A General Framework for Robust Monitoring of Multivariate Correlated Processes

Statistical process control (SPC) charts provide an important analytic tool for online monitoring of sequential processes. Conventional SPC charts are designed for cases when in-control (IC) process observations are independent and identically distributed at different observation times and the IC process distribution belongs to a parametric (e.g., normal) family. In practice, however, these model assumptions are rarely valid. To address this issue, there have been some existing discussions in the SPC literature for handling cases when the IC process distribution cannot be described well by a parametric form, and some nonparametric SPC charts have been developed based on data ranking and/or data categorization. However, both data ranking and data categorization would lose information in the original process observations. Consequently, the effectiveness of the nonparametric SPC charts would be compromised. In this paper, we make another research effort to handle this problem by developing a general process monitoring framework that is robust to the IC process distribution and short-ranged serial correlation. The new method tries to preserve as much information in the original process observations as possible. Instead of using data ranking and/or data categorization, it is based on intensive data pre-processing, including data decorrelation, data transformation, and data integration. Because the distribution of the pre-processed data can be approximated well by a parametric distribution, the design and implementation of the new method is relatively simple. Numerical studies show that it is indeed robust to the IC process distribution and effective for online monitoring of multivariate processes with short-ranged serial correlation.统计过程控制（Statistical Process Control，SPC）图为序贯过程的在线监测提供了重要的分析工具。传统SPC图的设计前提为：不同观测时刻下的受控（in-control，IC）过程观测值相互独立且同分布，且受控过程分布属于参数化分布族（例如正态（normal）分布）。但在实际应用中，这些模型假设极少能够成立。为解决这一问题，SPC领域已有诸多研究探讨了受控过程分布无法用参数化形式良好描述的场景，并基于数据排序与/或数据分类开发了若干非参数SPC图。然而，数据排序与数据分类均会丢失原始过程观测值中的信息，因此非参数SPC图的监测效能会受到损害。本文针对该问题展开研究，提出一种通用的过程监测框架，该框架对受控过程分布与短程序列相关具有鲁棒性。新方法尽可能保留原始过程观测值中的信息，摒弃了数据排序与/或数据分类的思路，而是基于精细化的数据预处理流程，包括数据去相关、数据变换与数据集成。由于预处理后的数据可通过参数化分布进行良好近似，因此新方法的设计与实现相对简便。数值仿真实验表明，该方法确实对受控过程分布具有鲁棒性，且可有效实现带有短程序列相关的多变量过程的在线监测。

搜集汇总

背景与挑战

背景概述

该数据集提供了一个用于多变量相关过程鲁棒监控的通用框架，旨在解决传统统计过程控制（SPC）图对独立同分布和参数分布假设的依赖问题。通过数据去相关、变换和集成等预处理方法，新框架在保留原始观测信息的同时，有效处理IC过程分布和短程序列相关性，适用于遗传学、环境科学、免疫学等多个领域的在线监控应用。