Two Micrometers, Two Answers, Thirty-Eight Rejects
A turned shaft is specified at 25.000 +/- 0.015 mm and is checked 100% with hand micrometers at the machine. Two operators measured the same five parts twice each. Operator A read part 1 as 24.994 and 24.996; Operator B read the same part as 24.988 and 24.990. The pattern repeats on every part: B reads consistently about 0.006 mm lower than A, while each operator repeats their own readings within 0.002-0.004 mm. Over the past week, 38 parts were rejected by B and 4 by A, and B's rejects cluster at the low limit. The production superintendent wants to raise the process mean by 0.006 mm to 'make the rejects go away.'
1. What do the numbers say? Is this a process problem or a measurement problem?
Read the worked answer
Put the numbers in tolerance units - that is what makes the diagnosis obvious:
- Repeatability (within one operator, same part): 0.002-0.004 mm, which is 7-13% of the 0.030 mm tolerance. That is acceptable.
- Reproducibility/bias (between operators): 0.006 mm, which is 20% of the tolerance - and it is a consistent offset on every part, in both trials, in the same direction.
A consistent offset is bias, not variation. Variation would show up as scattered readings; a fixed 0.006 mm gap that follows the operator and not the part points to the measurement system: an out-of-calibration micrometer, a different zero/setting master, measuring force (ratchet vs thimble), part temperature, cleanliness, or measuring over a different axial location on the taper.
The reject counts corroborate it: 38 vs 4 rejects, clustered at the low limit, is exactly the signature of one gauge reading low. The process is not moving; one of the two readings is wrong, and nobody knows which yet.
2. Why is raising the process mean by 0.006 mm the wrong fix?
Read the worked answer
It treats a measurement offset as if it were a process offset, and it has three failure modes:
- It hides the problem instead of correcting it. If B's micrometer is reading 0.006 low and the mean is raised by 0.006, B's parts will look centered - but A's parts will now read near the high limit, and A will start rejecting on the high side. The reject population moves; it does not shrink.
- It makes the true process off-center. If B is the accurate gauge and the process really is centered at 25.000, raising the mean 0.006 puts the true mean at 25.006, only 0.009 from the upper spec - about a third of the tolerance consumed to compensate for a gauge error.
- It destroys traceability. Both operators' records now mean different things, and any customer or audit data from this period is unusable.
The correct order of operations is always: qualify the measurement system, then judge the process. Adjusting the process to satisfy a bad gauge guarantees you will adjust it again.
3. Give the action plan, including what to do about the parts already accepted and rejected this week.
Read the worked answer
1. Stop the bleeding. Pull both micrometers from service and verify them against a certified setting master or gauge blocks at the size used. Replace or recalibrate the one that is off; identify the source of error (calibration due date, dropped tool, worn spindle, setting-master error) rather than just re-zeroing.
2. Qualify the measurement system properly. Run a formal gauge R&R - typically 10 parts spanning the tolerance, 3 operators, 3 trials, randomized order. Targets: %GRR of 10% or less is good, up to 30% may be acceptable for non-critical characteristics; anything above that cannot be used to disposition product against a 0.030 mm tolerance. Also standardize the method: measuring force, number of points, part temperature soak, cleanliness, and a written procedure.
3. Reinspect with the corrected system. Any part measured by the suspect gauge that fell within 0.006 mm of either limit must be re-measured. That is the entire low-limit reject group plus a band of accepted parts - a defined, finite population, not a general panic.
4. Close the loop. Record the escape in the corrective-action system, add gauge verification to the start-of-shift checklist, and confirm that final inspection/Q.A. was not also using the same out-of-calibration method.