Relational Structure of Measurement with Application on Specification of Freeform Surface

A contradiction is shown in this paper that, for contact surface measurement, if a measured surface profile is exactly coincident with the USL (upper specification limit), the measured result may still be out of specification. To understand and avoid this contradiction, a relational construction of measurement is proposed bases on the representational measurement theory. By observing the connection between measurement and inverse problem, measurement is modeled as a mapping from the preordered set of measurands (objects to be measured) to the partially ordered set of measured values. Thereby, a desired property of the specifications limits is derived, and a correction of the USL of surface profile is proposed.