Gauge R&R and Capability at Cedar Valley Machining
Cedar Valley Machining produces a 25.00 +/- 0.05 mm bore on a hydraulic manifold. A new air gauge was installed and the quality engineer ran a GR&R study: 10 parts, 3 operators, 3 trials, randomized. The report shows %GR&R (tolerance) = 31%, %contribution = 9.6%, ndc = 3, and the part-to-part range across the 10 parts was only 0.041 mm. The operators were the three shift inspectors; operator B averaged 0.008 mm lower than A and C across all parts. A capability study on 200 bores pulled from the last six weeks gives Ppk = 0.92 against the 0.10 mm tolerance. An I-MR chart of the same 200 points shows the first 90 points centered at 25.004 mm and the remaining 110 at 25.018 mm, with the moving range stable. The data were exported by part number, and three part numbers were mixed in the file. The plant manager has asked whether the process can be certified to Ppk >= 1.33 next month.
1. Interpret the GR&R results. Is the measurement system acceptable for this decision? State the criteria you applied and explain why %contribution and %tolerance disagree.
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Criteria applied (AIAG MSA logic)
- %GR&R of tolerance: <=10% acceptable, 10-30% marginal and acceptable only if gauge cost, risk, and the decision at stake justify it, >30% unacceptable.
- ndc (number of distinct categories) = 1.41 x (PV/GR&R); >=5 is desired, 4 is a bare minimum.
- Here: 31% of tolerance and ndc = 3. Both fail. The gauge cannot be used to accept or reject product against a 0.10 mm tolerance, and it certainly cannot support a customer-facing capability index.
Why 9.6% and 31% disagree %contribution compares gauge variance to total (gauge + part) variance, while %tolerance compares gauge variation to the specification width. The 10 study parts spanned only 0.041 mm, so part variance was artificially small and the percentage-of-total looks flattering. When parts are homogeneous and the decision is conformance, %tolerance governs. The study sample was also wrong for its purpose: a GR&R should sample parts across the expected process spread, not 10 near-identical parts.
Operator effect Operator B's 0.008 mm bias is 16% of the tolerance. That is an operator/technique effect, not random noise: check zeroing, seating force, part temperature, fixture location, and whether B was trained on the new gauge. Resolution should be at most one-tenth of the tolerance (0.01 mm) - verify.
Verdict: reject the gauge as it stands. Standardize the measurement procedure, retrain B, re-run the study with parts spanning the process range, and only then restart the capability question.
2. Evaluate whether Ppk = 0.92 supports the certification request. What is wrong with the study, and what would you do instead?
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Why the number cannot be used
- The process is not in statistical control. The I-MR chart shows two levels: 90 points at 25.004 and 110 at 25.018 - a 0.014 mm sustained shift. Those are two distributions, not one. A Ppk computed across a mixture describes neither. Capability indices presuppose a stable process; the index here is arithmetic, not information.
- The data are stratified. Three part numbers are pooled in one file. Different parts may have different means, different tolerances, or different process settings, so the overall standard deviation includes between-part variation that no single part experiences. Report capability per part family.
- The gauge inflates the denominator. With gauge variation at 31% of tolerance, observed variation is inflated, so Ppk is understated - but by an unknown amount, which is just as disqualifying.
- The sample is probably a convenience export. Six weeks of records may not cover all shifts, tool changes, operators, or material lots.
What to do
- First fix the measurement system, then find the cause of the 0.014 mm shift (tool wear, fixture, thermal drift, new material lot, gauge recalibration event) and restore control.
- Then stratify: control chart per part number, capability only on the in-control data, Cpk from rational subgroups and Ppk from the overall data, reported separately.
- Do not commit to a Ppk >= 1.33 certification date until an in-control, gauge-qualified study exists. Certifying on this data risks shipping out-of-spec parts under a document that says the process is capable.
3. Write the data collection plan for the re-study: what you measure, how you ensure the measurement is trustworthy, sampling, stratification variables, and analysis rules.
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1. Operational definition Bore diameter at a marked axial location, air gauge zeroed on a certified setting ring at 20 +/- 2 C, part soaked to room temperature, three readings averaged per bore, same fixture and seating procedure for everyone.
2. Measurement qualification (before any capability work)
- GR&R: 10 parts spanning the process range, 3 operators, 3 trials, randomized, target %GR&R of tolerance <=10% and ndc >=5.
- Bias and linearity against a certified ring/master across the tolerance range.
- Resolution <=0.01 mm; calibration status verified and recorded.
3. Sampling
- 25 subgroups of n = 5 per part family, taken in time order from routine production, covering all three shifts and at least two weeks, deliberately including one tool change and one lot change.
- No rework parts, no special 'good' samples. Log every part's subgroup timestamp.
4. Stratification variables recorded with each reading Part number, machine/spindle, shift, operator, tool life count, material lot, gauge ID, ambient temperature.
5. Analysis rules (agreed in writing before data collection)
- Chart first (I-MR or Xbar-R per part family). Only in-control data enter capability.
- Report Cpk (within) and Ppk (overall) separately, with confidence intervals; state the n behind each.
- If data are non-normal, use a non-normal capability method rather than forcing a normal fit.
- Report capability per part family, never pooled across families.
- Publish the reaction rule: any out-of-control subgroup triggers cause investigation before the next capability estimate.