Statistical measurement of resistors

[BradC]

G'day all,

My Ultrohm Plus resistors landed last night.

Among the order I have a set of 15 10K resistors. These were measured pre-shipping and I received a sheet with the listed deviations from nominal with an uncertainty of <0.5PPM (thanks Edwin!) at time of measurement.

20 odd days later they land in my mailbox and I decided to measure them before they've had a chance to settle down get over their jetlag.

I used hp3457a (which is now 3 months out of cal) on the 30K range and 100NPLC, took 4 wire absolute measurements and recorded those in a spreadsheet along side the supplied pre-shipping deviations.

Because my meter is out of cal, and even when it's in cal the 30K ohm range 1yr rating is +/- ~55ppm, I decided to look at this from an angle that does not have any reliance on the absolute accuracy of the meter and just see how the relative numbers fall out.

I took the mean absolute value of the measurements and used that to calculate deviations from the mean across the family. I used the supplied deviations to calculate absolutes, and did the same thing. I didn't need to do that for the calculations, but having those values meant I could calculate a family mean for the pre-shipping values (which was 10.00000147K).

These resistors (as-measured pre-shipping) deviated -10.8ppm to +23.5ppm from nominal(10.0K) and -10.9 to 23.4 from family average. My local measurements deviated -12.2 to 23.8 from average (which I was pretty damn happy about given the kit I'm using). Measured family absolute mean was 9.999612K.

The calculated differences between my deviation values and the supplied values range from -2.9ppm to 3.6ppm with a std-dev of 2. From that I can see a pretty strong correlation between my measured values and the supplied values. Using the two means, I can now speculate that my meter is reading ~39ppm low (which is well within the 1yr spec and is right on the edge of the 90 day spec - and it's now ~90 days out of cal).

Now, I'm relying on 2 things. The short term stability of my meter, and the 20 day stability of a set of freshly minted (and therefore drifting) PWW resistors.

The 24 hour accuracy rating on the meter is 10PPM + 5 counts, so one can intimate that could be the worst case short term stability. The resistors are unknown, but given my calculated deviations are within a handful of PPM of the supplied measurements, that might indicate that my local measurements are not too wide of the mark.

This doesn't take into account any family-wide drift of the resistors, but it does indicate there are no real outliers and everything calculates out quite nicely given the measured deviations are under a quarter of the potential local error sources.

These are 100PPM resistors, and the max deviation from 10.0K was 23.5ppm with a std-dev of 10 at time of shipping.

As this was only an exercise in validating assumptions and I don't plan to do anything with these figures I haven't calculated an error budget, didn't do anything to minimise the error sources and haven't bothered to calculate any uncertainties. What I did do was validate some assumptions I had about my meter and measurement techniques.

I plan on subjecting these resistors to some accelerated lifetime ageing and keep tabs on how they are moving relative to each other prior to putting them into the devices I bought them for, so there might be more to follow in the next couple of months.