Control quality assessment using fractal persistence measures

Abstract

Control Performance Assessment (CPA) has great practical importance. Control quality significantly affects final production throughput, efficiency and environmental impact. There are many approaches starting from time-domain methods, through Minimum Variance, Gaussian and non-Gaussian statistics up to alternative wavelet, fractal or entropy measures. Analysis of production data from process industry shows that signals are often described by non-Gaussian distributions, mostly fat-tail. On the other hand, simulations show that strong disturbances may significantly screen ability of proper detection. This work tests different approaches, i.e. Gaussian standard deviation and fat-tail distribution factors, integral indexes and focuses on persistence measures of rescaled range R/S plot. Robustness of above measures against disturbances with varying statistical properties is investigated. Results confirm that fractal measures may be applied as robust alternative to standard statistics.

Keywords: Control performance assessment; Crossover; Fat-tail distributions; Fractal measures; Hurst exponent.