Why accuracy and repeatability are different problems

Why a machine can be consistently wrong, and why that is the easier fault.

A machine is repeatable if it lands in the same place every time it is asked to, and accurate if that place is the one it was actually told to go to, and a machine can have all of one and none of the other, which is why the two are judged separately rather than assumed to come together.

What is actually happening

A machine that always stops four tenths of a millimetre short of where it was told to go is highly repeatable, since every single attempt lands in exactly the same wrong place, but it is not accurate, because that place is not the one it was actually commanded to reach. A machine that scatters its stops randomly around the correct position, sometimes short, sometimes past it, sometimes dead on, might average out to the right answer over many attempts and therefore look accurate in aggregate, but it is not repeatable, because no single attempt can be trusted to land where the others did. The two properties, which measurement work calls accuracy and precision, describe entirely different kinds of error, one a fixed offset that shows up the same way every time, the other a spread that shows up differently every time, and a machine can suffer from either one without the other at all, which is why the two are always measured and reported separately rather than folded into a single figure. A machine can even be excellent at one and poor at the other purely by design, since a cheap motor driving a very stiff, well-supported frame can be extremely repeatable despite carrying a large fixed offset, while an expensive, precisely calibrated motor bolted to a loose, wobbling frame can be genuinely accurate on average and still land somewhere slightly different every single time.

The dartboard comparison

Throwing a handful of darts at a board makes the difference obvious. A player whose darts land in a tight cluster just to the left of the bullseye is being wonderfully repeatable and consistently inaccurate, since every throw lands in the same wrong place, and the fix is simple, aim a little further right and the same tight cluster lands on the bull. A player whose darts scatter loosely all around the bullseye, some left, some right, some high, some low, is being accurate on average and not repeatable at all, and there is no single adjustment that fixes scatter, because the problem is not a consistent offset but a lack of consistency itself, a different fault entirely from the first player's. Watching the two players throw makes the distinction obvious in a way no amount of describing it can, since the first player's arm repeats the same motion every time and simply needs redirecting, while the second player's arm is doing something at least slightly different on every single throw.

The one number worth remembering

A machine offset by a fixed half a millimetre in the same direction every time can usually be corrected with a single number entered once, cancelling the offset entirely, while a machine that scatters by that same half a millimetre in random directions cannot be corrected by any single number at all, since there is no one adjustment that fixes an error that is different every time it appears. Measuring a machine's repeatability, running it to the same position many times over and recording how tightly those attempts cluster, is therefore a separate test from measuring its accuracy, and a report that gives only one of the two numbers is not describing the machine completely.

Why this matters in practice

A consistent offset is the easier fault precisely because it is fixable with a single correction applied once and trusted afterwards, while inconsistency has to be solved at its source, in whatever is producing the scatter, whether that is loose parts, worn surfaces, or backlash taken up differently from one attempt to the next. No amount of clever calibration can paper over an error that refuses to repeat itself, since calibration only ever works by subtracting a known, fixed amount, and there is nothing fixed to subtract from a scatter that lands somewhere different every time it is measured.