Integrity certificate: manufacturing SPC (Cpk / Xbar-R)
Re-run against these exact files on 2026-08-30.

Every line was measured, not asserted. The checks are ordinary pandas over
the CSVs sitting beside this file, so you can re-run them yourself.

  PASS  'Shaft Diameter': measured Cpk 1.58 vs target 1.67
  PASS  'Bore Diameter': measured Cpk 1.28 vs target 1.33
  PASS  'Housing Bolt Torque': measured Cpk 1.41 vs target 1.33
  PASS  'Valve Seal Thickness': measured Cpk 0.83 vs target 0.85
  PASS  'Bearing Race Width': measured Cpk 1.30 vs target 1.33
  PASS  Cp >= Cpk on all 5 processes (the Cp/Cpk identity)
  PASS  'Housing Bolt Torque' is off-center: Cp 1.94 > Cpk 1.41
  PASS  'Valve Seal Thickness' measures Cpk 0.83, below the 1.33 capability minimum
  PASS  UCL_xbar reconciles to grand_mean + A2 x Rbar on all 5 processes
  PASS  every subgroup's xbar equals the mean of its own 5 measurements, on all 450 subgroups
  PASS  every subgroup's r equals the range of its own 5 measurements, on all 450 subgroups
  PASS  'Shaft Diameter' (stable) trips a Western Electric rule on only 1.1% of subgroups
  PASS  'Bore Diameter' (stable) trips a Western Electric rule on only 0.0% of subgroups
  PASS  'Housing Bolt Torque' (stable) trips a Western Electric rule on only 3.3% of subgroups
  PASS  'Valve Seal Thickness' (stable) trips a Western Electric rule on only 1.1% of subgroups
  PASS  'Bearing Race Width' (tool-wear drift): 100% of its final subgroups trip a rule vs 0% before the drift started
  PASS  every subgroup has exactly 5 measurements, on all 450 subgroups
  PASS  subgroups.process_id has zero orphans against processes.csv
  PASS  measurements.subgroup_id has zero orphans against subgroups.csv
  PASS  every process has USL strictly greater than LSL

20 checks, 20 passing.

Composition, measured from these files:
  processes:     5
  subgroups:     450 (90 per process, 3 shifts/day x 30 days)
  measurements:  2,250 (5 per subgroup)

Sources for every named formula:
  Cp / Cpk                Montgomery, "Introduction to Statistical Quality
                           Control." Cp = (USL-LSL)/(6-sigma); Cpk = Cp x (1-k).
  sigma_within             Rbar/d2, d2=2.326 for n=5 (ASQ / Montgomery
                           Table VI, control chart constants).
  Control limits           UCL/LCL = grand_mean +/- A2 x Rbar, A2=0.577
                           for n=5, set from a 54-subgroup Phase I baseline.
  Western Electric Rules   Western Electric Statistical Quality Control
                           Handbook, 1956. Rules 1, 3, and 4 checked.

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