Detecting patterns in process data with fractal dimension

Abstract

In quality control discipline, pattern classification is focused on the detection of unnatural patterns in process data. In this paper, fractal dimension is proposed as a new classifier for pattern classification. Fractal dimension is an index for measuring the complexity of an object. Its applications were found in such diverse fields as manufacturing, material science, medical, and image processing. A method for detecting patterns in process data using the fractal dimension is proposed in this paper. A Monte Carlo study was carried out to study the fractal dimension ( D ) and the Y -intercept ( Y int ) values of process data with patterns of interest. The patterns included in the study are natural pattern, upward linear trend, downward linear trend, cycle, systematic variable, stratification, mixture, upward sudden shift, and downward sudden shift. Based on the results, the approach is effective in detecting such non-periodic patterns as the natural patterns, linear trends (at slope ≥0.2), systematic variable, stratification, mixture, and sudden shifts. For the cyclical pattern, although the D and Y int -values are not stable, the approach can provide useful information when the period of the cycle is greater than 2 and is less than or equal to half the window size (2<period≤ N /2). The minor drawbacks of this approach are that it is not sensitive for detecting linear trends with small slope and the slope of the original data is needed to detect the difference between upward and downward linear trends and the difference between upward and downward sudden shifts.