Aide in decision-making: contribution to uncertainties in three-dimensional measurement

Abstract

International audienceThe authorities of the standards organization International Organization of Standardization (ISO) advocate mastering any uncertainties in all parts of the industrialization process. In the three-dimensional (3D) measurement process, uncertainty is usually obtained at the end of a battery of tests. It is defined as a whole because it includes several types of errors, known systematic components, unknown systematic components and random components. Automated calculations of uncertainty can be made based on statistics. This method is based on statistical concepts, which are in accordance with " The Guide to the expression of the uncertainty in measurement " (GUM). It also enables us to generate uncertainties on the verification of ISO specifications (or specs in the ISO directives). In the course of this article, a usage will be presented that takes the knowledge of uncertainties into account: this usage will help the operator to take a decision on the conformance of a mechanical part in reference to its conformance to geometric tolerance

A robust method for axis identification

“…The knowledge of the covariance matrix makes it possible to define the volume where the estimated axis is found with a given risk. The limit of this volume is defined by the Statistical Confidence Boundary (SCB) [8] which is the "theoretical envelope obtained from first and second statistical moments of the parameters of position and orientation of the best-fitted surface to a given risk ˛" [8]. The dimensions of the SCB of the surface in a local 3D basis are defined by the Eigen analysis of the covariance matrix.…”

An Approach for the Evaluation of Sphericity Error and Its Uncertainty

“…Bachmann et al [13] proposed a method to get the correlation coefficients. In the method, the coefficients were regarded as a statistical vector .…”

“…Hall [12] proposed a computational technique that the uncertainty equation was automatically derived from the measurement function and need not be provided separately. Bachmann et al [13] presented an approach based on statistical concepts, which can generate uncertainties on the veri�cation of ISO speci�cations. �ecently, a calculation method for the uncertainty of spatial straightness least-square veri�cation was proposed in [14].…”

Increasing of surface quality in friction free-form surfaces of knee prosthesis

“…Fig. 10 illustrates the model obtained for such imperfection and its statistical limit envelop computed for two standard deviations [6].…”