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The Capability Study Nobody Should Trust

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The Capability Study Nobody Should Trust

A job shop machines aluminum housings with a bore specified at 25.00 ±0.05 mm. A new CMM was installed and qualified with a gage R&R study: 10 parts, 3 operators, 3 trials. Results: %GRR = 29% of tolerance, number of distinct categories = 3. The ten parts were five consecutive pieces from a single lot, spanning only 0.012 mm. A capability study run on that same lot reported Cpk = 1.45, and it has already been sent to the customer in draft. On the X-bar/R chart (n = 5, hourly), two X-bar points fell beyond the 3-sigma limits last week; in both cases the operator adjusted the tool offset, and average within-subgroup range rose from 0.008 to 0.013 mm afterward. A customer audit is in three weeks and PPAP-level evidence is expected.

1. Interpret the measurement system study. Can the capability result be submitted as evidence?

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The MSA is not adequate for the tolerance.

  • %GRR = 29% of tolerance sits at the top of the conditional band (rule of thumb: under 10% acceptable, 10-30% marginal and application-dependent, over 30% unacceptable). For a PPAP submission on a 0.10 mm window, marginal is not enough: nearly a third of the tolerance is consumed by the act of measuring.
  • ndc = 3 is the harder failure. Fewer than 5 distinct categories means the gage cannot reliably rank parts into more than a few buckets; it cannot support a capability index, control charting, or sorting decisions.
  • The part selection invalidates the study design. The ten parts spanned 0.012 mm of a 0.100 mm tolerance - about 12%. GRR studies must sample parts across the process range; with a narrow sample, the between-part term collapses and the error term dominates, which distorts both %GRR and ndc. This study must be redone with parts spanning the full range, ideally from multiple lots and both sides of the target.

Therefore the Cpk of 1.45 is not submittable. It was computed from one narrow lot, so it captures neither lot-to-lot variation nor the drift visible on the chart, and it is confounded with a measurement system that cannot resolve the feature. Withdraw the draft before the customer anchors on it - a retracted number costs less credibility than a defended one.

Sequence: fix the measurement system (fixture and clamping, probe calibration, operator technique standardization, program verification against a known artifact), re-run GRR with proper part selection, and only then re-baseline capability.

2. Two out-of-control points were followed by operator offset adjustments and rising within-subgroup range. What is happening and what should be done?

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This is tampering, and the chart is now measuring the operators.

  • A point beyond a 3-sigma limit is a signal to investigate, not an instruction to adjust. Adjusting the tool offset after every excursion converts a stable process into a wandering one and adds variation the process did not have. The rise in average within-subgroup range from 0.008 to 0.013 mm after the adjustments is the fingerprint: variability increased at the moment of intervention.
  • Before blaming the operators, check three preconditions: (1) are the control limits valid - from a stable baseline of at least 20-25 subgroups, not recalculated weekly? (2) is the measurement system capable of charting this feature, given the GRR result? (3) are subgroups rational - five consecutive parts describe within-cycle variation only, and will not see drift between cycles.
  • With a %GRR of 29%, some chart signals are measurement noise. Charting before fixing the MSA produces exactly this loop: false signals, adjustments, real variation.

Actions:

  1. Freeze offset changes; require a documented investigation before any adjustment.
  2. Re-establish limits from a clean, stable baseline after the MSA is fixed.
  3. Write a reaction plan that distinguishes the rules: one point beyond a limit = investigate; a run of 7 on one side = look for a shift; trend = look for tool wear. Tool wear on a machined bore is an expected, planned adjustment, not a special cause - that should be handled on a tool-life basis, not by chasing points.
  4. Retrain operators on the distinction between common and special cause and record it; this is a training gap, not a discipline issue.

3. Lay out the corrective action sequence for the next three weeks before the audit.

Read the worked answer

Order matters; doing these in parallel will produce another unusable study.

Week 1 - measurement system

  • Rebuild the GRR: parts spanning the full tolerance from at least three lots, 3 operators × 3 trials, randomized order, parts unmarked to operators.
  • Fix root causes of the error term: fixturing, probing strategy, temperature stabilization for aluminum, operator technique.
  • Acceptance gate: %GRR ≤ 10% of tolerance (or ≤ 30% of process variation for a marginal-use case) and ndc ≥ 5.

Week 2 - process baseline

  • Collect capability data over multiple shifts and lots with rational subgroups, after MSA acceptance.
  • Stratify by machine, lot, operator, and time; a single pooled Cpk will hide the strata that matter.
  • Verify stability on a properly limited chart before computing any index; an unstable process has no meaningful Cpk.

Week 3 - evidence package and audit readiness

  • Submit the corrected capability study with the MSA report, sampling plan, and stability evidence attached - the audit finding is usually about traceability of the method, not the number.
  • Document the tampering correction: reaction plan, retraining records, revised work instruction.
  • Communicate the withdrawal and resubmission to the customer proactively, with cause and containment.

What not to do: submit the 1.45 with a footnote. Auditors read footnotes.