Nonparametric multivariate control chart based on density-sensitive novelty weight for non-normal processes

Abstract

The control chart is one of the most important statistical process control tools and the traditional control charts mostly require a specific probability distribution to set up their control limits. However, in modern manufacturing, the processes often have a lot of complexity and variability. Most existing control charts cannot efficiently handle situations with nonlinear or multi-modal patterns of observations. One recent trend about control charts is based on the novelty score algorithms that can effectively describe and reflect the characteristics of the monitored data. In this paper, we propose a density-sensitive novelty weight (DNW) control chart using k-nearest neighbors (kNN) algorithm that can efficiently monitor a process when the distribution of observations is unknown. More importantly, our chart can fully utilize the in-control local density information which can be regarded as the amount of in-control process knowledge. We demonstrated the usefulness of the proposed chart in experiments with simulated data in terms of average run length, and showed that the proposed chart generated proper portions of false alarms in the dense and sparse regions in Phase-I monitoring procedure in a real-life data, the E.coli dataset from the University of California, Irvine (UCI) repository.