Considering the effects of tolerance, calculating the maximum and minimum acceptable values from a stated tolerance, and deciding whether a given measurement lies within the acceptable range.

What this dot point is asking

The SQA wants you to consider the effects of tolerance: understand what a stated tolerance means, calculate the maximum and minimum acceptable values, and decide whether a given measurement lies within the acceptable range.

What tolerance means

Tolerance is the acceptable variation around a target measurement. Nothing can be made or measured perfectly, so a tolerance states how far from the target a value is still allowed to be. It recognises that real manufacturing always has small variations, and that a part does not have to be exactly right to work, only close enough. Setting a sensible tolerance is a balance: too tight and too many good parts are rejected, too loose and parts that do not fit get through.

Tolerance is sometimes stated as a range rather than with the $\pm$ symbol, for example "between $19.5$ mm and $20.5$ mm", which means exactly the same thing. The width of the whole acceptable band is twice the tolerance, here $1$ mm, so a tighter band corresponds to a smaller tolerance value.

Deciding whether a value is within tolerance

Once you have the maximum and minimum, checking a measurement is a comparison: it is acceptable if it falls within the range, and rejected if it does not.

Examples in context

Tolerance is central to manufacturing and quality control: a machined part must fit its housing, a packaged food must be close to its labelled weight, a printed sheet must be the right size. Each rests on calculating the acceptable range from the target and tolerance, then judging whether a measurement falls inside it, the skills here. A tighter tolerance gives a better fit but is harder and costlier to achieve, a trade-off the SQA may ask you to consider.

In a quality-control check, several items are measured and you count how many pass and how many are rejected, which links tolerance to the statistics and proportion work elsewhere in the course. For example, if $3$ of $20$ parts fall outside tolerance, the reject rate is $\tfrac{3}{20} = 15\%$, a figure a factory would want to reduce by tightening its process rather than its tolerance.

Try this

Q1. A part is $30 \pm 0.4$ mm. State the maximum and minimum acceptable lengths. [2 marks]

• Cue. Maximum $30.4$ mm, minimum $29.6$ mm.

Q2. A drink is $250 \pm 5$ ml. Is a bottle of $256$ ml within tolerance? [2 marks]

• Cue. Range $245$ to $255$ ml; $256$ ml is outside.

Q3. A bar is $12 \pm 0.2$ cm. Is a bar of $11.9$ cm within tolerance? [2 marks]

• Cue. Range $11.8$ to $12.2$ cm; $11.9$ cm is within.