The majority logic criterion is applicable in the evaluation process of substitution boxes used in the advanced encryption standard (AES). The performance of modified or advanced substitution boxes is predicted by processing the results of statistical analysis by the majority logic criteria. In this paper, we use the majority logic criteria to analyze some popular and prevailing substitution boxes used in encryption processes. In particular, the majority logic criterion is applied to AES, affine power affine (APA), Gray, Lui J, residue prime, S 8 AES, Skipjack, and Xyi substitution boxes. The majority logic criterion is further extended into a generalized majority logic criterion which has a broader spectrum of analyzing the effectiveness of substitution boxes in image encryption applications. The integral components of the statistical analyses used for the generalized majority logic criterion are derived from results of entropy analysis, contrast analysis, correlation analysis, homogeneity analysis, energy analysis, and mean of absolute deviation (MAD) analysis.