A practical insight into multivariate process capability indices

Process capability indices are commonly used to summarize a process’s capability based on a single quality characteristic. However, modern production processes usually involve multivariate and often correlated quality characteristics, rendering univariate indices insufficient to fully assess the capability of a process. This has led to the development of multivariate process capability indices (MPCI). Even though various index formulations have been proposed in the literature, they differ greatly in their approach, interpretation and sensitivity to the parameters such as the “non-centeredness” of the process and the number of the quality characteristics as well as their correlation structure. In this Quality Quandaries, we examine a selection of the available MPCI. We then conduct a sensitivity analysis to examine how these indices respond to changes in certain process parameters. Finally, we illustrate these findings using a case study and emphasize the need for careful interpretation when applying MPCI in practice.