Foundations

Shared input variation belongs in the joint uncertainty description.

Sample the joint input model to approximate the output distribution.

Precision depends on which measurement conditions are held or changed.

Detectable change and response scale are different instrument properties.

Response depends on timescale, gain and phase.

A detection limit depends on the measurement procedure's false-presence probability α and false-absence probability β.

Results for quantities of the same kind are metrologically comparable when traceable to the same reference.

An ideal baseband signal containing no frequencies above B can be reconstructed from exact uniform samples at f_s>2B.

For a uniform rounding quantizer with step Δ and no overload, the error magnitude is at most Δ/2.

For repeated indications, the mean has variance Var(x̄)=(1/n²)Σ_iΣ_j Cov(x_i,x_j).

Instrumental drift is a continuous or incremental change in indication caused by changes in an instrument's metrological properties.

For a validated linear first-order sensor model τẏ+y=Kx with τ>0, a step to x_f gives y(t)=Kx_f+[y(0)−Kx_f]e^(−t/τ).

For a causal linear time-invariant sensor with specified initial state, output is the convolution of input with impulse response plus noise.

A normalized frequency-domain Tikhonov inverse G=H*/(|H|²+λ²|L|²) suppresses ill-conditioned frequencies instead of dividing by an arbitrarily small H.

For N observations of one stationary process with covariance C_ij, Var(mean)=N⁻²Σ_ijC_ij.

For linear observations z=Aθ+ε with known positive-definite covariance Σ and full-column-rank A, generalized least squares yields θ̂=(AᵀΣ⁻¹A)⁻¹AᵀΣ⁻¹z.

A network model can include per-instrument offsets, temporal drift, shared-reference effects and between-day variability alongside statistical noise.

A discrepancy term δ(x) represents inadequacy of the physical response model, distinct from repeatability noise and uncertain calibration parameters.

A physical phenomenon, an approach and a detailed procedure have different roles.

A complete measurement system can include more than one device.

Component names describe different measurement roles.

A displayed reading is only one part of a measurement result.

Changing an instrument response differs from determining its calibration.

An accepted comparison value need not be an exact true value.

Possible readings differ from a validated interval of measurement.

Instrument properties are specified within a domain of use.

Responding to a target differs from excluding interference.

An undetected input change differs from an interval with no output change.

Time stability differs from short-term repeatability.

A specification limit is not an uncertainty estimate.