Phase I Distribution-Free Analysis of Multivariate Data

In this study, a new distribution-free Phase I control chart for retrospectively monitoring multivariate data is developed. The suggested approach, based on the multivariate signed ranks, can be applied to individual or subgrouped data for detection of location shifts with an arbitrary pattern (e.g., isolated, transitory, sustained, progressive, etc.). The procedure is complemented with a LASSO-based post-signal diagnostic method for identification of the shifted variables. A simulation study shows that the method compares favorably with parametric control charts when the process is normally distributed, and largely outperforms other multivariate nonparametric control charts when the process distribution is skewed or heavy-tailed. An R package can be found in the supplementary material.

本研究开发了一种新型无分布自由 (distribution-free) 第一阶段 (Phase I) 控制图，用于多变量数据的回顾性监控。本文提出的方法基于多变量符号秩，可应用于独立数据或分组数据，能够检测任意模式的位置偏移（例如孤立型、短暂型、持续型、渐进型等）。该流程配套了基于套索 (LASSO) 的信号后诊断方法，用于识别发生偏移的变量。仿真研究结果显示，当过程服从正态分布时，该方法与参数型控制图相比表现更优；而当过程分布呈偏态或厚尾特征时，该方法的性能大幅优于其他多变量非参数控制图。相关R包 (R package) 可在补充材料中获取。