Neuromorphic computing uses spiking neuron network models to solve machine learning problems in a more energy-efficient way when compared to conventional artificial neural networks. However, mapping the various network components to the neuromorphic hardware is not trivial to realize the desired model for an actual simulation. Moreover, neurons and synapses could be affected by noise due to external interference or random actions of other components (i.e., neurons), which eventually lead to unreliable results. This work proposes a fault-tolerant spiking neural network mapping algorithm and architecture to a 3D network-on-chip (NoC)-based neuromorphic system (R-NASH-II) based on a rank and selection mapping mechanism (RSM). The RSM allows the ranking and rapid selection of neurons for fault-tolerant mapping. Evaluation results show that with our proposed mechanism, we could maintain a mapping efficiency of 100% with 20% spare rate and a fault rate (40%) more than in the previous mapping framework. The Monte Carlo simulation evaluation of reliability shows that the RSM mechanism has increased the mean time to failure (MTTF) of the previous mapping technique by 43% on average. Furthermore, the operational availability of the RSM for mapping to a 4 × 4 × 4 (smallest) and 6 × 6 × 6 (largest) NoC is 88% and 67% respectively.