Introduction of robust multivariate process capability indices

Process Capability Indices (PCIs) are essential for evaluating process performance, but their accuracy depends on correctly estimating distribution parameters. Classical methods, such as Maximum Likelihood Estimation (MLE), are highly sensitive to outliers, often leading to misleading conclusions about process capability. To address this issue, this study investigates robust estimation techniques enhancing the reliability of parameter estimation in the presence of contaminated data. Both univariate and Multivariate Process Capability Indices (MPCIs) are reviewed, and robust estimators for multivariate process parameters are investigated. Specifically, M-estimators are applied to define Robust Multivariate Process Capability Indices (RMPCIs), offering a more resilient alternative to traditional approaches. Simulation results and real-world applications confirm that RMPCIs outperform classical MPCIs under outlier contamination, ensuring more accurate and consistent quality assessments. The study demonstrates the practical value of RMPCIs in industrial environments and suggests further exploration of alternative robust estimators.