ISO 17025 Measurement Uncertainty Calculator
Use this calculator to estimate the combined and expanded measurement uncertainty according to ISO/IEC 17025 principles. This tool helps quantify various sources of uncertainty (Type A and Type B) to provide a comprehensive uncertainty budget.
units
Type A Uncertainty Components (Statistical Evaluation)
units
Standard deviation from a series of repeated measurements.
Number of measurements used to determine srep.
Type B Uncertainty Components (Other Sources)
units
Smallest division of the measuring instrument (e.g., 0.01 mm). Assumes rectangular distribution.
units
Expanded uncertainty from the instrument's calibration certificate.
Coverage factor used for Ucal,exp (e.g., 2 for approx. 95% confidence).
units
Estimated maximum drift or instability (e.g., ±0.005 units, input 0.005). Assumes rectangular distribution.
Final Uncertainty Parameters
Coverage factor for the final expanded uncertainty (e.g., 2 for approx. 95% confidence).
Calculation Results:
Enter values and click "Calculate Uncertainty" to see the results.
Understanding ISO 17025 Measurement Uncertainty
ISO/IEC 17025 is an international standard that specifies general requirements for the competence, impartiality, and consistent operation of laboratories. A critical aspect of this standard is the requirement for laboratories to estimate and report the measurement uncertainty associated with their test and calibration results.
What is Measurement Uncertainty?
Measurement uncertainty is a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand. In simpler terms, it's a quantitative indication of the doubt about the validity of a measurement result. No measurement is perfect; there's always some doubt about how well the measurement result represents the true value of the quantity being measured.
Why is it Important?
- Reliability: It provides a quantitative statement about the quality of a measurement result, enhancing its reliability.
- Comparability: Allows for comparison of results from different laboratories or against specifications/tolerances.
- Decision Making: Essential for making informed decisions, especially in critical applications like product quality control, safety, and legal compliance.
- Compliance: A mandatory requirement for accredited laboratories under ISO 17025.
Components of Measurement Uncertainty
Measurement uncertainty is typically evaluated using two main approaches:
- Type A Evaluation: Based on statistical analysis of a series of observations. This usually involves calculating the standard deviation of repeated measurements. The more measurements taken, the better the statistical estimate.
- Type B Evaluation: Based on means other than statistical analysis of a series of observations. This can include information from calibration certificates, manufacturer's specifications, reference data, experience, or other relevant information. Common distributions assumed for Type B uncertainties include rectangular (uniform), triangular, and normal distributions.
Key Terms Explained:
- Standard Uncertainty (u): The uncertainty of a measurement result expressed as a standard deviation.
- Combined Standard Uncertainty (uc): The standard uncertainty of a measurement result when that result is obtained from the values of a number of other quantities, equal to the positive square root of the sum of the variances and covariances of these other quantities, weighted according to how the measurement result depends on these quantities. In simpler cases, it's the square root of the sum of the squares of individual standard uncertainties (root-sum-of-squares).
- Expanded Uncertainty (U): A quantity defining an interval about the result of a measurement that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand. It is obtained by multiplying the combined standard uncertainty by a coverage factor (k).
- Coverage Factor (k): A numerical factor used to multiply the combined standard uncertainty in order to obtain an expanded uncertainty. It is chosen on the basis of the desired level of confidence (e.g., k=2 typically corresponds to approximately 95% confidence for a normal distribution).
How the Calculator Works (Simplified Model):
This calculator uses a simplified model to combine common uncertainty sources:
- Standard Uncertainty from Repeatability (urep): Calculated as srep / √n.
- Standard Uncertainty from Resolution (ures): Assumes a rectangular distribution, calculated as Res / √12.
- Standard Uncertainty from Calibration Certificate (ucal,std): Derived from the expanded uncertainty on a calibration certificate, ucal,std = Ucal,exp / kcal.
- Standard Uncertainty from Drift/Stability (udrift): Assumes a rectangular distribution for the given half-range, calculated as Range / √3.
- Combined Standard Uncertainty (uc): Calculated using the root-sum-of-squares method: √(urep2 + ures2 + ucal,std2 + udrift2).
- Expanded Uncertainty (U): Calculated as uc × k (desired coverage factor).
Example Calculation:
Let's use the default values in the calculator:
- Measured Value (X): 10.00 units
- Standard Deviation of Repeatability (srep): 0.01 units
- Number of Repeat Measurements (n): 5
- Instrument Resolution (Res): 0.01 units
- Calibration Certificate Expanded Uncertainty (Ucal,exp): 0.02 units
- Calibration Certificate Coverage Factor (kcal): 2
- Estimated Drift/Stability Range (Half-Range): 0.005 units
- Desired Coverage Factor (k): 2
Step 1: Calculate individual standard uncertainties:
- urep = 0.01 / √5 ≈ 0.00447 units
- ures = 0.01 / √12 ≈ 0.00289 units
- ucal,std = 0.02 / 2 = 0.01000 units
- udrift = 0.005 / √3 ≈ 0.00289 units
Step 2: Calculate Combined Standard Uncertainty (uc):
- uc = √(0.004472 + 0.002892 + 0.010002 + 0.002892)
- uc = √(0.00001998 + 0.00000835 + 0.00010000 + 0.00000835)
- uc = √(0.00013668) ≈ 0.01169 units
Step 3: Calculate Expanded Uncertainty (U):
- U = uc × k = 0.01169 × 2 ≈ 0.02338 units
Final Result: 10.00 ± 0.02 units (rounded)
Detailed Uncertainty Budget:
"; resultHtml += "Standard Uncertainty from Repeatability (urep): " + u_rep.toFixed(5) + " " + unit + ""; resultHtml += "Standard Uncertainty from Resolution (ures): " + u_res.toFixed(5) + " " + unit + ""; resultHtml += "Standard Uncertainty from Calibration (ucal,std): " + u_cal_std.toFixed(5) + " " + unit + ""; resultHtml += "Standard Uncertainty from Drift/Stability (udrift): " + u_drift.toFixed(5) + " " + unit + ""; resultHtml += ""; resultHtml += "Combined Standard Uncertainty (uc): " + u_c.toFixed(5) + " " + unit + ""; resultHtml += "Expanded Uncertainty (U) (k=" + desiredCoverageFactor + "): " + U.toFixed(5) + " " + unit + ""; resultHtml += "Final Result: " + measurementValue.toFixed(2) + " ± " + U.toFixed(2) + " " + unit + " (Rounded for display)"; document.getElementById("result").innerHTML = resultHtml; }