Application of Order Statistics in the Evaluation of Flatness Error: Sampling Problem

The main purpose of this initial paper is to demonstrate the application of order statistics in the estimation of form error from a CMM measurement. Nowadays, modern industry sets high standards for geometrical precision, surface texture and material properties. There are many parameters that can characterize mechanical part, out of which flatness error plays important in the assembly process and performance. Recently, due to the greater availability and price reduction, Coordinate Measurement Techniques have increased their popularity in the industry for on-line and off-line measurements as they allow automated measurements at relatively low uncertainty level. Data obtained from CMM measurements have to be processed and analyzed in order to evaluate component compliance with the required technical specification. The article presents an analysis of a minimal sample selection for the evaluation of flatness error by means of coordinate measurement. In the paper, a statistical approach was presented, assuming that, in the repetitive manufacturing process, the distribution of deviations between surface points and the reference plane is stable. Based on the known, statistical distribution, order statistics theorem was implemented to determine maximal and minimal point deviation statistics, as it played a dominant role in flatness error estimation. A brief analysis of normally distributed deviations was described in the paper. Moreover, the case study was presented for the set of the machined parts which were components of a machine tool mechanical structure. Empirical distributions were derived and minimal sample sizes were estimated for the given confidence levels using the proposed theorem. The estimation errors of flatness values for the derived sample sizes were analyzed and discussed in the paper.