An extensive series of investigations inthe United Kingdom has shown that the variations in CIELAB space can be described and overcome by the use of ellipsoid tolerance volumes in which the dimensions in the hue, chroma and lightness directions are varied according to the location in color space of the color standard. The CMC color difference formula defines this variation in numerical tolerance, allowing the use of a single-number pass/fail tolerance to be applied to all colors of a given product.