A Micrometer With a Known Error, a Marginal Reading, and a Failing Gage R&R
A machinist checks shafts of 25.000 ± 0.015 mm on the shop floor with a 0-25 mm micrometer with 0.001 mm resolution and manufacturer accuracy of ±0.004 mm. The annual calibration certificate has just returned showing an as-found error of +0.007 mm at the 25 mm point; the three previous cycles were +0.002, +0.003, and +0.004 mm. The calibration laboratory states U = 0.003 mm at k = 2. A gage R&R study on this characteristic produced EV = 0.008 mm and AV = 0.005 mm using ten parts. One shaft reads 25.013 mm and the operator wants to accept it; another reads 25.017 mm and is about to be scrapped. Production is 900 shafts per day and every shaft is measured once, by hand, with no second check.
1. Evaluate the measurement system against the 0.030 mm tolerance. What are the dominant components and what do you do first?
Read the worked answer
GRR and percent of tolerance:
- GRR = square root of (EV squared + AV squared) = square root of (0.008 squared + 0.005 squared) = square root of (0.000064 + 0.000025) = square root of 0.000089 = 0.0094 mm
- Percent of tolerance = 0.0094 / 0.030 = 31.4%
Verdict: above 30% of tolerance is unacceptable under the usual MSA convention (under 10% acceptable; 10-30% conditional, subject to the importance of the characteristic and the cost of the gage). This is a general dimensional characteristic measured at the point of decision, so there is no case for calling 31% conditional.
Dominant component: EV (repeatability, 0.008) is larger than AV (reproducibility, 0.005) - the variation is in the gage and the technique, not in operator-to-operator differences. Look at anvil and spindle face flatness and parallelism, spindle friction and ratchet use, clamping force, cleanliness of the faces, and part temperature versus gage temperature. A hand micrometer on a warm part from a machining centre will show repeatability of this size; let the part and gage equalize and re-run the study.
Resolution check: 0.001 mm is 1/30 of the tolerance, which is fine; resolution is not the problem.
A separate and more urgent finding: the as-found error of +0.007 mm exceeds the manufacturer's accuracy specification of ±0.004 mm. The gage was out of tolerance in service. That is a calibration failure requiring an impact assessment on product measured since the last known-good calibration, not just an adjustment. Note also that U = 0.003 mm from the laboratory is 10% of the tolerance and is small compared with the 0.0094 mm GRR - the calibration laboratory is not the weak link; the shop-floor measurement is.
2. The gage has been adjusted and is now reading true. Decide what should happen to the two shafts, and state the decision rule you are applying.
Read the worked answer
First, separate the records. Readings taken before the adjustment carry the +0.007 correction and readings taken after do not. If the two sets are mixed in the inspection records, every downstream decision on those parts is unreliable. This is a traceability problem, not a metrology problem, and it is why the adjustment must be dated and flagged in the record.
Apply the correction to pre-adjustment readings: true value = reading minus 0.007 mm.
- Shaft reading 25.013: true value about 25.006 mm. Inside the limits of 24.985 to 25.015.
- Shaft reading 25.017: true value about 25.010 mm. Also inside the limits.
So scrapping the 25.017 shaft is a wrong decision - it is a good part, and the error is in the measurement, not the part.
Now the decision rule. A reading of 25.006 mm is not the same as knowing the shaft is 25.006 mm. With GRR of 0.0094 mm, a guard band is required if you want to control the risk of accepting out-of-tolerance product. Using the measurement uncertainty as the guard band, the accept zone becomes 25.000 ± (0.015 - 0.0094), i.e. about 24.9944 to 25.0056 mm. The 25.006 mm true value sits right at the edge of that zone, and the 25.010 mm value is outside it.
Judgement to state: with a 31% GRR, this measurement system cannot resolve a 0.030 mm tolerance on a single reading. Both shafts are in the "cannot decide" band. Re-measure with a better system (comparator stand, air gage, or multiple readings averaged with the part at 20 °C) before accepting or scrapping either one, and record the decision rule you used so the choice of guard band is not made case by case by the operator.
3. Review the calibration history. What interval and systemic actions do you recommend, and what evidence supports them?
Read the worked answer
The trend: +0.002, +0.003, +0.004, +0.007 mm at successive annual calibrations. The last step is +0.003 mm in one year, against an accuracy allowance of ±0.004 mm. At that drift rate the gage exceeds its own specification about 16 months after a zeroed calibration - before the next annual due date. A 12-month interval is therefore too long on the evidence, not as a matter of opinion.
Recommendations:
- Shorten the interval, e.g. to 6 months, then review. Take the first two 6-month results and lengthen again only if the as-found error stays small - intervals should be set by observed drift, not by habit or by the manufacturer's default.
- Set an as-found acceptance limit tied to the gage's accuracy specification (±0.004 mm here) and define what happens on a fail: adjust, tag, and trigger the impact assessment. Passing a calibration after adjustment is not the same as having been in tolerance in service.
- Do the impact assessment on product measured during the out-of-tolerance window: identify the serial/lot range, the characteristic, and whether any reading fell in the guard band. With a +0.007 error the measurement was biased high, so parts near the upper limit may have been wrongly scrapped (cost) and parts that read conforming at 25.015 and below may actually have been up to 25.022 (risk).
- Fix the interval-change process, not just this gage: the fact that every micrometer in the crib may be on the same 12-month default is a system finding. Stratify the recall list by drift history.
- Reduce the manual single-reading exposure. At 900 shafts/day measured once by hand with 31% GRR, a fixture-mounted comparator or an in-process gage removes operator technique from the measurement and is likely cheaper than the scrap and escapes it is causing.