What is a specification?

According to ISO 9000:2000 a Specification is defined as "a Document stating requirements".
Another definition of Specification is "The engineering requirement for judging acceptability of a particular characteristic. Chosen with respect to functional or customer requirements for the product, a specification may or may not be consistent with the demonstrated capability of the process (if it is not, out-of-specification parts are certain to be made). A specification should never be confused with a control limit"
A specification might contain the ideal measurement, tolerances for these measurements, material type and the processes to be used for manufacturing the product.
Here an example for a Specification of zylindrically shaped shaft:
Material to be used: Steel
Machinery to be used: Lath

Requirement for the Diameter: 1000mm
The minimum Diameter for the shaft is: 995mm
The maximum Diameter for the shaft is: 1005mm
The range were the diameter is allowed to fall in is 10mm. The tolerance therefore is 0.5% .

Specifications might also be given for Service Processes

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