The paper concerns the analysis and the design of the measurement process by which position tolerances on mechanical parts are checked using Coordinate Measuring Machines (CMM). This measurement process is widely used in industry to guarantee the good functioning of millions of components and assemblies. The analysis aims to evaluate measurement uncertainty as generated by both the random error related to coordinate retrieval and the sampling error inherent to CMMs. By simulating random error via computer, the measurement process is fully recreated. Then an extensive computer experimentation, combining Montecarlo simulation and Design of Experiment (DoE), is performed. The study has revealed interesting statistical properties of the two-dimensional position error with useful practical implications, disproving a number of rules of thumb accepted by engineers. Another contribution is the use of the uncertainty analysis to design an efficient measurement process.
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