Statistical process control for the fractal dimension of a time series. (1st January 2012)

• Record Type: Journal Article
• Authors: Tong, Jingjing; Chimka, Justin R.
• Is Part Of: International journal of quality engineering and technology. Volume 3:Number 1(2012)
• Page Start: 20
• Page End: 30
• Publication Date: 2012-01-01
• Subjects: chaos theory -- climate data -- complexity -- fractal dimension -- quality engineering -- self-similarity -- statistic process control -- time series; Engineering -- Quality control -- Periodicals; Systems engineering -- Periodicals; 620.0045
• Languages: English
• ISSNs: 1757-2177

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.