Continuum fault trees

The motivation for this paper is the observation that combinations of small deviations in continuous performance parameters can combine to cause failure of an entire system, even though no one of these deviations is sufficient of itself to cause any failure. To be able to trace the change of continuous parameters and predict their transfer to non-permissible regions of the system state space, we suggest construction of continuum fault trees, which allow combinations of small, continuous deviations of system parameters as well as discrete failures. The construction of continuum fault trees suggests also developing equation bi-graphs, a causal diagram visualizing and combining all continuous performance parameters. The bi-graphs serve several purposes, one of which is the explication of feedback loops and hidden loops, that allow identification of hazards attributed to the loops as a whole rather than to individual components. Construction of both bi-graphs and continuum fault trees is demonstrated on the example of an automobile engine, the performance of which is presented by an analytical model. We consider the potential for employing continuum fault trees for analysis of AI-driven systems, as their performance is built on neural networks that have underlying continuous analytical models. An example for this is also provided.