Title: Statistical process control for the fractal dimension of a time series

Authors: Jingjing Tong; Justin R. Chimka

Addresses: Department of Industrial Engineering, University of Arkansas, Fayetteville, AR 72701, USA. ' Department of Industrial Engineering, University of Arkansas, Fayetteville, AR 72701, USA

Abstract: The fractal dimension (FD) of a time series can be estimated to measure its self-similarity or complexity. By arbitrarily dividing a series of data in time and estimating the FD of each part one can monitor observations of complexity or self-similarity using statistical process control methods. After estimating FD through Suleymanov et al.'s approach and transforming the FD series into a normally distributed dataset, we finally show in the example that the transformed FD of a time series is well suited to statistical process control with respect to the normal distribution assumption and its expected Type I errors. And we conclude that fractal theory and process control can be integrated to objectively and systematically monitor the complexity of a time series.

Keywords: chaos theory; climate data; complexity; fractal dimension; quality engineering; self-similarity; statistic process control; SPC; time series.

DOI: 10.1504/IJQET.2012.046155

International Journal of Quality Engineering and Technology, 2012 Vol.3 No.1, pp.20 - 30

Published online: 27 Mar 2012 *

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