Statistical Approach to Assessments of Geometrical Accuracy

Statistical properties of the minimax assessments of the geometric accuracy are investigated. The cases when a distribution of the point deviations differs from the normal distribution are especially considered. Among such cases, the roundness deviations of the profile, which is composed of few harmonics, is of fundamental importance. A set of the point positions within the minimum zone (MinZ) is considered as a random sampling, and the width of the MinZ presents the sampling range. Range distributions vs. the number of the harmonics, amplitude ratios, and the number of points of measurements are considered. Information about the power spectrum of the measured profile is applied for numerical estimations of the uncertainty through the use of these distributions; this information yields a large dividend in accuracy of the uncertainty assessments. An application example is simulated.