Coverage Factor

The coverage factor (k) bridges the gap between the combined standard uncertainty (a one-standard-deviation estimate) and the expanded uncertainty that is reported on calibration certificates and used for decision-making. By convention, k=2 is used for approximately 95% coverage probability, meaning there is about a 95% chance that the true value lies within the reported uncertainty interval. For higher confidence levels, k=3 provides approximately 99.7% coverage.

The choice of coverage factor depends on the effective degrees of freedom and the desired confidence level. When the effective degrees of freedom are large (>30), k=2 provides close to 95% coverage for a normal distribution. When degrees of freedom are limited, a larger k value from the Student's t-distribution is needed. For example, with 5 effective degrees of freedom, k=2.57 is needed for 95% coverage. Some applications (nuclear, safety-critical) may require k=3 or higher for additional confidence.

For calibration management, the coverage factor is a standard element of uncertainty reporting. Calibration certificates should state the expanded uncertainty along with the coverage factor and the approximate confidence level. ISO 17025 requires that calibration certificates include sufficient information for users to understand the reported uncertainty, including the coverage factor. Most routine calibrations use k=2, but the laboratory should verify that this provides adequate coverage given the effective degrees of freedom in each uncertainty budget.