The effect of dead-time and pile-up in counting experiments may become a significant source of uncertainty if not properly taken into account. Although analytical solutions to this problem have been proposed for simple set-ups with one or two detectors, these are limited when it comes to arrays where time correlation between the detector modules is used, and also in situations of variable counting rates. In this paper we describe the dead-time and pile-up corrections applied to the n_TOF Total Absorption Calorimeter (TAC), a 4π γ-ray detector made of 40 BaF2 modules operating at the CERN n_TOF facility. Our method is based on the simulation of the complete signal detection and event reconstruction processes and can be applied as well in the case of rapidly varying counting rates. The method is discussed in detail and then we present its successful application to the particular case of the measurement of 238U(n, γ) reactions with the TAC detector.