  Estimating the correlation coefficient has been a daunting work with the
increasing complexity of dataset's pattern. One of the problems in
manufacturing applications consists of the estimation of a critical process
variable during a machining operation from directly measurable process
variables. For example, the prediction of surface roughness of a workpiece
during finish turning processes. In this paper, we did exhaustive study on the
existing popular correlation coefficients: Pearson correlation coefficient,
Spearman's rank correlation coefficient, Kendall's Tau correlation coefficient,
Fechner correlation coefficient, and Nonlinear correlation coefficient.
However, no one of them can capture all the nonlinear and linear correlations.
So, we represent a universal non-linear non-parametric correlation measurement,
g-correlation coefficient. Unlike other correlation measurements, g-correlation
doesn't require assumptions and pick the dominating patterns of the dataset
after examining all the major patterns no matter it is linear or nonlinear.
Results of testing on both linearly correlated and non-linearly correlated
dataset and comparison with the introduced correlation coefficients in
literature show that g-correlation is robust on all the linearly correlated
dataset and outperforms for some non-linearly correlated dataset. Results of
the application of different correlation concepts to surface roughness
assessment show that g-correlation has a central role among all standard
concepts of correlation.
