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Uncertainty of staging a short line scale standard on longer measuring machine?


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I have a measuring machine that measures up to 1000mm in length, but my traceable standard is only 400mm long. When I calibrate I align the standard parallel , start at the left side and measure every 10mm to check for accuracy deviations. I then move the scale to the right, overlapping approx. 20mm, align it parallel and measure from the left end of the scale (every 10mm) to the end at 400mm. Then again , covering the full 1000mm of measurement range.

My question is; how do I include the multiple use of this scale into my uncertainty calculation.

I think I need to include the following in my uncert calc. for each range; (in addition to repeatability, temperature effects, etc.)
What am I forgetting about (or don't know!) about staging a line scale standard like this?

0-400 mm
uncert of std.

400-780 mm
2x uncert of std
max error found in 0-400 mm range

780-1000 mm
3x uncert of std.
max error found in 0-400 mm range
measurement uncertainty for measuring error in 0-400 mm
max error found in 400-780 mm range
measurement uncertainty for measuring error in 400-780 mm

Thanks to all!
If I am picturing this correctly, every time you move your scale you start with a new reference on your measuring machine.
If you do that you are only checking linearity for a 400 mm span, not for the full 1000 mm range.
Since each 400 mm segment is measured independently you would only be using the uncertainty of the standard, not multiples of it.
But you will not be making a 1000 mm linearity measurement.


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Yes, I move the scale each time, but the starting point of each move is overlapping the previously measured zone. So, the accuracy for range 2 and range 3 are dependent on the uncertainty and any bias seen in all previous ranges. Does accounting for the previous bias then get me to the full 1000 mm? If not why not?
What you have here is a very conservative estimation of the 1000 mm uncertainty.
Simple algebraic addition of the contributors will give you the largest uncertainty value. If you can live with the larger uncertainty then you are fine.
If you need to reduce the uncertainty then you will need to take steps to determine any correlations that can be combined to reduce the total uncertainty.

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