Micrometer Zero Error and Borderline Pins in a 200-Piece Batch
A batch of 200 turned steel pins is to be supplied to a nominal diameter of 25.00 mm with a tolerance of ±0.05 mm. The inspector uses a 0–25 mm outside micrometer with 0.01 mm graduations and a ratchet stop. When the micrometer is closed on its anvils, it reads +0.02 mm. Ten pins are measured and the readings are: 25.03, 25.06, 24.98, 25.01, 25.04, 24.97, 25.05, 25.02, 25.07 and 24.99 mm. The inspector says all readings are 'within 25.00 ± 0.05' except 25.06 and 25.07, which he wants to scrap. The production supervisor argues that the micrometer zero error is small and the two high readings are 'just at the limit'. The customer requires 100% conformance and asks for the inspection record. You are the quality trainee asked to settle the dispute.
1. Correct the ten readings for zero error and classify each as accept, rework or reject against 25.00 ± 0.05 mm.
Read the worked answer
Zero error +0.02 mm means the micrometer over-reads; true size = reading − 0.02 mm. Corrected values: 25.01, 25.04, 24.96, 24.99, 25.02, 24.95, 25.03, 25.00, 25.05 and 24.97 mm. Limits are 24.95 to 25.05 mm. On corrected values all ten are within limits, so the inspector's scrap decision on 25.06 and 25.07 is wrong: they become 25.04 and 25.05. However, 24.95 and 25.05 sit exactly on the limits. Mark them 'hold for confirmation', not 'accept' or 'reject', because measurement uncertainty can put the true value outside. The result is no rejects from this sample on corrected values, but two borderline parts require re-measurement.
2. Why is it unsafe to accept a reading exactly at the tolerance limit without considering measurement uncertainty? What would you do before signing the record?
Read the worked answer
A reading exactly at the limit is not proof of conformance. The micrometer has its own uncertainty from graduation, anvil flatness, temperature, operator feel and zero error, so the true diameter could be 25.051 or 24.949 mm. Good practice uses a decision rule: guard-band the limit or re-measure with a calibrated instrument of known uncertainty. Before signing, check calibration status, re-zero, measure each borderline pin three times at 20 °C, use a comparator or bore gauge if available, and record raw and corrected values. If it is still at the limit, ask the customer to accept a documented deviation or rework the part. Do not scrap good parts on an uncorrected reading, and do not pass borderline parts silently.
3. The inspector measured only 10 pins from 200. What sampling and documentation would you require for 100% conformance?
Read the worked answer
The customer requires 100% conformance, so a 10-piece sample is not enough evidence for 200 pins. Use 100% inspection with a calibrated micrometer or, better, go/no-go limit gauges for speed, with the micrometer for borderline parts. Record instrument ID, calibration date, zero error, temperature, operator, date, each reading and the accept/reject decision. Segregate accepted, rework and rejected bins. Check first-off, last-off and any reset. If sampling is allowed, use a statistically valid plan agreed with the customer; otherwise 100% inspection is feasible for 200 pieces. Sign the record only after the borderline parts are resolved.