= Metrological traceability
<Metrological traceability> is a property of a measurement result: a documented, unbroken sequence of <measurement calibrations> relates it to a stated reference, and every link contributes to its <measurement uncertainty>. The reference can be a practical realization of a <measurement unit>, a measurement procedure or a <measurement standard>.<International vocabulary of metrology by JCGM>[VIM3 entry 2.41, definition and notes 1–5]{ref}
Consider an original mass-measurement chain: a reference <measurement standard> calibrates a working mass, which is used for <instrument calibration> of a <balance>, which weighs an object. Suppose the reference contributes $2\,\mathrm{mg}$ of <standard uncertainty>, the transfer adds an independent $3\,\mathrm{mg}$, and the final weighing adds an independent $4\,\mathrm{mg}$. With unit sensitivity to these additive contributions,
$$
u=\sqrt{2^2+3^2+4^2}\,\mathrm{mg}=\sqrt{29}\,\mathrm{mg}\simeq5.4\,\mathrm{mg}.
$$
The intermediate working mass has $\sqrt{13}\,\mathrm{mg}$ of <standard uncertainty>. That value already includes the reference contribution; adding the same $2\,\mathrm{mg}$ again at the final step would double-count it. Correlated contributions require <covariance> terms rather than the independent-input calculation.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[Appendix A, equation A-3]{ref}
Documentation must identify the reference, comparison procedures, dates, applicable conditions and uncertainty contributions. A certificate or instrument label alone does not supply the complete chain for every later result. <Metrological traceability> also does not ensure that the resulting <measurement uncertainty> is small enough for the intended use.
Back to article page
