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A measuring chain is one successive signal path through a measuring system, beginning at a sensor and ending at an output element. The VIM illustrates this with both an electro-acoustic chain and a mechanical chain; a measuring chain need not be electronic.^[ref]

Consider an original force measurement: a load cell produces an electric potential difference, an amplifier scales that signal, an analog-to-digital converter encodes it, and software converts the code to a force value. This is one measuring chain within the larger measuring system, which also includes its excitation supply, references and mounting arrangements. The load cell acts as a measuring transducer.

In an ideal linear model, let sensor response be $S=2\mathrm{mV}{\mathrm{N}}^{-1}$, amplifier gain $G=100$, and converter step $q=1\mathrm{mV}$ per code increment. If the additive output offset is $n_0=10$ increments, the numerical output isThus $n=610$ implies $F=(610-10)/200=3\mathrm{N}$. These are stipulated teaching values, not measured equipment performance.

The example exposes why measurement calibration must describe the relevant path. Changing amplifier gain changes the relation between output and force even if the load cell is untouched. A saturated stage can also discard information that later conversion cannot restore. Gain uncertainty, offsets, instrumental drift and finite conversion steps contribute at different points; treating the final display's increment as the whole measurement uncertainty overlooks those contributions.

A measuring transducer is a device whose output quantity has a specified relation to its input quantity and is used in measurement. VIM examples include a thermocouple, a strain gauge and a Bourdon tube.^[ref] A measuring transducer provides a link in a measuring chain; it need not itself display a finished measurement result.

For an original pressure readout, choose a linear modelwith pressure $p$, output electric potential difference $V$, transducer sensitivity $S=2\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, and offset $V_0=1\mathrm{mV}$. An output $V=201\mathrm{mV}$ then corresponds to $p=100\mathrm{kPa}$. An amplifier, analog-to-digital converter and display can follow the transducer, each contributing to the whole measuring system.

The inverse calculation $p=(V-V_0)/S$ exposes distinct uncertainty contributions. Holding the other inputs fixed, a small output change $\delta V$ changes inferred pressure by $\delta V/S$; a small offset error changes it by $-\delta V_0/S$. An output increment $0.2\mathrm{mV}$ corresponds to $0.1\mathrm{kPa}$ for the stipulated sensitivity, but does not establish a total measurement uncertainty of that size.

Characterize the relevant range, temperature conditions, response time and possible instrumental drift during measurement calibration. The relation can be nonlinear, in which case local transducer sensitivity is the appropriate derivative rather than one gain valid everywhere. The definition also allows input and output quantities of the same kind; it does not require changing from a mechanical quantity to an electrical one. A sensor denotes the part directly affected by the phenomenon being sensed, whereas a complete measuring chain can contain further measuring transducers.

Transducer sensitivity describes how much the output of a measuring transducer changes when its input changes. For an output $y$ responding smoothly to input $x$, a local model usesVIM defines sensitivity of a measuring system through the quotient of corresponding indication and input changes, noting that sensitivity can depend on the input value and that the changes used must be appreciable relative to resolution.^[ref] The derivative is the smooth local limit of that response ratio.

For an original pressure-to-potential transducer, stipulateIts transducer sensitivity isAt $p=100\mathrm{kPa}$, the output is $0.310\mathrm{V}$ and the sensitivity is $4\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Across the finite interval from $100$ to $110\mathrm{kPa}$, output changes by $41\mathrm{mV}$, so the measured response ratio is instead $4.1\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Specify the operating point or interval rather than treating these two slopes as contradictory.

An output increment $q=0.2\mathrm{mV}$ corresponds locally to input-referred resolution $q/|S|=0.05\mathrm{kPa}$ at the first operating point. This conversion is not a complete uncertainty statement. Increasing electronic gain can enlarge output noise as well as the signal; detector saturation can flatten the response and destroy local invertibility.

Estimate transducer sensitivity with known input steps, repeated outputs and checks for changing zero, loading and temperature. In a linear response $y=Sx+b$, a constant offset $b$ cancels from differences; a changing offset does not. Retain both the sensitivity relation and its uncertainty in measurement calibration, and propagate the relevant contributions when reporting a measurement result.