Verifying a Coating Thickness Gauge Against a Certified Shim
A technician verifies an eddy-current coating thickness gauge using a certified shim of 50.0 µm with an expanded uncertainty of ±1.0 µm (k = 2). Ten readings give a mean of 52.3 µm and a standard deviation of 2.1 µm. The gauge specification is ±3% of reading, and the product specification is 50 ± 8 µm. The technician calculates the standard error as 2.1/√10 = 0.66 µm, notes that the difference from the shim is 2.3 µm, which is larger than the standard error, and concludes that the gauge is out of tolerance and should be withdrawn. The production supervisor points out that individual readings on product range from 47 µm to 55 µm and asks whether the gauge can still be used for acceptance. The laboratory has no other gauge available, and a shipment is due.
1. Evaluate the technician's statistical reasoning about bias, standard error, and gauge acceptance.
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The technician is comparing the wrong quantities. The standard error of 0.66 µm describes the uncertainty of the mean of ten readings, not the expected scatter of a single measurement and not the gauge bias. The observed difference of 2.3 µm is a bias estimate. To test whether it is statistically significant, use a t-test: t = 2.3 / 0.66 ≈ 3.45 with 9 degrees of freedom. The critical value at 95% confidence is about 2.26, so the bias is statistically significant. Statistical significance, however, does not by itself establish fitness for purpose.
The gauge specification is ±3% of reading; at 50 µm that is ±1.5 µm. The observed bias of 2.3 µm exceeds that specification before considering the shim uncertainty, so the gauge is out of its manufacturer's tolerance and should not be treated as fully conforming. The technician's conclusion that it should be withdrawn is directionally reasonable for a calibrated reference instrument, but the supervisor's question is different: can it still be used for product acceptance? That depends on the product tolerance and the measurement uncertainty, not on the gauge specification alone.
2. Determine whether the gauge is fit for accepting product at 50 ± 8 µm, and recommend a defensible path forward.
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The product tolerance is 42 µm to 58 µm, a width of 16 µm. The gauge's single-measurement standard deviation is 2.1 µm. Combining repeatability with the shim uncertainty (0.5 µm standard) gives a standard uncertainty of about √(2.1² + 0.5²) ≈ 2.16 µm, and an expanded uncertainty of about 4.3 µm at k = 2. The test uncertainty ratio is approximately 16 / 4.3 ≈ 3.7, which is marginal but not disqualifying for many industrial acceptance decisions. If the 2.3 µm bias is corrected, the gauge can support acceptance decisions away from the limits.
However, the bias must be corrected and the correction documented. With a guard band of 4.3 µm, the acceptance limits become about 46.3 µm and 53.7 µm. Product readings from 47 µm to 55 µm include values above 53.7 µm, so parts near the upper limit are indeterminate and cannot be accepted on this gauge without further evidence. The defensible path is: correct the bias, verify with the shim and a second thickness, use guard-banded acceptance, and retest near-limit parts with a higher-accuracy method. The gauge may be used for screening or for product well inside the limits, but not for final acceptance of near-limit parts. Record the verification, bias correction, uncertainty budget, and the decision rule so the shipment decision is transparent.