Multivariate process capability analysis with decision-maker preferences

Abstract

A process capability analysis is an invaluable technique for assessing the efficacy of a system by determining its alignment with customer expectations. In the context of a manufacturing process with multiple correlated variables, the use of multivariate methods is essential for the analysis of quality characteristics. In the literature, there have been various proposals for MPCI (multivariate process capability indices) based on different approaches, including the proportion of non-conforming items or PCA (principal component analysis). In this context, a novel approach to capability analysis with multiple responses of varying degrees of importance has been proposed, termed WAMP (Weighted Arithmetic Mean with Prioritization). The findings indicated that the WAMP method demonstrated greater robustness than the SAM (simple arithmetic mean) and SGM (simple geometric mean) approaches. However, the WAM (weighted arithmetic mean) and WGM (weighted geometric mean) methods also exhibited satisfactory performance in accordance with the established acceptance criteria. The method was evaluated using both simulated and experimental data, demonstrating its efficacy in scenarios with varying degrees of correlation. When a greater weight is assigned to a single original variable, the MPCI is observed to be similar in value to that of the original variable with the highest weight when considered univariately. When equal weights are assigned to two original variables, the MPCI is situated within the capability indices of the original variables with the highest weight. Furthermore, it was observed that the performance of the MPCI improves with an increase in correlation. In conclusion, WAMP has been demonstrated to be a valuable and effective tool for capability analysis in systems with multiple correlated responses of varying degrees of importance.