Abstract

Monitoring multivariate and high-dimensional data streams is often an essential requirement for quality management in manufacturing and service sectors in the Industry 4.0 era. Identifying a suitable distribution for a multivariate data set, especially when the number of variables is much larger than the sample size, is often challenging. Consequently, in a high-dimensional set-up, that is, when the number of variables under investigation exceeds sample size, parametric methods are generally not reliable in practice. There are various nonparametric schemes based on data depth for multivariate process monitoring, which are applicable only when the sample size is reasonably larger than the number of variables in the process but not in a high-dimensional set-up. We discuss that most of these charts are not robust when the true process parameters are unknown. There are, however, some nonparametric schemes for a high-dimensional process, when true process parameters are known. Nevertheless, when process parameters are unknown, a highly robust nonparametric scheme for monitoring high-dimensional processes is not yet available. In this paper, we propose some Shewhart-type nonparametric monitoring schemes based on specific distance metrics for surveillance of multivariate as well as high-dimensional processes. Our proposed charts are easy to implement, interpret and also advantageous in simultaneous monitoring of multiple aspects. We discuss the design and implementation issues in details. We carry out a performance study using Monte Carlo simulations and illustrate the proposed methods using a dataset related to industrial production.

摘要

监控多变量和高维数据流往往是工业4.0时代制造和服务行业质量管理的基本要求。为多元数据集确定合适的分布，尤其是当变量数量远大于样本量时，通常具有挑战性。因此，在高维设置中，即当调查的变量数量超过样本量时，参数方法在实践中通常不可靠。有多种基于数据深度的非参数方案可用于多变量过程监控，这些方案仅适用于样本大小合理大于过程中变量数量的情况，但不适用于高维设置。我们讨论了当真正的过程参数未知时，这些图表中的大多数都不可靠。然而，当真正的过程参数已知时，对于高维过程有一些非参数方案。然而，当过程参数未知时，还没有一种用于监测高维过程的高度稳健的非参数方案。在本文中，我们提出了一些基于特定距离度量的休哈特型非参数监测方案，用于监测多变量和高维过程。我们提出的图表易于实施、解释，并且在多个方面的同时监测方面也有优势。我们详细讨论了设计和实现问题。