Modelling uncertainty associated with comparative coordinate measurement through analysis of variance techniques

Over the last few years, various techniques and metrological instruments have been proposed to achieve accurate process control on the shop floor at low cost. An efficient solution that has been recently adopted for this complex task is to perform coordinate measurement in comparator mode in order to eliminate the influence of systematic effects associated with the measurement system. In this way, more challenging parts can be inspected in the shop floor environment and higher quality products can be produced while also enabling feedback to the production loop. This paper is concerned with the development of a statistical model for uncertainty associated with comparative coordinate measurement through analysis of variance (ANOVA) techniques. It employs the Renishaw Equator comparative gauging system and a production part with thirteen circular features of three different diameters. An experimental design is applied to investigate the influence of two key factors and their interaction on the comparator measurement uncertainty. The factors of interest are the scanning speed and the sampling point density. In particular, three different scanning speeds and two different sampling point densities are considered. The measurands of interest are the circularity of each circular feature. The present experimental design is meant to be representative of the actual working conditions in which the automated flexible gauge is used. The Equator has been designed for high speed comparative gauging on the shop floor with possibly wide temperature variation. Therefore, two replicates are used at different temperature conditions to decouple the influence of environmental effects and thus drawing more refined conclusions on the statistical significance.