In several biomedical applications that require the signal processing of biological data, the starting procedure for noise reduction is the ensemble averaging of multiple repeated acquisitions (trials). This method is based on the assumption that each trial is composed of two additive components: (i) a time-locked activity related to some sensitive/stimulation phenomenon (ERA, Event Related Activity in the following) and (ii) a sum of several other non time-locked background activities. The averaging aims at estimating the ERA activity under very low Signal to Noise and Interference Ratio (SNIR). Although averaging is a well established tool, its performance can be improved in the presence of high-power disturbances (artifacts) by a trials classification and removal stage. In this paper we propose, model and evaluate a new approach that avoids trials removal, managing trials classified as artifact-free and artifact-prone with two different weights. Based on the model, a weights tuning is possible and through modeling and simulations we show that, when optimally configured, the proposed solution outperforms classical approaches.