Efficient empirical determination of maximum permissible error in coordinate metrology

Maximum permissible errors (MPEs) are an important measurement system specification and form the basis of periodic verification of a measurement system's performance. However, there is no standard methodology for determining MPEs, so when they are not provided, or not suitable for the measurement procedure performed, it is unclear how to generate an appropriate value with which to verify the system. Whilst a simple approach might be to take many measurements of a calibrated artefact and then use the maximum observed error as the MPE, this method requires a large number of repeat measurements for high confidence in the calculated MPE. Here, we present a statistical method of MPE determination, capable of providing MPEs with high confidence and minimum data collection. The method is presented with 1000 synthetic experiments and is shown to determine an overestimated MPE within 10% of an analytically true value in 99.2% of experiments, while underestimating the MPE with respect to the analytically true value in 0.8% of experiments (overestimating the value, on average, by 1.24%). The method is then applied to a real test case (probing form error for a commercial fringe projection system), where the efficiently determined MPE is overestimated by 0.3% with respect to an MPE determined using an arbitrarily chosen large number of measurements.