Twelve Overdue Gauges Out of Eighty
During an internal audit of a machining cell, 12 of 80 gauges in use were found without a current calibration sticker; three of them had been used on a safety-critical bore dimension. The cell supervisor proposes to send the 12 gauges out, retrain the two operators, and rewrite the calibration procedure to require a monthly self-check. The audit report lists a minor nonconformity and the corrective action is due in 30 days. The quality manager wants to know how far to push containment, whether the root cause is acceptable, and what evidence will be needed to close the action. The site has 640 gauges in total and a calibration database that is updated only when the metrology clerk processes paperwork.
1. Twelve of eighty is 15%. Give an approximate 95% confidence interval and state what containment the interval supports.
Read the worked answer
Using the normal approximation to the binomial:
- p̂ = 12/80 = 0.15
- SE = sqrt(0.15 × 0.85 / 80) = sqrt(0.001594) = 0.0399
- 95% CI ≈ 0.15 ± 1.96 × 0.0399 = 0.072 to 0.228, i.e. roughly 7% to 23%
(A Wilson or exact interval gives a similar span, about 8.5% to 24.5%; the normal approximation is adequate here.)
What this means for containment. Across 640 gauges, a rate between 7% and 23% implies something like 45 to 145 gauges potentially out of calibration - not 12. The 12 found are a sample, not the population. Therefore:
- Containment cannot be limited to the 12. Perform a 100% verification of the gauge population, starting with the machining cell and any cell sharing the same crib or calibration route, then the site.
- Product containment: every dimension measured with a gauge past its due date since that date must be identified and either re-measured with a verified gauge or formally risk-assessed. The safety-critical bore is first and should be handled as a potential product nonconformity, not as an audit finding.
- The safety-critical items probably justify escalation of the classification, since the finding has product impact and not just documentation impact.
2. Is 'the operator forgot to check the sticker' an acceptable root cause? What root cause would you require before accepting a corrective action?
Read the worked answer
No. It restates the symptom, cannot be verified, and cannot be reversed by any action other than training - which is why retraining the two operators is not a corrective action. It also fails to explain why 12 gauges failed across a cell with more than two users.
A root cause must be specific, causal and testable. The evidence in the setup points to a system cause: the calibration database is updated only when the metrology clerk processes paperwork, so the due-date list is not the same as the physical gauge population, and nothing prevents an overdue gauge from being issued or used. A defensible root-cause statement looks like:
Gauges are released from the tool crib and returned to service without any check against the calibration due date, and the calibration database is reconciled only when paperwork is processed, so the system has no reliable record of which physical gauges are overdue and no barrier at the point of use.
Corrective actions that follow:
- A physical-to-record reconciliation of all 640 gauges, then a periodic one.
- A hold at the point of issue: no gauge leaves the crib without a scan against the due date.
- A visual due-date indicator on the gauge itself, and colour-coding by recalibration month.
- Escalation or blocking of the gauge in the calibration database when it passes its due date.
Retraining may be a supporting action, but the acceptance criterion for the action is that the system, not the operator's memory, prevents use of an overdue gauge.
3. The effectiveness check samples 60 gauges after 60 days and finds none overdue. Is that sufficient evidence to close the corrective action?
Read the worked answer
Partially. It is real evidence, but it is not sufficient on its own.
What the data support. With 0 findings in 60, the rule of three gives a 95% upper confidence bound of about 3/60 = 5%. So the data are consistent with an overdue rate anywhere from 0% to 5%.
- Against the 15% baseline (95% CI 7%–23%), a 5% upper bound is a genuine and statistically meaningful improvement. The corrective action demonstrably reduced the failure rate.
- It cannot demonstrate zero, and 60 out of 640 is small enough that a failing cell could be missed entirely. If the failures were clustered by cell or by crib, a random 60 may sample mostly from the cells that were already fine.
What closure should require instead, or in addition:
- A process measure rather than an attribute sample: 100% automated reconciliation of the 640-gauge database against the physical crib, with a target of zero unresolved discrepancies - this tests the mechanism, not a sample of its output.
- A monthly trend chart of the count of overdue gauges, with the acceptance criterion set in advance (for example, zero overdue in two consecutive full-population audits).
- An audit of the point-of-use control: attempt to withdraw an overdue gauge from the crib and confirm the system blocks it. A control that has never been tested has not been verified.
- Confirmation that product containment from the original finding is complete and that the safety-critical bore has been dispositioned.
Set the effectiveness metric and the sample size before the action is implemented; choosing them after the result is known is how CAPA verification becomes paperwork.