Metrology / quality control §

• CMM (coordinate measuring machine): a probe contacts the part surface at many points; the software reconstructs the geometry. Accuracy ±2–8 µm (high-end: ±1 µm), depending on machine class per ISO 10360-2:2009. Used for final inspection of machined and cast parts.
• Optical metrology: structured light, laser triangulation, or confocal microscopy. Non-contact; used for surface topography, 3D scanning, and in-line inspection.
• Interferometry: a laser interferometer measures displacement with nanometer resolution. Used for calibrating CMMs and for high-precision optics.
• Calipers, micrometers, gauges: hand-held instruments for shop-floor inspection. Accuracy ±0.01 mm (calipers) to ±0.001 mm (micrometers).

CMM probe schematic:

• Stylus profilometer: a diamond tip traces the surface; Ra, Rz, and other parameters are computed. Resolution 0.001 µm (vertical), 0.1 µm (lateral).
• Optical profilometer (white light, confocal): non-contact; maps 3D surface topography over large areas. Used for thin films, coatings, and textured surfaces.
• Surface roughness standards: ISO 21920-2:2021 defines parameters (Ra, Rq, Rz, Rmax). Typical values: as-cast Ra 10–50 µm; as-machined (milling/turning) Ra 1.6–6.3 µm (3.2 µm is the common default; 0.8 µm requires a dedicated finishing pass); ground Ra 0.2–0.8 µm; polished Ra < 0.1 µm.

Surface roughness profile (Ra, Rz, Rmax):

• Tensile test: a coupon is pulled until fracture; yield strength, ultimate tensile strength, and elongation are measured. (ISO 6892-1)
• Hardness test: Brinell, Rockwell, or Vickers. An indenter is pressed into the surface; the indentation size gives the hardness.
• Spectroscopy: optical emission (OES) or X-ray fluorescence (XRF) measures the chemical composition of a metal lot.
• Non-destructive testing (NDT): ultrasonic, radiographic, eddy-current, or dye-penetrant inspection to detect internal or surface defects without destroying the part. X-ray CT is particularly important for additive manufacturing parts.

• Control charts: X-bar and R charts track the mean and range of a measured characteristic over time. If the process is in control, the measurements fall within the control limits (±3σ).
• Process capability (Cpk): Cpk = min((USL − X̄) / (3σ), (X̄ − LSL) / (3σ)). Uses within-subgroup variation (σ estimated from the average range R̄/d₂). Cpk ≥ 1.33 is the minimum for most industries; Cpk ≥ 1.67 for aerospace.
• Process performance (Ppk): Ppk = min((USL − X̄) / (3σ_overall), (X̄ − LSL) / (3σ_overall)). Uses overall variation (σ computed from all individual measurements). Ppk ≤ Cpk always; a large gap signals special-cause variation between subgroups.
• Pareto analysis: rank defects by frequency to identify the most impactful issues.
• Root-cause analysis: 5-Why, fishbone (Ishikawa) diagram, or FMEA (failure mode and effects analysis) to identify and address the source of a defect.

Control chart example (in-control vs. out-of-control):

Interactive simulation — X-bar and R control chart with live data:

• Calibration: an instrument is compared to a reference standard of known accuracy. The calibration certificate records the uncertainty of the measurement.
• Traceability: the reference standard is traceable to a national metrology institute (NIST, PTB, NPL) or to the SI base units.
• Calibration interval: set by the instrument’s stability, usage, and the required uncertainty. Typically 1–12 months.
• Measurement uncertainty: the range within which the true value lies, with a stated confidence level. Expressed as ±x µm at 95 % confidence.

Metrology traceability hierarchy:

• PDCA cycle (Plan–Do–Check–Act): the core loop of ISO 9001:2026. Plan: define quality objectives and metrology requirements. Do: execute the manufacturing and inspection processes. Check: compare measurement results to specification (SPC, Cpk). Act: implement corrective actions and update procedures.
• Document control: every measurement procedure, calibration certificate, and inspection record is a controlled document with a revision history. AS9100D adds requirements for configuration management and traceability of aerospace parts.
• Role in metrology: the QMS defines when to calibrate, who is authorized to perform inspections, how non-conforming results are dispositioned (use-as-is, rework, scrap), and how measurement data is retained for audit.
• Internal and external audits: periodic reviews verify that the metrology program is being followed. Aerospace (AS9100D) and medical (ISO 13485) industries require third-party audits.

1. Specification: LSL = 24.990 mm, USL = 25.010 mm. Tolerance = 0.020 mm.
2. Process capability:
   • Cpk (upper) = (USL − X̄) / (3σ) = (25.010 − 25.002) / (3 × 0.004) = 0.008 / 0.012 = 0.67
   • Cpk (lower) = (X̄ − LSL) / (3σ) = (25.002 − 24.990) / (3 × 0.004) = 0.012 / 0.012 = 1.00
   • Cpk = min(0.67, 1.00) = 0.67
3. Assessment: Cpk = 0.67 < 1.33. The process is not capable. The upper tail is too close to the USL.
4. Corrective action: Adjust the tool offset to center the process at 25.000 mm. Re-measure. If σ remains 0.004 mm, Cpk = (25.010 − 25.000) / (3 × 0.004) = 0.010 / 0.012 ≈ 0.83. If Cpk is still < 1.33, reduce σ by improving the machine’s repeatability or the fixture’s rigidity.
5. SPC: Set up an X-bar and R control chart with control limits at X̄ ± 3σ. Monitor the process in real time; investigate any point outside the limits.

Visual: control chart for the 50 measurements

The red points near the USL line illustrate why Cpk = 0.67: the process mean is shifted toward the upper specification limit, so the upper tail has insufficient margin.