Accuracy, Resolution, and Decision Rules on Incoming Inspection
A supplier's inspection certificate for machined bushings lists "accuracy: ±0.5 mm" and "resolution: 0.01 mm." The drawing calls for an outside diameter of 25.00 ± 0.30 mm. Incoming inspection uses a digital caliper with 0.01 mm resolution; ten repeat readings on a certified 25.000 mm gauge block give a mean of 25.04 mm and a range of 0.04 mm. Ten readings on a production bushing give a mean of 25.28 mm and a range of 0.06 mm. The inspector plans to reject the lot, arguing that the supplier's ±0.5 mm "accuracy" means any result within 0.5 mm of the limit is unreliable, and that the caliper's 0.01 mm resolution makes the 25.28 mm reading definitive. The customer's contract is silent on decision rules. The supplier disputes the rejection and asks for the basis of the decision.
1. Distinguish accuracy, resolution, uncertainty, and error as they apply to this measurement, and identify the inspector's conceptual mistakes.
Read the worked answer
Accuracy is the closeness of a measured value to the true value; it is a qualitative concept unless expressed as a bias with an uncertainty. Resolution is the smallest change the instrument can display, here 0.01 mm. Resolution is not accuracy: a caliper can display 0.01 mm while being biased by 0.04 mm, as the gauge-block check shows. Uncertainty is a quantified interval that characterizes the dispersion of values attributable to the measurement, including repeatability, bias correction, resolution, and reference-standard uncertainty. Error is the difference between a measured value and the true value.
The inspector makes three mistakes. First, the supplier's "accuracy: ±0.5 mm" is a specification or tolerance statement, not the measurement uncertainty of the caliper, and it cannot be transferred to the inspection result. Second, the 0.01 mm resolution does not make 25.28 mm definitive; repeatability and bias still apply. Third, rejecting because a result is within 0.5 mm of a limit confuses the supplier's product tolerance with the inspection measurement uncertainty. The relevant questions are whether the caliper is fit for the 0.60 mm tolerance width and what decision rule the parties will use.
2. Apply a defensible decision rule to the 25.28 mm result and recommend how to resolve the dispute.
Read the worked answer
First correct the known bias. The gauge-block mean is 25.04 mm against 25.000 mm, so the caliper reads about 0.04 mm high. The corrected bushing mean is approximately 25.28 - 0.04 = 25.24 mm. The tolerance limits are 24.70 mm and 25.30 mm. The repeatability standard deviation can be estimated from the range: for n = 10, s ≈ 0.06 / 3.078 ≈ 0.0195 mm. The standard uncertainty of the mean is about 0.0195 / √10 ≈ 0.006 mm. Including resolution (0.01 / √12 ≈ 0.003 mm) and the gauge-block uncertainty, a reasonable expanded uncertainty is on the order of 0.04 mm (k = 2).
Using a guard-banded decision rule, the acceptance limit becomes 25.30 - 0.04 = 25.26 mm. The corrected mean of 25.24 mm is below that limit and conforms, but the margin is only about 0.02 mm. Without bias correction, 25.28 mm would exceed the guard band and the result would be indeterminate, not a clear rejection. The parties should agree in writing on the decision rule, the bias correction, and the uncertainty budget. If the contract requires simple acceptance, 25.28 mm is still below 25.30 mm, but the measurement risk near the limit should be acknowledged. A second measurement with a higher-accuracy micrometer would be the most defensible resolution.