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

Area of Science:

• Quality Control
• Statistical Process Monitoring
• Healthcare Analytics

Background:

• Multivariate control charts are vital in healthcare but traditionally handle only continuous or categorical data.
• Mixed-type data presents challenges for existing control chart methods, especially with limited historical data.
• There is a need for robust statistical process monitoring tools capable of handling mixed-type data in healthcare settings.

Purpose of the Study:

• To develop and introduce three novel distribution-free control charts for monitoring mixed-type processes.
• To address the limitations of existing methods in managing complex data with limited historical information.
• To provide a practical and effective tool for quality control in healthcare, particularly for monitoring complex patient data.

Main Methods:

• The proposed approach computes distances between observations and a reference point, reducing data to a single dimension.
• Ranks of these one-dimensional distances are used to create monitoring statistics.
• A new distance measure specifically designed for mixed-type data is introduced to aid dimensionality reduction.

Main Results:

• The developed distribution-free control charts demonstrate effectiveness in monitoring mixed-type processes.
• Simulation experiments validate the proposed method's performance across various scenarios.
• The approach successfully handles complexity, even with limited historical in-control data.

Conclusions:

• The introduced control charts offer a robust solution for monitoring mixed-type data in quality control applications.
• The novel distance measure and rank-based statistics provide effective dimensionality reduction.
• The method's applicability is confirmed through simulations and a real-world heart disease example, highlighting its value in healthcare.