Nonparametric Phase-II control charts for monitoring high-dimensional processes with unknown parameters

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.