Measurement Uncertainty – Full Worked Numerical Example
This example demonstrates step-by-step uncertainty calculation for a GC analysis result under ISO 17025 methodology.
Step 1 – Measurement Data (Repeatability)
Five replicate GC measurements of Benzene concentration (%):
1.24, 1.27, 1.25, 1.26, 1.23
Mean (x̄): 1.25 %
Standard Deviation (s): 0.015 %
This is Type A uncertainty (statistical).
Step 2 – Convert to Standard Uncertainty (Type A)
Standard uncertainty:
uA = s / √n
uA = 0.015 / √5
uA = 0.0067 %
Step 3 – Identify Type B Uncertainty Sources
- Calibration standard uncertainty = 0.010 %
- Instrument resolution uncertainty = 0.005 %
- Temperature variation effect = 0.004 %
Convert all to standard uncertainty (already standard values).
Step 4 – Combined Standard Uncertainty
Use Root Sum Square (RSS) method:
uc = 0.013 % (combined standard uncertainty)
Step 5 – Expanded Uncertainty
Apply coverage factor k = 2 (95% confidence):
U = k × uc
U = 2 × 0.013
U = 0.026 %
Step 6 – Final Reported Result
Benzene Concentration = 1.25 % ± 0.03 % (k = 2, 95% confidence level)
Rounded expanded uncertainty to two significant digits.
Important Notes
- Always include coverage factor (k)
- State confidence level
- Recalculate after calibration change
- Update uncertainty after method modification
Measurement uncertainty strengthens lab credibility during audits.