Fluctuation scaling of color variability in automotive metallic add-on parts

Abstract

Color matching between the car body and assembled add-on parts is a complex process that increases the costs and time in automotive manufacturing. We have investigated the statistical properties of color coordinates for color matching in automotive metallic coatings. CIELAB lightness L*, red-green a*, and blue-yellow b* coordinates were calculated by using multi-angle spectrophotometric reflectance measurements from a broad range of metallic coatings from different manufacturers. We found that trial-to-trial L* variations are related to a self-similar stochastic process. The sample variance and the sample mean value of L* calculated over different viewing angles are correlated across painted pieces. A power function model describes the data quite well. This power function corresponds to a wide spread phenomenon known as fluctuation scaling in many engineering process. We also found that the sample skewness and the sample kurtosis of L*, a*, and b* follow a U-shaped pattern and a generalized version of fluctuation scaling. The exponent of fluctuation scaling in the skewness–kurtosis plane depends on the cardinal directions, L*, a*, and b*. This suggests that different flake-shaped pigments mediate trial-to-trial correlations of color coordinates. We conclude that fluctuation scaling provides a powerful approach for better prediction of lightness flop variations and for better color quality control between car manufacturers and suppliers of add-on parts.