Spatial Risk Assessment: A Case of Multivariate Linear Regression

The acceptance or rejection of a measurement is determined based on its associated measurement uncertainty. This decision-making process inherently carries the risk of errors, including the possible rejection of compliant measurements or the acceptance of non-conforming ones. This study introduces a mathematical model for the spatial evaluation of global risk to both producers and consumers, grounded in Bayes' theorem and with the application of a decision rule incorporating a guard band. The proposed model is well-suited for risk assessment within the framework of multivariate linear regression. The model's applicability was demonstrated through an example involving the flatness of the workbench table surface of the CMM. The least-risk direction on the workbench was identified, and risks were calculated under varying selections of the reference planes and differing measurement uncertainties anticipated in future measurement processes. Model evaluation was conducted using performance metrics derived from confusion matrices. The spaces of the most used metrics over the domain limited by the dimensions of the CMM workbench were constructed. Using the tested metrics, the optimal widths of the guard band were determined, which ensures the smallest values of the global producer's and consumer's risk.