# Defining precision in a mechanical movement

I have a device which rotates on a stepper motor through a belt and pulley system. I would like to know both the positional accuracy and precision of this movement.

It is of my opinion that this should be determined by taking a large number of measurements to random angles to give a bell curve then using the offset of the mean from 0 error to define the positional accuracy and defining the precision of the movement as 3 sigma.

The rest of the office are of the opinion that accuracy is the range of errors when rotating to random points and precision is the range of errors when rotating to a determined point, away to a random point, then back to the determined point.

Is this just me applying my past experience in manufacturing to a problem that doesnt require it or is there merit in my method and everyone else is just specifying range, which is not what they really want?

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Does this help with figuring out what they are? – Glen_b Mar 13 '14 at 10:17
Yes, I did come across that but the lack of general concensus caused me to doubt wether or not I was just overthinking the situation. – Will.W Mar 13 '14 at 10:53
Note that though "precision" vs "accuracy" is just a terminological matter, its important to think about what the range of a finite sample is supposed to be estimating. – Scortchi Mar 13 '14 at 11:02
And also that the errors after "rotating to a determined point, away to a random point, then back to the determined point", whatever you call them, are different measurements, which your colleagues may have some good motivation for proposing. – Scortchi Mar 13 '14 at 11:31

People use the two terms more or less interchangeably in daily life, which is why this can be confusing. In fact, your office has it exactly backwards. Precision doesn't require an external reference, but accuracy does.

Let's start by thinking about a scale. Suppose we measure the mass of an object many times. If the balance reads 1.0001 grams, 1.0000 grams, 0.9999 grams, 1.0000 grams, 0.9999 grams, then we might say that is is very precise, because the values are tightly clustered together. This is true even if the object really weighs 10 grams! However, a scale that consistently reads 1.000 grams when measuring a 10 gram object is not very accurate.

Precision is entirely "internal"--it's a description of how reliable or repeatable something is. Accuracy, however, measures accuracy according to an external standard (say, a known weight). There's an ISO proposal to call that definition of accuracy "trueness", which might help with your confusion.

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Would it be correct then to use '0' error as my reference value and my measured value to be deviation from this? For example, if I rotated to 37º and measured 37.01º, my value becomes 0.01. Then the next rotation is 245º and it's measurement 245.03º, giving a second value of 0.03º. Ignoring the resultant position and only recording the error? – Will.W Mar 13 '14 at 11:05
Record the target positions and the error - plotting one against the other may show something of interest. – Scortchi Mar 13 '14 at 11:17

• I'd highly recommend to spell out what you refer to with your terms (which should of course be used according to their general definition).
The fact that you encounter confusion already within your office underlines this.

• Also you need to be clear whether you report mean error (bias) and standard deviation or whether you calculate total expected error (and which error level you use for that) or report percentiles of observed error.

• It is also highly important to report which mechanical procedure you followed (the two different procedures outlined by your office are likely to yield different results).

In particular, I'd look at

• error for one positioning step vs. cumulative error over many such steps (use a sensible positioning scheme for application(s) you have in mind).
• error as function of the length of the movement
• error of returning to a starting position after movement(s)
• error when changing driving direction vs. error when going on in the same direction
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I found a document by the World Meteorological Organization which in turn is referencing UKAS M3003 which gives helpful guidelines on calculating uncertainty (which I had been calling accuracy, thanks Matt for the ISO proposal!), trueness and precision being components of this.

http://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf

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