Criticality assessment for multivariate process monitoring: Development of a weighted χ 2 control chart

Multivariate process monitoring offers numerous advantages for quality practitioners, including the ability to assess multiple variables using a single chart, thereby controlling overall type 1 error rates. However, in practical quality monitoring scenarios, different quality characteristics often possess varying levels of risks, customer value, and costs. Assigning equal weights to all variables may not accurately reflect the reality of quality monitoring practice, potentially reducing the effectiveness of critical measures. To bridge the gap between multivariate process monitoring and real-world quality monitoring, this research proposes a criticality assessment framework to be conducted prior to designing a multivariate monitoring system. By incorporating relative weights, this approach aims to maintain the power to detect changes in critical variables while controlling the overall false alarm rate. To demonstrate the practical implementation of this framework, we apply it to a Hotelling χ2 chart, resulting in the development of a critical-to-X chart. The proposed criticality assessment framework offers significant advancements in multivariate process monitoring, enabling quality practitioners to effectively prioritize variables based on their levels of risk and importance. This approach not only enhances the accuracy and efficiency of quality monitoring, but also offers a degree of protection of key variables in high-dimensional settings and aligns with the dynamic nature of quality improvement efforts. The findings of this research have far-reaching implications for researchers and industries looking to optimize their quality management systems and drive continuous improvement.