Abstract
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.
Highlights
When a measurement instrument is purchased from some instrument vendor, the user of the instrument generally requires a guarantee that that instrument will perform in such a way that the measurements produced by that instrument can be trusted
The method is applied to a real test case, where the efficiently determined Maximum permissible errors (MPEs) is overestimated by 0.3% with respect to an MPE determined using an arbitrarily chosen large number of measurements
We propose a method of statistical MPE determination; using the smallest number of repeat measurements of calibrated features possible to determine an MPE in a particular measurement case
Summary
When a measurement instrument is purchased from some instrument vendor, the user of the instrument generally requires a guarantee that that instrument will perform in such a way that the measurements produced by that instrument can be trusted. Trust is established by the rigorous application of specification standards frameworks, which are, in turn, agreed internationally by experts in industry and academia. To this end, in dimensional measurement, the ISO 10360 series [1] is used in the first instance for performance verification of co-ordinate measurement systems [2]. Following the initial performance verification test upon delivery, performance verification is commonly used to periodically check the continued performance of a measurement system. Performance verification relies on checking the test system’s ability to meet certain performance metrics and is not possible if a system has no supplied performance metrics
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