Engineering & Technology · Production Metrology, Tolerances & Assembly

Inspection methods, measurement systems and uncertainty

A result of 50.08 mm appears to lie inside a 49.90–50.10 mm specification. A second line on the report gives expanded uncertainty U = 0.04 mm. The central number and the specification have not changed, but the decision now needs more care than comparing two printed decimals.

Use Measurement, Units & Engineering Evidence and Sketches, Models & Technical Communication for measurement and drawing ideas. Manufacturing Processes supplies context for process choices; the chapter explains its own elementary limit and stack calculations. These are original teaching cases, not drawing-standard compliance claims or equipment specifications.

Back to the chapter

After reading, you can

Choose inspection evidence for the actual feature and interpret a near-limit result using an explicitly stated decision rule.

Match the method to the feature

Inspection may use contact or optical measurements, coordinate data, functional gauges or other methods appropriate to the requirement. Their outputs answer different questions. A functional gauge may address a selected mating condition; a coordinate dataset may support a defined calculation of size or position. Neither label alone explains the complete measurement process.

Define the measurand, references, sampling locations, support and environmental conditions. Include the procedure for obtaining the reported value from observations. Display resolution, repeatability, calibration and a result’s uncertainty describe different aspects of the system. A finely divided display is not evidence that all of them are small.

A central value is not the entire result

For this constructed exercise, suppose A is reported as 50.00 mm and B as 50.08 mm, each with U = 0.04 mm and coverage factor k = 2. Treat that U as supplied information. The figure shows the associated expanded intervals; it does not assert a guaranteed range of true values or derive a coverage probability from k alone.

Choose an illustrative conservative rule: accept under this classroom rule only when the entire reported expanded interval lies within the specification; otherwise collect further evidence or use the documented disposition process. A meets that chosen criterion. B’s interval extends to 50.12 mm, so it does not. This is a stated teaching decision rule, not a universal standard or a claim that B is certainly nonconforming.

The classroom specification is 49.90–50.10 mm. A is 50.00 mm with assumed expanded uncertainty U0.04 mm (k2), plotted 49.96–50.04. B is 50.08 mm with the same U, plotted 50.04–50.12. The intervals are uncertainty statements under a supplied model, not guaranteed bounds on true values.

Record temperature and the correction model

Dimensions can depend on temperature. In a simple supplied linear-expansion model, a 100 mm length with coefficient 12 × 10⁻⁶ K⁻¹ changes by 100 × 12 × 10⁻⁶ × 20 = 0.024 mm over a 20 K increase. The coefficient and constant-coefficient assumption are invented inputs for this calculation, not a recommendation for a named material.

That possible shift is large enough to matter in a close dimensional comparison. It is not itself the uncertainty of the result. Actual evaluation must consider the material, temperature information, correction model and their uncertainties, along with other important contributors. Preserve raw observations and the applied method so the reported result can be reconstructed.

Apply one declared rule without claiming certainty

A’s expanded interval is 50.00 − 0.04 = 49.96 mm to 50.00 + 0.04 = 50.04 mm. It lies within 49.90–50.10 mm. B gives 50.04 to 50.12 mm and crosses the upper specification limit by 0.02 mm.

Under our stated containment rule, A is accepted and B needs follow-up. The conclusion depends on that rule and the supplied uncertainty statements. It does not turn uncertainty intervals into certain physical bounds, establish every product requirement, or authorise changing the specification after seeing the result.

Try the reasoning

Does a central value inside the limits settle every inspection decision?
Show the answer and reasoning
No. The measurement evidence and the agreed decision rule matter, particularly near a specification limit.
Is U = 0.04 mm a drawing tolerance?
Show the answer and reasoning
No. U is the supplied expanded measurement uncertainty. The specification limits separately describe permitted product variation.
Does the 0.024 mm expansion calculation give a measurement uncertainty?
Show the answer and reasoning
No. It is a predicted change under a supplied model. The uncertainty of a corrected result needs evaluation of the relevant inputs and other contributors.

What to carry forward

Define the feature, method, conditions and decision rule. Keep uncertainty, predicted corrections and product tolerances distinct.

References

Teaching resources and research supporting this lesson’s explanations and examples.