We present a new approach to design fault tolerant artificial neural networks (ANNs). Additionally, this approach allows estimating the final network reliability. This approach is based on the Mutation Analysis technique and is used during the training process of the ANN. The basic idea is to train the ANN in the presence of faults (single-fault model is assumed). To do so, a set of faults is injected into the code describing the ANN. This procedure yields mutation versions of the original ANN code, which in turn are used to train the network in an iterative process with the designer until the moment when the ANN is no more sensible to the single faults injected. In other words, the network became tolerant to the considered set of faults. A practical example where an ANN is used to recognize electrocardiogram (ECG) and to measure ECG parameters illustrates the proposed methodology. Keywords: Artificial Neural Networks; Mutation Analysis; Fault-Tolerant Computing Systems; Reliability Estimation; Electrocardiogram Recognition.