Large-scale decentralized systems of autonomous agents interacting via asynchronous communication often experience the following self-healing dilemma: Fault-detection inherits network uncertainties making a faulty process indistinguishable from a slow process. The implications can be dramatic: Self-healing mechanisms become biased and cost-ineffective. In particular, triggering an undesirable fault-correction results in new faults that could be prevented with fault-tolerance instead. Nevertheless, fault-tolerance alone without eventually correcting persistent faults makes systems underperforming as well. Measuring, understanding and resolving such self-healing dilemmas is a timely challenge and critical requirement given the rise of distributed ledgers, edge computing, the Internet of Things in several application domains of energy, transport and health. This paper introduces a novel and general-purpose modeling of fault scenarios. They can accurately measure and predict inconsistencies generated by fault-correction and fault-tolerance when each node in a network can monitor the health status of another node, while both can defect. In contrast to related work, no information about the computational/application scenario, overlying algorithms or application data is required. A rigorous experimental methodology is designed that evaluates 696 experimental settings of different fault scales, fault profiles and fault detection thresholds, each with almost 9 million measurements of inconsistencies in a prototyped decentralized network of 3000 nodes. The prediction performance of the modeled fault scenarios is validated in a challenging application scenario of decentralized and dynamic in-network aggregation using real-world data from a Smart Grid pilot project. Findings confirm the origin of inconsistencies at design phase and provide new insights how to tune self-healing mechanisms at design phase. Strikingly, the aggregation accuracy is well predicted as shown by high correlations and low root mean square errors when calibration methods with application-independent features are applied.