interpolation in calibration what is your opinion on the subject?

[USMCPMEL]

So I more or less got into a fight with another tech at my lab over this the other day. He believes that it is not s sound method for performing a calibration. Opinions?

[silv3rstr3]

There are a couple mathematical theorems that deal with linear and non-linear maps.  I've been told in the past to extrapolate data on calibrations due to a lack of our standards capabilities.  But my personal opinion with past experiences is that the scale may be linear but the equipment can be damaged and not achieve its full scale capability.  Unless you test the span of the UUT how do you know for sure?

[USMCPMEL]

In my case I was checking a pressure chart recorder at the pressures that the customer wanted me to check it at and I was being argued with because they did not exactly match the points on the chart.

[silv3rstr3]

lol.  If they are that concerned with the accuracy between the lines there are data acquisition systems for pressure.  Only catch is that the customers gotta stop being cheap cuz you pay for what you get!

[OlDave]

I don't see any reason NOT to interpolate the reading for that item.

When I went through tech school at Lowry they actually taught you how to interpolate a reading. Of course that was back when everything you were testing had an analog meter on it, even the majority of your standards were analog. Of course they also taught you to tap the meter to eliminate hysteresis and to line your eyeball up with the reflection in the mirrored scale (or glass of the faceplate) to eliminate parallax. All lost arts.

I am pretty much telling my age with this post and I am guessing that USMCPMEL is pushing 60 also, and the person that was arguing is under 40. Just a guessin...

[silv3rstr3]

You are correct about my age but incorrect about what they teach in PMEL school still.  I am well aware parallax errors and familiar making proper readings on old school analog meters.  Just spit balling old timer but have you seen a mirrored scale on a paper chart recorder in your life?

[OlDave]

no, if the paper is that shiny the ink would probably smear.

[Hawaii596]

INTERPOLATION is inherent.  I would even say there is no such thing as NOT interpolating on many instruments.  That is what LINEARITY is about, I think.  No instrument gets 100% calibrated.  The proportion of calibrated points along a scale, etc., is a factor of what interpolations are considered reasonable to provide adequate confidence in the linearity of the meter (or what ever it is).  If you cal at 25%, 50%, 75% and 100% of a meter's range, the intervening points are all considered to have some degree of confidence that they will also implicitly also be in spec.  The same (for another example) goes with an RF Power Sensor.  You don't check every single frequency, just an adequate number of points to consider there to be adequate confidence that the interpolation done in the intervening frequencies willl yield "good" results. 

EXTRAPOLATION is a little different story.  For brevity, I won't really go there.  But INTERPOLATION between specified and tested points is absolutely considered part of the linearity of the instrument.  The question I think is how much distance is adequate or allowable between interpolation points.  Just my 2 cents.

[silv3rstr3]

I was reading some mathematic theory on it and there are a few different solutions they discuss with a whole lot formulas and I lost interest.  I don't know either how many test points are considered sufficient.  But earlier today I noticed something calibrating an attenuator.  If I go by the air force procedure and pick 6 evenly points across the frequency range it passes.  But for the hell of it I ran a THRU sweep and then swept the attenuator on a PSA doing 600 test points and it fails at points when I look at the data in a spreadsheet.  So I'm not sure what's the most legit way on that.

[Hawaii596]

I think that is the big question.  I remember a long time ago, I used to calibrate General Microwave brand 18 GHz RF Power Sensors with the Weinschel system.  There were some "holes" in various narrow frequency bands from high input power.  Setting the number of points to test at made the difference between pass or fail, as those "holes" would or would not have been caught.  But in something like an analogue DC volt meter, that isn't nearly as critical.  Each different equipment type will have its own characteristic inherencies; and interpolation related risk will vary.

Things like RF devices I think are one of the most critical to adequate number of points. 

But regarding the original post, I think it depends on what type instrument is involved as to how many points are needed.  But regardless, the interpolation will be there.  The question is what kind of spread between points will be acceptable for that instrument.

[CalLabSolutions]

I think this is a good read on the topic..
http://www.callabmag.com/?p=3107
Mike

[USMC kalibrater]

Hawaii is on the right track
There is interpolation (there are many ways to do this, spline, cubic spline, straight line best fit (mx+b) etc) which "fit" the unknown data between measured points into EXPECTED outputs based on a function that describes the known outputs of the known inputs.
It is not 100% reliable, as you have all seen and noted samples of holes and such.  To be fair though, the intent of interpolation is to "define" the infinite number of untested points across the range of the device.  Hence if you are providing interpolated data the safe bet is to ensure you are testing each point that is deemed critical for actual performance and rechecking interpolated points when they do not seem to fit the function.
Extrapolation is the forecasted continuation of a particular function.  In other words you check a device to less than 100% of its span interpolate the data for the points you could measure then extend that function beyond the limits you were able to test.
While extrapolation has some value it is easy to see where it can be misused.  Additionally, its use would automatically require a limitation be placed on the device being tested since the device could not have been tested to 100% of its range basically rendering the untested portion unusable to most customers anyhow.

Does this answer the original question?

[USMC kalibrater]

With respect to how many test points to take. 
This becomes of function of the size of the range being tested, the performance characteristics of the device within that particular range as well as some other considerations that may vary per device an application.
Each method of interpolation has its owns sets of rules for minimum amount of points required and when adding more data begins to have little effect on the outcome.
To get a better understanding of this I would just suggest you take a few statistics courses. 

[silv3rstr3]

You should just stick to meters and scopes....

[USMC kalibrater]

You should just stick to meters and scopes....