Quality Management, Metrology and Reliability
This domain tests whether you can build a traceable measurement with a stated uncertainty, make a conformance decision that survives challenge, and quantify product reliability from data rather than from suppliers' adjectives.
Traceability and uncertainty
- Traceability is an unbroken chain of calibrations to SI units, in Hong Kong typically anchored through the Standards and Calibration Laboratory of the Innovation and Technology Commission.
- Calibration establishes the relationship to a reference; verification only confirms a limit. A calibration certificate without uncertainty is incomplete.
- GUM (JCGM 100) uncertainty budget: Type A from repeated readings, u = s/√n; Type B from certificates (u = U/k), resolution (u = resolution/(2√3)) and influence quantities. Combine as u_c = √(Σu_i²) and expand with U = k·u_c, k = 2 for about 95%.
- ISO 14253-1 decision rules: with a guard band, conformance is only proven when the measured value is inside the tolerance by more than U.
Dimensional metrology
- ISO 286 limits and fits, ISO 1101 GD&T, ISO 10360 for CMM acceptance (MPE_E) and ISO 5725 for method precision.
- Standard reference temperature is 20 °C; steel expands about 11.5 µm per metre per kelvin, so a 500 mm part measured 5 K hot is about 29 µm longer.
Reliability
- R(t) = exp(−λt); MTBF = 1/λ for a constant failure rate. Series R = ΠR_i; parallel R = 1 − Π(1 − R_i).
- Availability A = MTBF/(MTBF + MTTR). Weibull shape β < 1 infant mortality, β = 1 random, β > 1 wear-out.
- Accelerated testing uses Arrhenius acceleration factors AF = exp[(Ea/k)(1/T_use − 1/T_stress)] to compress time.
Worked example
A 25.000 mm gauge is checked against a certificate giving U = 2.0 µm at k = 2, with repeatability s = 1.5 µm over 10 readings and 1 µm resolution. Standard uncertainties: 1.0 µm (certificate), 0.47 µm (s/√10), 0.29 µm (resolution). u_c = √(1.0² + 0.47² + 0.29²) = 1.14 µm, so U = 2.3 µm. Against a tolerance of ±0.010 mm, a reading of 24.991 mm is accepted because 24.991 + 0.0023 = 24.9933, still inside 24.990 mm.
Traps that cost marks
- Dividing the standard deviation by n rather than √n.
- Quoting an expanded uncertainty without its coverage factor.
- Ignoring temperature correction on long parts.
- Adding MTBFs of series items instead of adding failure rates.