expanded uncertainty

**Expanded Uncertainty** ($U$) is the **combined standard uncertainty multiplied by a coverage factor to provide a confidence interval** — $U = k cdot u_c$, where $k$ is typically 2 (providing approximately 95% confidence) or 3 (approximately 99.7% confidence) that the true value lies within the stated interval. **Expanded Uncertainty Details** - **k = 2**: ~95% confidence level — the most common reporting convention. - **k = 3**: ~99.7% confidence level — used for safety-critical or high-consequence measurements. - **Reporting**: $Result = x pm U$ (k = 2) — standard format for reporting measurement results with uncertainty. - **Student's t**: For small effective degrees of freedom, use $k = t_{95\%, u_{eff}}$ from the t-distribution. **Why It Matters** - **Communication**: Expanded uncertainty communicates measurement quality in an intuitive way — "the true value is within ±U with 95% confidence." - **Conformance**: Guard-banding uses expanded uncertainty to prevent accepting out-of-spec product — adjust limits by ±U. - **Standard**: ISO 17025 accredited labs must report expanded uncertainty with measurement results. **Expanded Uncertainty** is **the confidence interval** — combined uncertainty scaled by a coverage factor to provide a meaningful confidence statement about the measurement result.