Combined Standard Uncertainty
Definition
The overall standard uncertainty of a result, obtained by combining all Type A and Type B component uncertainties in quadrature (square root of the sum of squared components weighted by sensitivity coefficients). Denoted u_c.
- Symbol
- u_c
- Method
- Sum of squared components in quadrature
- Components combined
- Type A and Type B uncertainties
- Field
- Measurement uncertainty / proficiency testing
Common questions
Why combine uncertainties in quadrature rather than simply adding them?+
Quadrature addition (square root of the sum of squares) reflects that independent random error sources are unlikely to all reach their maximum simultaneously, so it gives a statistically realistic combined uncertainty rather than an overly conservative worst-case sum.
What is the practical difference between Type A and Type B components that feed into u_c?+
Type A components are evaluated statistically from repeated measurements, such as a standard deviation from replicate runs, while Type B components come from other information like calibration certificates, manufacturer specifications, or prior data, and both are weighted by sensitivity coefficients before being combined.
Related terms
- Expanded Uncertainty
- The combined standard uncertainty multiplied by a coverage factor k, chosen to achieve a stated coverage probability. For a normal distribution, k...
- GUM
- Guide to the Expression of Uncertainty in Measurement. The international standard, maintained by eight metrology and standardisation bodies, that defines Type A...
- Type a Uncertainty
- Uncertainty evaluated by statistical analysis of a series of observations. The standard uncertainty is the standard deviation of the mean (standard error)...
- Type B Uncertainty
- Uncertainty evaluated by means other than statistical analysis of repeated measurements. Sources include calibration certificates, instrument specifications, reference data, and expert scientific...
- Z-Score (Proficiency Testing)
- A performance statistic in PT defined as z = (x - X) / s_PT, where x is the laboratory's result, X is...