Explain what is meant by a tolerance, and explain how a designer decides the tolerance to place on a dimension, referring to function, cost and assembly. [1...

A tolerance is the permitted variation in a stated dimension, expressed using upper and lower limits. It is needed because manufacturing processes cannot make every component at one exact size. [2]

1. Function: the function determines the fit required. A shaft that must rotate freely in a bearing requires clearance at every possible combination of shaft and bearing sizes. A component that must be held firmly requires interference at every combination. The limits must therefore be chosen together, not independently. [3]
2. Cost: a narrower tolerance increases cost because it may need slower, more accurate processes and better machines, more frequent measurement and inspection, and causes more rejected components. A tolerance tighter than the function needs adds cost but no useful performance. [3]
3. Assembly: tolerances can accumulate in a chain of components. Several dimensions that are each within their individual limits may combine to give too much total variation, preventing correct assembly. The designer must allow for this cumulative variation. [2]

The best decision is the widest tolerance that still guarantees the required function and assembly in the worst-case combination of component sizes.