The study aims to correlate the mean gap voltage variation and wire breakage occurrences during the wire EDM of Inconel 718. A novel approach to predict the wire breakage is introduced by considering the mean gap voltage variation ($\Delta$Vm) as an indicator of the instabilities in the spark gap. Such instabilities are regarded as the primary reason for wire breakages and inferior part quality of wire electric discharge machined components. The parameter $\Delta$Vm is a process data obtained as the difference between servo voltage and mean gap voltage (Vm). It was found experimentally that if the value of $\Delta$Vm crosses a threshold limit, the process interruptions through wire breakages were observed. In order to predict the wire breakage situations, the study models $\Delta$Vm using adaptive neuro fuzzy inference system (ANFIS). Based on central composite design (CCD) of response surface methodology (RSM), 31 experiments were conducted and $\Delta$Vm is recorded as the response. The input parameters considered were pulse on time, pulse off time, servo voltage and wire feed rate. The ANFIS model was found very accurate in predicting $\Delta$Vm, based on which wire breakage alerts can be given. The capability of the model is further confirmed by verification experiments. EDS and microstructural analysis further revealed the effect of $\Delta$Vm on wire wear and part quality. Higher value of $\Delta$Vm resulted in greater wire wear and inferior part quality. The surface finish and flatness error of machined parts were measured to compare the part quality.