New Generation Geometrical Product Specification (GPS) Backed Flatness Error Estimation and Uncertainty Analysis

Muhammad Ilyas Khan*, Shuyuan Ma
School of Mechanical Engineering, Beijing Institute of Technology (BIT), Beijing, China

© Khan and Ma; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (, which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address  correspondence to  this  author  at   the  School  of  Mechanical  Engineering,  Beijing  Institute of  Technology (BIT),  Beijing,  China; Tel: +8618810324915; Fax: +86 10 68914256; E-mail:


Measurement and verification are one of the prime stages in the entire course of geometrical products in new generation of geometrical product specifications (GPS) standard. Like other kinds of form tolerances, flatness error is one of the important characteristics affecting the functionality and quality of machined components; sufficient efforts have long been made to determine the flatness error close to the true value based on the minimum zone method (MZM) and still needs continual improvement. This paper presents real coded genetic algorithms referred as Efficient Genetic Algorithms (EGA) for flatness error based on minimum zone method having good precision, repeatability and fast convergence rate. This paper also presents evaluation procedure for measurement uncertainty in flatness error based on new generation geometrical product specifications (GPS). Uncertainty in flatness error has been determined and evaluation procedure is provided to prove the conformance or non-conformance by taking into account the uncertainty in measurement. The contributing factors in measurement uncertainties have been identified and then quantified. The flatness error and evaluation theory in this paper are in the framework of new generation GPS standard. Two practical examples have been presented to show the effectiveness of EGA and shed some light on the uncertainty evaluation theory based on new generation GPS standard.

Keywords: Flatness error, genetic algorithms, measurement uncertainty, minimum zone method (MZM), new generation geometrical product specifications (GPS).