Random uncertainty propagation in estimates of sphere parameters from coordinate measurements

Measurements of reference spheres are widely used in verification and calibration of coordinate measuring systems. In this paper, a model for the propagation of random errors in the estimation of sphere parameters is outlined. The dependence of the error propagation on sampling area and sample density is demonstrated using both simulated and measured data. The model can be used to characterise the random error of a coordinate measurement system. It can also be used to determine the error limits on a single sphere parameter estimate or to determine the required sampling strategy to ensure that the confidence limits on an estimate remain within predetermined bounds.