Calculation model
The workbench applies first-order propagation. Each standard uncertainty u(xi) is multiplied by its signed sensitivity coefficient ci. Independent contributions combine by root-sum-of-squares. Entered correlation coefficients add the covariance terms 2ρij·ci·cj·u(xi)·u(xj). Correlations are validated together because an arbitrary set of pairwise values may not describe a possible correlation matrix.
Type A, Type B, and distribution conversion
Type A and Type B identify how a component was evaluated: statistical methods or other information. They do not mean “random” and “systematic.” Repeatability accepts a sample standard deviation and observation count, producing s/√n and defaulting to n − 1 degrees of freedom. Rectangular, triangular, and U-shaped half-widths divide by √3, √6, and √2. Expanded or normally stated inputs use the divisor you supply.
Effective degrees of freedom and coverage
For mutually independent inputs, Welch–Satterthwaite estimates effective degrees of freedom from the fourth powers of the signed contributions and their component degrees of freedom. Automatic coverage truncates finite νeff down to the next integer and calculates the two-sided Student-t factor for the selected probability. With nonzero correlations, this workbench does not apply that independent-component approximation; use a documented manual factor or a more suitable statistical treatment.
Important validation boundary
This is a transparent first-order arithmetic workbench, not a complete uncertainty evaluation or accreditation decision. You remain responsible for defining the measurand and measurement model, identifying every significant effect, preventing double counting, converting units through valid sensitivity coefficients, justifying distributions and correlations, treating drift and resolution correctly, and choosing a reporting rule. Strong nonlinearity, asymmetric distributions, constrained quantities, small-sample complications, or a non-Gaussian output may require model reformulation or Monte Carlo propagation.
Frequently asked questions
Should every Type B component have infinite degrees of freedom?
No. Blank means infinity only when that approximation is justified by the information supporting the component. Enter a finite value when the reliability of the estimated standard uncertainty calls for it.
Can negative sensitivity coefficients reduce uc?
The sign does not affect an independent component's squared contribution, but it matters in covariance terms. A correlation can reinforce or cancel variance depending on the signs of both coefficients and ρ.
Does k = 2 always mean 95% confidence?
No. It is often a reporting convention and is approximately 95% only under suitable distribution and degrees-of-freedom conditions. The report labels a manually entered k without inferring a probability.
Why is automatic Student-t disabled after adding correlation?
The implemented Welch–Satterthwaite expression is the conventional independent-component approximation. Rather than silently overstate its scope, the workbench preserves the correlated uc result and requires a separately justified manual coverage factor.
Authoritative guidance
JCGM Working Group 1 maintains the GUM suite. NIST TN 1297 documents the law of propagation and covariance terms, Type B distribution conversions, effective degrees of freedom and coverage factors, and reporting expectations.
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