Uncorrelated Standard-Uncertainty Combiner
Combine standard-uncertainty contributions that have already been propagated through the measurement model,expressed in the output unit and verified uncorrelated. Apply only a documented coverage factor selected outside this worksheet.
Document the restricted calculation
This worksheet accepts final standard contributions qi=|ci|u(xi) in the output unit. Determine the measurement model,sensitivity coefficients,standard uncertainties,correlations,degrees of freedom and coverage-factor policy before entering values.
Reported expression
Combined standard uncertainty uc
Expanded uncertainty U
Coverage factor k
Relative expanded uncertainty
Recorded contributions
Equations actually implemented
| 数量 | Equation | 范围 |
|---|---|---|
| Entered contribution | qi=|ci|u(xi) | Must already be a standard uncertainty contribution in the output unit. The worksheet does not derive ci or u(xi). |
| Combined standard uncertainty | uc=√Σqi² | Restricted to contributions verified uncorrelated in the stated first-order model. |
| Expanded uncertainty | U=k uc | k is supplied with an external justification;the worksheet does not map k to a coverage probability. |
| Relative expanded uncertainty | 100U/|y| | Descriptive ratio only;undefined at y=0 and not a conformity rule. |
Standardizing common inputs before entry
| Available information | Standard uncertainty before sensitivity propagation | 边界 |
|---|---|---|
| Mean of n independent repeat observations | u(x̄)=s/√n | Only when the estimator/model is the mean and the repeatability design is applicable;record degrees of freedom. |
| Certificate expanded uncertainty Ucert with stated kcert | u=Ucert/kcert | Use the certificate’s exact statement,unit and coverage basis. |
| Symmetric rectangular bounds±a | u=a/√3 | If the entered value is the full width w=2a,use u=w/√12. |
| Symmetric triangular bounds±a | u=a/√6 | Use only when that distribution is justified. |
| Digital resolution increment δ | u=δ/√12 | JCGM100:2008 F.2.2.1 for equal probability over one indication interval;check for double counting with observed repeatability. |
Sources and standards boundary
JCGM100:2008(E),GUM1995 with minor corrections distinguishes TypeA and TypeB evaluation,uses sensitivity coefficients in the first-order law of propagation,treats uncorrelated and correlated inputs separately,and defines U=k uc. Its AnnexG shows that k=2 corresponds to95.45% only for the stated normal-distribution case;finite effective degrees of freedom and other distributions change the relation.
VIM3 item2.33 says an uncertainty budget should include the measurement model,input estimates and uncertainties,covariances,probability distributions,degrees of freedom,evaluation type and coverage factor. That is why this page is labelled a restricted combiner rather than a complete uncertainty-budget calculator.
ISO/IEC17025:2017 is current Edition3,published2017-11 and confirmed2023. The public ISO card establishes status and scope,but not the exact uncertainty-evaluation clauses;those requirements remain NEEDS_LICENSED_SOURCE. A numerical result from this page does not establish laboratory competence,method validation,traceability or ISO/IEC17025 conformity.
已修正的内容
The former page automatically described its result as GUM/ISO17025-compliant despite omitting the measurement model,sensitivity coefficients,correlations,degrees of freedom and coverage-factor justification. It hard-coded k=2 as “95% confidence” and k=3 as99.7%,which is only valid under specific distribution and degrees-of-freedom conditions. The replacement requires a documented k and makes no automatic probability statement.
The previous “resolution” preset divided the displayed increment by√3;JCGM100:2008 F.2.2.1 gives δ/√12 for a digital indication interval δ,so the preset could double that component. All presets and pre-filled results were removed. Generic “value/divisor” fields were replaced with final standard contributions in the output unit,strict parsing and source/model records. User-entered units are now written with textContent,not injected through innerHTML.
