Capability Slide Built on a Shaky Gage
On a metal-stamping line the critical characteristic is flange width, specified 25.0 ± 0.4 mm. A capability study is due. The team ran a Gage R&R with 3 operators, 10 parts and 3 trials; all parts came from one afternoon's production and span only 0.15 mm. Results: %GRR = 29% of tolerance, number of distinct categories = 3. A separate attribute study of the "scratch" defect found 78% agreement between inspectors. A control chart of the last 200 flanges shows two points above the upper control limit that no one has explained. A draft slide already circulating says "Cp = 1.33, process capable."
1. In what order should the team address these findings, and what does each finding tell you?
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Order: stability, then measurement, then capability. Capability numbers computed on an unpredictable process or through an unvalidated gage are decoration.
- Special cause first. Two unexplained points above the UCL mean the process is not in statistical control, so its mean and sigma are not predictable. Find the assignable cause (shift change, coil lot, die change) before anything else.
- Variable gage. %GRR of 29% of tolerance is in the marginal-to-unacceptable band by conventional AIAG guidance (under 10% generally acceptable; over 30% unacceptable), and ndc = 3 is below the usual 5-category expectation. Nearly a third of the spec band is consumed by measurement variation, so real part variation cannot be separated from gage noise. Also note the study design: parts from one afternoon spanning 0.15 mm do not represent the process range, so the study should be repeated with parts spanning the expected spread.
- Attribute gage. 78% agreement between inspectors means the scratch definition is not operational. Fix it with limit samples, photo standards and controlled lighting, then re-run the agreement study (with within-rater agreement, not just between).
- Then re-baseline and compute capability.
2. The slide says "Cp = 1.33, process capable." What is wrong with using it, and what do you tell the sponsor?
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Three independent problems:
- Cp assumes stability. With two out-of-control points, the process is not predictable, so a capability index has no meaning. The number describes a process that is not the one running next week.
- Measurement error is inside the number. With %GRR at 29% of tolerance, observed variation is inflated by gage and operator effects. The true capability is unknown - the slide could be understating or overstating it, and there is no way to tell which.
- Cp ignores centering. Cp says nothing about whether the mean sits off target; Cpk does. A "capable" Cp with an off-center mean still produces out-of-spec parts.
Message to the sponsor: "The number is not usable yet - not because the process is bad, but because we measured it with a gage that eats a third of the tolerance, on a process that was moving. Give us two weeks to fix the measurement and find the special cause, then I will give you a number you can defend to the customer."
Also agree in advance which indices will be reported: Cpk for short-term, stable, in-control performance and Ppk for overall, and specify sample size and subgrouping.
3. Write the essential elements of the baseline data collection plan.
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Before collection: re-run the Gage R&R on a validated gage/fixture, obtain acceptable discrimination (ndc ≥ 5), and finalize the scratch operational definition with limit samples.
Plan content:
- What: flange width (variable), scratch count per unit (attribute).
- Definition: measurement location on the flange, gage, fixture, and clamping method; scratch = visible mark ≥ __ mm, per photo standard.
- Sampling: rational subgroups by machine and shift, parts drawn across the full production sequence (not one hour), with the sample target large enough to estimate sigma and detect the current defect level.
- Stratification: machine, shift, die, coil supplier lot, operator, day of week. These are candidate X's and the analysis is only as good as the strata collected.
- Who/where: named collectors trained on the definition, logged directly to a controlled spreadsheet or gage system, not transcribed later.
- Integrity checks: calibration status recorded, duplicate measurements on a sample to confirm reproducibility, and a rule that data collection pauses and the process owner is notified when a special cause appears.
Rule: no capability calculation until the stratification shows the process is stable within each stratum, or the strata are modeled explicitly.