The superior performance of Deep Neural Networks (DNNs) has led to their application in various aspects of human life. Safety-critical applications are no exception and impose rigorous reliability requirements on DNNs. Quantized Neural Networks (QNNs) have emerged to tackle the complexity of DNN accelerators, however, they are more prone to reliability issues. In this paper, a recent analytical resilience assessment method is adapted for QNNs to identify critical neurons based on a Neuron Vulnerability Factor (NVF). Thereafter, a novel method for splitting the critical neurons is proposed that enables the design of a Lightweight Correction Unit (LCU) in the accelerator without redesigning its computational part. The method is validated by experiments on different QNNs and datasets. The results demonstrate that the proposed method for correcting the faults has a twice smaller overhead than a selective Triple Modular Redundancy (TMR) while achieving a similar level of fault resiliency.