In multi-causal analysis, the independence of causal influence (ICI) assumed by the noisy-OR (NOR) model can be used to predict the probability of the effect when several causes are present simultaneously, and to identify (when it fails) inter-causal dependence (ICD) between them. The latter is possible only if the probability of observing the multi-causal effect is available for comparison with a corresponding NOR estimate. Using electromagnetic interference in an integrated circuit as a case study, the data corresponding to the probabilities of observing failures (effect) due to the injection of individual (single cause) and simultaneous electromagnetic disturbances having different frequencies (multiple causes) were collected. This data is initially used to evaluate the NOR model and its existing derivatives, which have been proposed to reduce the error in predictions for higher-order multi-causal interactions that make use of the available information on lower-order interactions. Then, to address the identified limitations of the NOR and its existing derivatives, a new deterministic model called Super-NOR is proposed, which is based on correction factors estimated from the available ICD information.