Time irreversibility is one of the fundamental properties of nonequilibrium complex brain activities and is relevant to various neurological conditions, e.g., epilepsy. However, the estimation of the joint probability distribution for quantitative time irreversibility (qTIR) is not trivial, and the application of qTIR in characterizing epileptic brain signals has received little attention. In this paper, we employ equal-value permutations instead of raw vectors to simplify qTIR, and we apply subtraction-based parameters to measure the probabilistic differences in order patterns for qTIR considering the forbidden permutations. We demonstrate that our simplified method, validated by chaotic and reversible model series and their surrogates, is equivalent to methods measuring the probabilistic difference between forward–backward vectors and the probabilistic difference between symmetric vectors. In characterizing epileptic brain electric activities, seizure electroencephalograms (EEGs) have the strongest qTIR due to the development of synchronous neuronal firing, and the qTIR of seizure-free EEGs lies between that of the healthy control and ictal EEGs. Overall, we conduct a comprehensive analysis of permutation-based qTIR for nonlinearity detection, and our findings regarding qTIR in epileptic EEGs improve our understanding of nonequilibrium epileptic brain electrical activity and might even contribute to predicting epileptic seizures.