Defining color tolerances numerically continues to be a topic of intense interest in colorimetry. A technique was developed to evaluate formula performance that incorporated visual uncertainty. In this technique, visual uncertainty was represented by randomized equal color-difference ellipsoids or randomized visual color differences. STRESS, a multivariate statistical tool, was employed to quantify these randomized equal color-difference ellipsoids or visual color differences. The STRESS clouds were composed of the STRESS values between the randomized equal color-difference ellipsoids and T 50 equal color-difference ellipsoids, or between the randomized visual color differences and T50 visual color differences where T 50 represented visually determined tolerances equivalent to an anchor-pair stimulus. These STRESS values clouds were taken as rulers to evaluate whether one color-difference formula over-, under- or well-fitted a specified color-difference dataset, based on an F-test. This technique is a necessary addition to the current deviation evaluation metrics, e.g., PF/3. In follow-on research, a Euclidean color space was developed with the color-difference formula based on IPT color space for supra-threshold color differences. The color-difference formula has similar chromatic modeling to CIE94. A lightness transformation function was applied to model color difference along lightness. A rotation matrix on the chromatic plane was also applied to achieve better characteristics of the color space. A step-wise optimization was performed to achieve better consistency and remove conflicts between different color-difference datasets. The evaluations include STRESS, F-test, hue constancy and equal color-difference ellipsoid shape. It was shown by the evaluation results that the Euclidean color space could be a potential candidate of a future color model useful for defining industrial color tolerances.
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