Spatial Risk Assessment: A Case of Multivariate Linear Regression

The acceptance or rejection of a measurement is determined based on its associated measurement uncertainty. In this procedure, there is a risk of making incorrect decisions, including the potential rejection of compliant measurements or the acceptance of non-conforming ones. This study introduces a mathematical model for the spatial evaluation of the global producer’s and global consumer’s risk, predicated on Bayes’ theorem and a decision rule that includes a guard band. The proposed model is appropriate for risk assessment within the framework of multivariate linear regression. Its applicability is demonstrated through an example involving the flatness of the workbench table surface of a coordinate measuring machine. The least-risk direction on the workbench was identified, and risks were quantified under varying selections of reference planes and differing measurement uncertainties anticipated in future measurement processes. Model evaluation was performed using confusion matrix-based metrics. The spaces of the commonly used metrics, constrained by the dimensions of the coordinate measuring machine workbench, were constructed. Using the evaluated metrics, the optimal guard band width was specified to ensure the minimum values of both the global producer’s and the global consumer’s risk.