Rectangular, triangular and normal distributions in uncertainty budgets
The assumed distribution sets the divisor that turns a limit into a standard uncertainty: √3 for rectangular, √6 for triangular, k for normal.
A Type B component usually starts life as a half-width a: a specification of ±a, a resolution of 2a, a drift limit of ±a. To become a standard uncertainty it must be divided by a factor that depends on the assumed probability distribution.
Divisors
- Rectangular (all values within ±a equally likely): u = a/√3.
- Triangular (values near the centre more likely): u = a/√6.
- Normal (from a certificate at coverage factor k): u = U/k.
- U-shaped (e.g. sinusoidal variation, mismatch): u = a/√2.
When in doubt, rectangular is the conservative and conventional choice for limits and resolution.
Frequently asked questions
- Which distribution for a digital display resolution?
- Rectangular, with half-width equal to half the resolution: a 0.1 °C display gives u = 0.05/√3 ≈ 0.029 °C.
- Which distribution for a manufacturer's accuracy specification?
- Rectangular unless the manufacturer states a confidence level, in which case treat it as normal at that level.
References
- [1]JCGM 100:2008 — Guide to the expression of uncertainty in measurement (GUM)
General technical guidance written against the cited sources. It is not regulatory or legal advice and does not replace the applicable standard, guideline or a qualified reviewer's judgement.
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Combine Type A and Type B components per the GUM: divisors by distribution, sensitivity coefficients, u_c, effective degrees of freedom and U at k = 2.
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Type A vs Type B uncertainty evaluation
Type A uses statistics on repeated observations; Type B uses any other information. Both produce standard uncertainties that combine the same way.
Resolution as an uncertainty component
A digital display of resolution d contributes a rectangular component of half-width d/2, giving u = d/(2√3) ≈ 0.29 d. For a 0.1 °C logger that is 0.029 °C — often the largest term in its calibration.