The maximum and minimum limit values a product can have and still meet customer requirements.
Tolerance is the permissible limit or limits of variation in:
1. a physical dimension,
2. a measured value or physical property of a material, manufactured object, system, or service,
3. other measured values (such as temperature, humidity, etc.).
4. in engineering and safety, a physical distance or space (tolerance), as in a truck (lorry), train or boat under a bridge as well as a train in a tunnel (see structure gauge and loading gauge).
5. in mechanical engineering the space between a bolt and a nut or a hole, etc..
Dimensions, properties, or conditions may vary within certain practical limits without significantly affecting functioning of equipment or a process. Tolerances are specified to allow reasonable leeway for imperfections and inherent variability without compromising performance. A variation beyond the tolerance (for example, a temperature that's too hot or too cold) is said to be non-compliant, rejected, or exceeding the tolerance (regardless of if this breach was of the lower or the upper bound). If the tolerance is set too restrictive, resulting in most objects run by it being rejected, it is said to be intolerant.
It is often desirable to specify the largest possible tolerance while maintaining proper functionality. Closer or tighter tolerances are more difficult, and hence costly, to achieve. Conversely, larger or looser tolerances may significantly affect the operation of the device. A primary concern is to determine how wide the tolerances may be without affecting other factors or the outcome of a process. This can be by the use of scientific principles, engineering knowledge, and professional experience. Experimental investigation is very useful to investigate the effects of tolerances: Design of experiments, formal engineering evaluations, etc.
A good set of engineering tolerances in a specification, by itself, does not imply that compliance with those tolerances will be achieved. Actual production of any product (or operation of any system) involves some inherent variation of input and output. Measurement error and statistical uncertainty are also present in all measurements. With a normal distribution, the tails of measured values may extend well beyond plus and minus three standard deviations from the process average. One, or both, tails might extend beyond the specified tolerance.
The process capability of systems, materials, and products needs to be compatible with the specified engineering tolerances. Process controls must be in place and an effective Quality management system, such as Total Quality Management, needs to keep actual production within the desired tolerances. A process capability index is used to indicate the relationship between tolerances and actual measured production. The choice of tolerances is also affected by the intended statistical sampling plan and its characteristics such as the Acceptable Quality Level. This relates to the question of whether tolerances must be extremely rigid (high confidence in 100% conformance) or whether some small percentage of being out-of-tolerance may sometimes be acceptable.