Assessing the variability of colour-rendering indices using a random test-colour method

This paper addresses the way in which the random selection of different sets of samples influences the values of two colour-rendering indices analogous to the ones proposed by the International Commission on Illumination (CIE Publ. 13.3, 1995), Ra, and the Illuminating Engineering Society (IES Technical Memorandum TM-30-15, 2015), Rf. We report results found for 11 light sources, representative of current indoor and outdoor lighting, using a database with 12 123 spectral reflectance factors from real objects. For these 11 light sources, the differences between official Ra and Rf values and those computed using 100 iterations with 6000 random samples from our database proved to be in the range [−13, 2] and [−15, −1], respectively, the highest differences corresponding to sources with narrow peaks in their spectral power distributions. For 100 random subsets of 10 samples from our database, the average standard deviations of the 11 light sources for indices analogous to Ra and Rf were 8 and 5 (or 2 and 1 using 110 samples) respectively. The standard deviations in computed Ra and Rf values, using subsets with different numbers of samples n, can be modelled as inversely proportional to the square root of n. We propose a method to estimate these standard deviations for n = 6000 using reduced sets of 10 spectral reflectance factors.