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In engineering, tolerance is the permissible limit of variation in 1) a physical dimension, 2) a measured value or physical property of a material, manufactured object, system, or service, or 3) other measured values (such as temperature, humidity, 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.

Contents 1 Engineering tolerances 2 Electrical component tolerance 3 Mechanical component tolerance 4 Considerations when setting tolerances 5 An alternative view of tolerances 6 See also 7 References

The tolerance may be specified as a factor or percentage of the nominal value, a maximum deviation from a nominal value, an explicit range of allowed values, be specified by a note or published standard with this information, or be implied by the numeric accuracy of the nominal value. Tolerance can be symmetrical, as in 40±0.1, or asymmetrical, such as 40+0.2/−0.1.

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.

However exacting the requirements, there will always be an acceptable tolerance; an exact value is totally meaningless in most cases. What do we mean by, say, a diameter of 1 mm exactly? Is it permissible to add or remove a couple of atoms? What about thermal expansion or contraction? Wear? Do we mean as accurately as we can measure with a micrometer in a machine shop? Or must it be accurate within a fraction of a wavelength of light, for optical use?

Tolerance is different from safety factor, but an adequate safety factor will take into account relevant tolerances as well as other possible variations.

An electrical specification might call for a resistor with a nominal value of 100 Ω (ohms), but will also state a tolerance such as "±1%". This means that any resistor with a value in the range 99 Ω to 101 Ω is acceptable. For critical components, one might specify that the actual resistance must remain within tolerance within a specified temperature range, over a specified lifetime, and so on.

Many commercially available resistors and capacitors of standard types, and some small inductors, are often marked with coloured bands to indicate their value and the tolerance. High-precision components of non-standard values may have numerical information printed on them.

Dimensional tolerance is related to, but different from fit in mechanical engineering, which is a designed–in clearance or interference between two parts. For example, if a shaft with a nominal diameter of 10 millimeters is to have a sliding fit within a hole, the shaft might be specified with a tolerance range from 9.964 to 10.000 millimeters and the hole might be specified with a tolerance range from 10.04 to 10.076 millimeters. This would provide a clearance fit of somewhere between 0.04 millimeter (largest shaft paired with the smallest hole) and 0.112 millimeter (smallest shaft paired with the largest hole). In this case the size of the tolerance range for both the shaft and hole is chosen to be the same (0.036 millimeter), but this need not be the case in general.

When designing mechanical components, standardized tolerances are often used. The standard (size) tolerances are divided into two categories: hole and shaft. They are labeled with a letter (capitals for holes and lowercase for shafts) and a number. For example: H7 (hole) and h7 (shaft). H7/h6 is a very common standard tolerance which gives a rather tight fit, but not so tight that you can't put the shaft in the hole by hand. The tolerances work in such a way that for a hole H7 means that the hole should be made slightly larger than the base dimension (in this case for an ISO fit 10+0.015-0, meaning that it may be up to 0.15mm larger than the base dimension, and 0mm smaller). The actual amount bigger/smaller depends on the base dimension. For a shaft of the same size h6 would mean 10+0-0.009, which is the opposite of H7. This method of standard tolerances is also known as Limits and Fits and can be found in ISO 286-2 (Link to ISO catalog).

An analysis of fit by Statistical interference is also extremely useful: It indicates the frequency (or probability) of parts properly fitting together.

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.

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.

Some people (Genichi Taguchi, and others), suggest that traditional two-sided tolerances are analogous to "goal posts" in a football game: It implies that all data within those tolerances are equally acceptable. The alternative is that best product has a measurement which is precisely on target. There is an increasing loss which is a function of the deviation or variability from the target value of any design parameter. The greater the deviation from target, the greater is the loss. This is described as the "Taguchi loss function" or "quality loss function".

• process capability
• Specification (technical standard)
• statistical process control
• Taguchi methods
• Tolerance stacks
• Verification and Validation‎

• Pyzdek, T, "Quality Engineering Handbook", 2003, ISBN 0824746147
• Godfrey, A. B., "Juran's Quality Handbook", 1999, ISBN 007034003
• ASTM D4356 Standard Practice for Establishing Consistent Test Method Tolerances