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.