Accuracy and tolerance
Accuracy means how close a made part is to the size on the drawing. No machine or person is perfect, so the designer sets a tolerance: the amount a size may vary and still be acceptable.
- 50.0 ± 0.2 mm: upper limit 50.2 mm, lower limit 49.8 mm.
- Tolerance range = upper limit − lower limit = 0.4 mm.
- Tolerances can be on length, mass, angle, colour shade, or stitch length in textiles (for example 4 ± 0.5 stitches per cm).
Why not make every tolerance tiny?
Tighter tolerances need better machines, slower work and more checking, so cost goes up. Designers make tolerances tight only where parts must fit together (a bearing in a shaft) and looser elsewhere (the outside of a box).
Quality control, quality assurance and TQM
Quality control (QC)
Checking products against the specification by inspection and testing: measuring sizes, checking finish, testing strength. Faulty items are rejected, reworked or recycled. QC finds faults.
Quality assurance (QA)
A system that makes sure quality is built in from the start: agreed standards, approved suppliers, trained staff, written procedures and checks at every stage. QA prevents faults. Firms can be certified to an international standard such as ISO 9001.
Total quality management (TQM)
Every worker is responsible for quality and looks for small improvements all the time (in Japanese, kaizen). Quality circles are small worker groups that meet to solve quality problems.
How to make parts accurately
- Jig: guides the tool so a hole or cut is in the same place every time (a drilling jig).
- Fixture: holds the work firmly in the same position on a machine.
- Template / pattern: a shape you draw or cut round, so every piece has the same outline (paper patterns in textiles).
- Datum: one edge or point all measurements are taken from, so errors do not add up.
- CNC machines and lasers: follow coordinates from CAD, repeat to about 0.01 mm, and do not get tired.
- Marking out with a try square, marking gauge and scriber is more accurate than a pencil.
Measuring and checking
- Steel rule: about ±0.5 mm. Vernier or digital caliper: about ±0.02 mm. Micrometer: about ±0.01 mm.
- Go/no-go gauge: a fixed gauge with two ends at the two limits. A good part goes into the GO end and not the NO-GO end. Fast, and needs no reading.
- Sampling: testing every product is slow and some tests destroy the product, so a sample (for example 1 in 20) is tested and results are plotted to spot trends before parts go out of tolerance.
- Visual checks and test rigs: colour against a shade card, seams pulled on a strength tester, a check-weigher for food packets.
Try it
Measure 10 pencils (or 10 A4 sheets, or 10 coins) with a ruler. Write down the longest and shortest. If the target were the average ± 1 mm, how many would pass? Then use the last 3D step: tighten the tolerance and reduce the machine spread to see the reject rate change.
Key formulas and definitions
- Upper limit = nominal size + tolerance; lower limit = nominal size − tolerance
- Tolerance range = upper limit − lower limit
- Reject rate (%) = rejected parts ÷ parts checked × 100
- A part passes if lower limit ≤ measured size ≤ upper limit
Worked examples
1. A shaft is specified as 25.0 ± 0.1 mm. Give the upper and lower limits and the tolerance range.
Upper 25.1 mm, lower 24.9 mm, range 0.2 mm.
2. Parts measure 25.05, 24.88, 25.10, 25.12 mm with the limits above. Which pass?
25.05 and 25.10 pass (inside 24.9 to 25.1). 24.88 is too small and 25.12 too big, so they fail.
3. A sample of 40 parts has 3 rejects. What is the reject rate?
3 ÷ 40 × 100 = 7.5%.
4. Explain the difference between QC and QA for a T-shirt factory.
QC: inspectors check finished T-shirts for size, stitching and colour and reject faulty ones. QA: the whole system: approved fabric suppliers, trained machinists, written standards and checks after cutting, sewing and printing, so faults are prevented.
Common mistakes
- Thinking ± 0.2 mm means a range of 0.2 mm. The range is from −0.2 to +0.2, which is 0.4 mm.
- Using QC and QA as the same thing. QC inspects products; QA is the system that prevents faults.
- Believing a tighter tolerance is always better. It raises cost and is only needed where parts must fit.
- Measuring every part from the previous mark. Use one datum edge so small errors do not add up.