Abstract

Profile monitoring is an important tool for quality control. Most existing profile monitoring approaches focus on monitoring a single profile. In practice, multiple profiles also widely exist and these profiles contain rich correlation information that can benefit the monitoring of interested/target profile. In this article, we propose a transfer learning framework to extract profile-to-profile inter-relationship to improve the monitoring performance. In this framework, profiles are modeled as a multi-output Gaussian process (MGP), and a specially designed covariance structure is proposed to reduce the computational load in optimizing the MGP parameters. More importantly, the proposed framework contains features for dealing with incomplete samples in each profile, which facilitates the information sharing among profiles with different data collection costs/availability. The proposed method is validated and compared with various benchmarks in extensive numerical studies and a case study of monitoring ice machine temperature profiles. The results show the proposed method can successfully transfer knowledge from related profiles to benefit the monitoring performance in the target profile. The R code of this paper would be available as on-line supplementary materials.

摘要

轮廓监控是质量控制的重要工具。大多数现有的配置文件监控方法专注于监控单个配置文件。在实践中，也广泛存在多个配置文件，这些配置文件包含丰富的相关信息，有助于监控感兴趣/目标配置文件。在本文中，我们提出了一个迁移学习框架来提取配置文件到配置文件的相互关系以提高监控性能。在该框架中，轮廓被建模为多输出高斯过程（MGP），并提出了一种特殊设计的协方差结构来减少优化 MGP 参数的计算量。更重要的是，所提出的框架包含处理每个配置文件中不完整样本的功能，这有助于具有不同数据收集成本/可用性的配置文件之间的信息共享。在广泛的数值研究和监测制冰机温度曲线的案例研究中，对所提出的方法进行了验证并与各种基准进行了比较。结果表明，所提出的方法可以成功地从相关配置文件中转移知识，从而有利于目标配置文件中的监控性能。本文的 R 代码将作为在线补充材料提供。