Calculating measurement uncertainty with the 5M method
During an ISO 17025 or EN 9100 qualification audit, the auditor asks for the measurement uncertainty budget behind the inspection of a tight H6 tolerance of 15 microns. The metrologist has to list and quantify each uncertainty component with the 5M method, to validate the ISO 14253-1 decision rule.
Breaking down and calculating uncertainty with the 5M
| 5M axis | Source of uncertainty | Evaluation method (Type A / B) |
|---|---|---|
| Means | Accuracy error and resolution of the instrument | Type B (calibration certificate) |
| Milieu (environment) | Thermal expansion from the temperature difference | Type B (expansion formula) |
| Manpower | Repeatability of the operator’s positioning | Type A (standard deviation over 10 readings) |
| Material | Surface finish and distortion of the part | Type B (geometric estimate) |
| Method | Misalignment and probing strategy | Type B (geometric calculation) |
All values are given for the reference environmental conditions of 20 °C.
Combining the uncertainty components
The combined standard uncertainty uc is the root sum square of the individual standard uncertainties ui: uc = sqrt(u1^2 + u2^2 + u3^2 + u4^2 + u5^2). The expanded uncertainty U with a coverage factor k=2 (95% confidence interval) is U = 2 * uc. To go further into metrological follow-up, read our article on calibrating a micrometer to ISO 3611.
The ISO 14253-1 decision rule and the reduced acceptance zone
Under ISO 14253-1, the expanded uncertainty U is taken off the part’s tolerance limits. The conformance zone shrinks by U at each end, to guarantee that no bad part is accepted.
Example: an uncertainty budget for a ⌀40 H6 bore
H6 tolerance = 16 µm. 5M budget: Means (u1 = 0.8 µm), Milieu (u2 = 1.2 µm), Manpower (u3 = 0.5 µm), Material (u4 = 0.4 µm), Method (u5 = 0.6 µm). 1. uc = sqrt(0.64 + 1.44 + 0.25 + 0.16 + 0.36) = sqrt(2.85) = 1.69 µm. 2. Expanded uncertainty U (k=2) = 3.38 µm. Verdict: the acceptance zone [40.000; 40.016] shrinks to [40.0034; 40.0126 mm].
Shop-floor pitfalls in an uncertainty budget
The first pitfall is ignoring the thermal expansion of the part. The second is forgetting the resolution of the digital display. The third comes from underestimating the operator’s repeatability. To automate your metrology reports, discover CoteCote and its inspection module.