coverage factor

**Coverage Factor** ($k$) is the **multiplier applied to the combined standard uncertainty to obtain the expanded uncertainty** — $U = k cdot u_c$, chosen to provide a specified level of confidence (typically 95% or 99.7%) that the true value lies within the expanded uncertainty interval. **Coverage Factor Values** - **k = 1**: ~68% confidence (1 standard deviation) — rarely used for reporting. - **k = 2**: ~95% confidence — the default for most measurement reports and calibration certificates. - **k = 3**: ~99.7% confidence — used for safety-critical applications and process control (3σ limits). - **Student's t**: When effective degrees of freedom are small (<30), use $k = t_{p, u_{eff}}$ from tables instead of $k = 2$. **Why It Matters** - **Risk Balance**: Higher $k$ reduces the risk of the true value being outside the stated uncertainty — but widens the interval. - **Welch-Satterthwaite**: The effective degrees of freedom ($ u_{eff}$) determine the appropriate $k$ — calculated from individual component DOF. - **Context**: Always state the coverage factor and confidence level — "U = 0.5nm (k=2, 95% confidence)." **Coverage Factor** is **the confidence multiplier** — scaling combined uncertainty to provide a desired level of confidence in the measurement result.