A Capability Study Built on a Worn Gauge and One Cavity
A precision stamping cell produces a bearing seat with a print tolerance of 0.050 mm. The quality engineer reports Cpk = 1.45 from 120 parts collected over three days. The customer reports interference fits at assembly. The measurement system study was done two years ago and showed percent GRR = 31% of tolerance; the gauge is on a two-year calibration cycle and was last calibrated 26 months ago. The 120 parts were all taken from cavity 1 on the night shift, because that shift's supervisor cooperated. The data are mildly skewed, and the engineer calculated Cpk using the overall standard deviation without checking normality. Three operators measure with a handheld micrometer; the fixture is worn. The Black Belt is asked whether the process is capable and whether the team can proceed to Analyze.
1. Assess whether Cpk = 1.45 is trustworthy. Identify each threat and explain its likely effect on the estimate.
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The estimate is not trustworthy for a capability claim. The measurement system has percent GRR = 31% of tolerance, which is too large for a 0.050 mm tolerance; measurement variation consumes a substantial share of the specification and makes any capability index unstable, even if random error tends to attenuate rather than inflate capability. The gauge is 26 months past its two-year calibration, so bias or drift is possible and the direction is unknown. Sampling only cavity 1 on nights omits between-cavity, between-shift, and lot-to-lot variation, so the study likely understates total process variation and overstates Cpk. Using the overall standard deviation instead of a within-subgroup estimate changes the index's meaning: Cpk is conventionally based on within-subgroup sigma, while Ppk uses overall sigma; mixing the two without stating which is reported confuses the claim. Mild skew also violates the normal-based Cpk assumption; the index may misstate the tail area that produces interference fits. The team should not proceed to Analyze as if capability were demonstrated; it should first establish a valid measurement system and a representative, stable baseline.
2. Design a measurement-system and sampling plan before capability is re-estimated. Include sample-size logic, stratification, and acceptance criteria.
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First, calibrate or replace the gauge and repair or replace the worn fixture. Then run a gauge R&R with three operators, ten parts spanning the production range, and three trials per operator, randomized and blinded. Acceptance: percent GRR below 10% of tolerance is preferred; below 30% may be acceptable only with a documented decision rule, and the number of distinct categories should be at least five. If the micrometer cannot meet this, change the measurement method, for example a fixture-mounted comparator. For capability, first demonstrate stability with a control chart using rational subgroups across shifts and cavities. Then sample randomly across all cavities, shifts, lots, and operators, with at least 100–125 parts for a capability estimate and enough subgroups to estimate within variation. Stratify by cavity and shift so variance components can be compared. If the data remain non-normal, use a non-normal capability method or transform, and report Ppk alongside Cpk with confidence intervals. Freeze the sampling plan and record the calibration status before collecting the baseline.
3. What should be reported to the customer now, before the new study is complete?
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Report that the previously reported Cpk = 1.45 is not supported by a valid measurement system or representative sampling, so the process capability is currently unproven. Do not simply retract the number without a containment action: state that the team is containing suspect product through increased inspection or sorting at the bearing-seat interface, and provide the containment scope and exit criteria. Share the root causes of the data invalidity: overdue calibration, 31% GRR, single-cavity night-shift sampling, and normal-model misuse. Commit to a dated plan for calibration, gauge R&R, stratified sampling, and a re-estimated capability with confidence intervals. If the customer requires a capability number immediately, present the old estimate only as an unverified historical value and explain why it cannot be used for acceptance. The message should separate product containment from process capability: containment protects the customer now; the new study will determine whether the process can meet the 0.050 mm tolerance.