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Engineer Quality Management study materials
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Engineer Quality Management: Measurement Systems Analysis and Metrology

Engineer Quality Management · Work through your exam, one topic at a time.

All guide sections

Measurement Systems Analysis and Metrology

What the exam tests

Gage R&R interpretation, discrimination, bias/linearity/stability, attribute agreement, and calibration traceability. Expect %GRR and ndc computations plus verdict selection.

Core rules

  • Repeatability is equipment variation under one appraiser; reproducibility is appraiser variation. GRR = square root of (EV squared + AV squared).
  • %GRR can be expressed against study variation or against tolerance; state which one you used. AIAG guidance: under 10% acceptable, 10-30% conditionally acceptable depending on criticality and cost, over 30% unacceptable.
  • Number of distinct categories ndc = 1.41 x (PV/GRR); 5 or more is required to use the system for process control.
  • Discrimination: the measurement increment should be no coarser than one tenth of the tolerance (rule of tens). Bias is systematic offset, linearity is bias changing across the range, stability is drift over time.
  • Attribute systems use agreement within appraiser, between appraisers, and against a reference, with kappa above roughly 0.75 considered acceptable.
  • Calibration must be traceable to national standards through an unbroken chain with documented uncertainty; test uncertainty ratio of 4:1 or better is customary, and guard bands protect against false accept/reject.

Worked example

Tolerance 0.20 mm; repeatability sigma 0.006, reproducibility sigma 0.004. GRR sigma = square root(0.000036 + 0.000016) = 0.0072. Six-sigma spread = 0.0433, so %GRR against tolerance = 21.6%, conditionally acceptable. With part sigma 0.05, PV = 0.30 and ndc = 1.41 x (0.30/0.0433) = 9.8, rounded down to 9. Verdict: usable for control, but justify or improve before tightening tolerances.

Traps that cost marks

Reporting %GRR against tolerance when the study variation basis gives a different verdict. Using parts that do not span the process variation, which makes ndc meaningless. Confusing calibration (traceability) with capability. Ignoring resolution limits. Confounding appraiser with technique by letting operators use different fixtures.