A Note on the Multivariate Process Capability Index MCpm

Important features of multivariate process capability indices are comparability, interpretability and ease of implementation. When poor process capability is indicated by an index, the user should determine why the process is incapable (e.g. excessive variability or off‐target process mean). One of the most used multivariate process capability indices is MCpm because it provides assessments of process precision and accuracy. In this work, we study and discuss a peculiarity of MCpm: processes that are equivalent in terms of precision, accuracy and MCpm index, after the occurrence of the same increase in the process variability, can have different values of the index. Because MCpm is often used for comparing processes, this behaviour may cause comparability difficulties. Therefore, we suggest how to take into account this specific behaviour for avoiding erroneous conclusions.