and design selection can have devastating consequences. I once worked for a company that selected a power supply topology where the switching FETs at the time "met" spec but did not always preform causing the product to not meet it's intended MTBF. It took more than 5 years for FET technology to improve before preforming the application they were being used. Needless to say it was an expensive design choice.

I feel like we live in a golden age of vastly more reliable parts that meet spec, are far more often near nominal spec, and are rarely DOA. Back when I was a kid, I had to test every new part, because occasionally I’d find one that was out-of-spec or DOA.

"Lies, damned lies and statistics!" ;-) 73 - Dino KLØS

The self heating is interesting to see. Curious what the TCR is.

Good job demonstrating variation overall. One comment on your graphical analysis. Performing a sort from lowest to highest does not reveal anything. Regardless of the tolerance, 5% in this case, you will always have the same looking graph because there will be lowest and highest values. If a manufacturer is fixated on quality and manages to produce a high amount of precisely 1K resistors, then your graph would be flat in the middle, but the cost of those resistors would be quite high. I think the resistor measurements in order on the tape and plotted would be more interesting because you might not see randomness all the time but perhaps drift moving upwards or downwards or perhaps oscillation, highs then lows repeating, indicating a somewhat uncontrolled process. I love exploring and teaching variation, and the boring details of it, as a 6s MBB.

Thanks 👍

It's interesting that the variation is uniform and does not follow a 'normal distribution', so I guess the QC of the manufacturing process is good? Is what you call 'deviation the Standard Deviation, or the Coefficient of Variation?

My statistics prof friend wants to know if the dataset is available so she can run an eCDF on it...

Don't forget that those measurements must be done at a specific temperature, because temperature affects resistance. This is why for example those Tesla superchargers didn't work in the -20F temperatures in Chicago. The components drifted too far out of spec.

No bell curve...

Do I wanna know why you bought five thousand 1k resistors?🤔

Are the lot 2% or 5%? Red or Gold?

That’s a crapload of resistors.

Why did you bought carbon instead of metal film resistors. Also you should have purchased 1% tolerance instead of 5%.

macbook is amazing but also expensive Sir