Observed manufacturing variation contains both real part-to-part variation and variation introduced by the measurement system.

Measurement-system analysis (MSA) asks whether the measurement process is good enough to distinguish the product variation that matters.

A common study is gauge repeatability and reproducibility (gauge R&R):

• repeatability: variation when the same measurement system repeatedly measures the same part under essentially the same conditions;
• reproducibility: variation associated with different operators, setups or other defined measurement conditions.

A simple variance model is

$$\sigma_{obs}^2\approx\sigma_{part}^2+\sigma_{meas}^2.$$

If observed standard deviation is $0.030$ mm and estimated measurement-system standard deviation is $0.018$ mm, then an estimate of actual part variation is

$$\sigma_{part}\approx\sqrt{0.030^2-0.018^2} \approx0.024\ \mathrm{mm}.$$

The measurement contribution is therefore too large to ignore.

A gauge R&R study deliberately measures several parts repeatedly and, when relevant, with multiple operators so those components can be separated statistically.

A production process can appear unstable or incapable when the real problem is noisy measurement. Conversely, a measurement system can hide meaningful process changes if its resolution and repeatability are poor.

MSA therefore comes before trusting capability indices or control charts based on measured dimensions.