Fractal geometry statistical process control for non-linear pattern-based processes

Abstract

This article suggests a new Statistical Process Control (SPC) approach for data-rich environments. The proposed approach is based on the theory of fractal geometry. In particular, a monitoring scheme is developed that is based on fractal representation of the monitored data at each stage to account for online changes in monitored processes. The proposed fractal-SPC enables a dynamic inspection of non-linear and state-dependent processes with a discrete and finite state space. It is aimed for use with both univariate and multivariate data. The SPC is accomplished by applying an iterated function system to represent a process as a fractal and exploiting the fractal dimension as an important monitoring attribute. It is shown that data patterns can be transformed into representing fractals in a manner that preserves their reference (in control) correlations and dependencies. The fractal statistics can then be used for anomaly detection, pattern analysis, and root cause analysis. Numerical examples and comparisons to conventional SPC methods are given.