The Total Colorant Sensitivity of a Color Matching Recipe: An Approach to Colorant Weighting and Tinctorial Strength Errors Shahram Peyvandi, 1 * Seyed Hossein Amirshahi, 2 Boris Sluban 3 1 Department of Color Physics, Institute for Colorants, Paint and Coating, Tehran, Iran 2 Department of Textile Engineering, Amirkabir University of Technology, Tehran, Iran 3 Faculty of Mechanical Engineering, Smetanova 17, Maribor SI-2000, Slovenia Received 24 September 2006; revised 8 September 2007; accepted 26 September 2007 Abstract: The repeatability of the recipe color can be affected by several different types of inevitable inaccura- cies in the coloration process. Two of the major causes of poor target-color reproducibility are the (random) weigh- ing and (proportional) strength errors. This article describes alternative definitions of colorant strength sensi- tivity and total colorant sensitivity of a dyeing recipe. The influences of the maximal colorant weighing and strength errors are taken into account in order to bring the magni- tudes of the two treated types of sensitivity into a mutu- ally realistic balance between each other. The quantifica- tions of precision and accuracy of a color matching rec- ipe are also developed and combined into a single- number measure of recipe quality. The listed quantities are expected to be useful in selecting the most reliable one(s) among the different formulations for the same standard color. The methods are presented for calculating numerical estimates of the newly introduced quantities. The precision and accuracy of the coloration process are investigated in laboratory experiments involving repeated dyeings. Ó 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 300 – 306, 2008; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/col.20418 Key words: color formulation; color matching; color sen- sitivity; color strength INTRODUCTION It is reasonable to expect that using large quantities of the same dyes from the same suppliers in an identical dyeing process will give repeatable color results (when measuring samples dyed with equal percentages of dye). The color of a product can be affected by small changes in the dye- ing process and conditions of coloration. The color of the product is also affected by minor variations in colorant strength, which would be varied by changes in several factors such as particle size, homogeneity of the mixture, completeness of dye formation, preparation of dispersion, molecular structure of colorant, and so on. The color strength of a dye could be defined as a measure of its ability to impart color to other material, it is characterized by the absorption in the visible spectrum. 1 A concept of color sensitivity of a recipe was devel- oped by Sluban and Nobbs, 2 when the random (weighing) errors in colorant concentrations are the only reason for variations in the recipe color of repeat dyeings. However, errors in effective concentration are related to weighing errors and the variation in tinctorial strength from changes in mixing and dyeing process. In 1986, Alman 3 published the results obtained by computer simulation of the impact of concentration-independent weighing errors and concen- tration-dependent strength errors in quaternary-pigmented systems. He demonstrated that the impact of strength error is highest at middle concentrations and lowest at very low concentrations. Further, he showed that the impact of random weighing error is highest at low con- centrations and that it decreases rapidly with any increase in colorant concentration. Sluban 4 mutually compared *Correspondence to: Shahram Peyvandi (e-mail: peyvandi@icrc.ac.ir). V V C 2008 Wiley Periodicals, Inc. 300 COLOR research and application