Difference equation systems analysis3/25/2023 ![]() ![]() For example, if a customer only accepts a product that has a CMC(2 : 1) color difference of 0.5 units or less, a commercial factor of 2.0 would be used for that customer. The commercial factor allows the user to change the size of the acceptability ellipsoid and still have a 1.0 unit of color difference be acceptable. Some computer programs multiply the CMC( l : c) color difference by a commercial factor, CF. It is because of the customer variability in acceptability limits that a single total color difference tolerance calculated from a color difference equation is rarely adequate. In addition, the size of the ellipsoid needed to define the acceptability of a product will vary from customer to customer. The same discussion would apply to CIE94( k L, : k C : k H).Īlthough the textile industry seems to have settled on a CMC l : c ratio of 2 : 1, different industries may prefer different ratios. The CMC( l : c) equation will be used to discuss the setting of color tolerances. Fixing the ratios of l to c or of k L to k C to k H will define the shape of the acceptability ellipsoid in color space. The CMC( l : c) and CIE94( k L : k C : k H) color difference equations attempt to compensate for tolerance preferences in lightness, chroma and hue. That is why textile acceptability data plots as ellipsoids in CIELAB color space. Inspectors in the textile industry are the least tolerant of hue differences, more tolerant of chroma differences and the most tolerant of lightness differences. In the CIELAB color difference equation the lightness, chroma and hue components of the color difference are weighted equally. One CIELAB unit of color difference was sized to signify the limit of a commercially acceptable color match in the textile industry. It can be useful to set a warning tolerance to let the supplier know when the coloring process might be drifting out of limits. ![]() Sometimes a temporary standard is used until the process capability can be determined. Tolerance limits should be based on the process capability of the supplier to make the color. ![]() The tolerance should agree with a visual evaluation of acceptability and may vary with the color of a product. If a tolerance is too tight, the supplier might not be able to supply the product at all or have to charge a higher price for the product. If a tolerance is too loose, the product might not be acceptable to the purchaser. Both should be able to live with the tolerance. Examples of products with liberal tolerances are color-coded electronic wires, colored masonry and the porcelain insulators on electric poles.Ī color tolerance is an agreement between the supplier and the customer. Products which are small, made from difficult to color material, have large texture and/or gloss variations or are viewed at a distance, typically have liberal color tolerances (ASTM 0004). Finishes of high priced consumer products, such as automobiles and major appliances, typically have very tight color tolerances. The major problem with the setting of color tolerances is that not only do they vary from industry to industry, but from customer to customer within any given industry. Tolerance limits specify how far a batch can differ from the standard and still be acceptable for use. Marcus, in AZimuth, 1998 2.4.8 Color tolerancesĬolor difference equations provide the ruler for instrumentally determining the color difference between a standard and a trial. ![]()
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