Capability Reported with a Questionable Gauge and Stratified Process
A Tier 1 automotive supplier machines aluminum housings. The bore diameter specification is 25.000 ±0.030 mm. The quality engineer reports Cpk = 1.33 from 300 parts, measured by one inspector using a new digital micrometer with 0.001 mm resolution. The customer requires Cpk ≥ 1.67. A gauge study used three operators, ten parts, and three trials; the reported gauge R&R is 28% of tolerance, but the study used parts from a single lot and operators who had practiced together. Data collection used subgroups of five consecutive parts every four hours over three weeks; three raw-material lots and two cutting-tool grades were used. Fourteen parts with obvious burrs were excluded because they were called measurement outliers. The process owner wants to send the Cpk report to the customer and start a capability improvement project. Production is 1,200 parts per day.
1. Evaluate whether the reported Cpk = 1.33 can be used to judge the customer requirement. Identify at least four specific weaknesses.
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The reported Cpk cannot be used as submitted. First, gauge R&R of 28% of tolerance is too high for capability decisions; measurement variation is consuming a large share of the specification and making the index unreliable. The gauge study also used a single lot and operators who had practiced together, so it did not represent production variation or normal operator differences.
Second, the fourteen burred parts were excluded as measurement outliers without evidence. Burrs are real process output; excluding them biases capability upward and hides a possible defect mode. Third, the sampling plan is not suitable for the process structure. Consecutive parts every four hours capture short-term variation but may miss lot-to-lot and tool-grade shifts. A Cpk index assumes a stable process; no control chart stability evidence is presented. Fourth, bias and linearity were not assessed, so the micrometer could be offset across the bore range.
The correct conclusion is that the process may or may not meet 1.67, but the current number is not defensible. The customer report should wait for a valid MSA and a stability check.
2. Design the measurement and data-collection plan you would execute before re-reporting capability. Include sample structure and acceptance criteria.
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First, repeat the MSA with ten production parts spanning the process range, including parts near both specification limits and from all three lots. Use three operators, three trials, random order, and blind measurement. Acceptance: gauge R&R below 10% of tolerance is preferred; below 30% may be conditionally acceptable only with action and a clear statement; number of distinct categories should be at least five. Add bias against a calibrated standard and linearity across the bore range.
If MSA is acceptable, collect a stratified capability study: at least 25 subgroups of five parts, covering all three material lots, both tool grades, and all shifts. Record lot, tool grade, shift, and time. Run an Xbar-R or Xbar-S chart to verify stability. Calculate capability by stratum and overall only if the process is stable; otherwise report Ppk or performance by stratum and investigate the shifts. Do not exclude burred parts; classify them as a separate defect category. Predefine that the customer submission occurs only after MSA acceptance and a stable process with Cpk at or above 1.67.
3. The process owner says, 'Just shift the mean by 0.010 mm and resubmit.' What is your response?
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A mean shift may be a legitimate later action if the process is stable, centered incorrectly, and the measurement system is proven. It is not a valid response to this situation. With gauge R&R at 28% and an unrepresentative study, the reported mean and capability may both be wrong. Excluding burred parts also means the true distribution is unknown.
The first step is to validate the measurement system, then stratify by lot, tool grade, and shift. If the process is unstable, a mean shift will not make it capable. If the process is stable but off-center, centering can be part of the improvement; however, if variation is too large, shifting the mean will simply move defects from one specification limit to the other. A 0.010 mm shift without data could also overrun the upper limit. Tell the customer the truthful status: the original Cpk is not reportable, a valid study is in progress, and containment protects shipments in the interim.