Measurement trueness

Measurement trueness describes how closely the mean of indefinitely many replicate measured values would agree with a reference value. It concerns systematic error, rather than the random spread described by measurement precision. The VIM treats measurement trueness as qualitative: a numerical error or bias estimate is not itself a numerical value of trueness.^[ref]

An original measurement model separates the two issues:Here $b$ is a fixed offset from the stipulated reference and $\epsilon$ is random measurement error. Thus $\mathbb{E}[X]-x_{\mathrm{ref}}=b$, while the standard deviation of individual readings is $\sigma$. For $n$ independent random variables following this same model, averaging givesMore readings reduce the random scatter of the mean without removing $b$.

For a stipulated length example, instrument A has $b=0.40\mathrm{mm}$ and $\sigma =0.10\mathrm{mm}$; instrument B has $b=0$ and $\sigma =0.50\mathrm{mm}$. A is more precise, while B's limiting mean agrees better with the reference. With 25 independent readings each, the means have standard deviations $0.02\mathrm{mm}$ and $0.10\mathrm{mm}$ respectively, and their expected offsets remain $0.40\mathrm{mm}$ and zero. These are chosen model parameters, not experimental determinations.

Experimentally, compare repeated readings of a stable measurement standard with its assigned value under specified conditions. A finite observed mean difference estimates an offset; its interpretation includes sampling variation and the reference's measurement uncertainty. Determine an appropriate correction through measurement calibration, apply it in the measurement model, and check it with further reference measurements. Neither a small sample spread nor a single reading equal to the reference establishes measurement trueness.