Distribution-free control charts for mixed-type data based on rank of interpoint distances

Multivariate control charts have found wide application in healthcare, yet they primarily cater to continuous or categorical variables. However, the emergence of mixed-type data has sparked interest in adapting traditional control charts to handle such complexity. Unfortunately, existing methods often struggle to effectively manage this complexity, particularly in scenarios with limited historical in-control data. In response, this article introduces three distribution-free control charts specifically designed for monitoring mixed-type processes. The proposed approach revolves around computing distances between observations and a specified point, thereby reducing the data to a single dimension. Subsequently, the ranks of these one-dimensional distances are leveraged to develop monitoring statistics. Furthermore, to facilitate dimensionality reduction, a novel distance measure tailored for mixed-type data is introduced. Extensive validation of our proposed method is conducted through comprehensive simulation experiments. Moreover, we demonstrate the practical applicability of the proposed method using an example related to heart disease.