Dynamic Hybrid Fault Modeling and Extended Evolutionary Game Theory for Reliability, Survivability and Fault Tolerance Analyses

We introduce a new layered modeling architecture consisting of dynamic hybrid fault modeling and extended evolutionary game theory for reliability, survivability, and fault tolerance analyses. The architecture extends traditional hybrid fault models and their relevant constraints in the Agreement algorithms with survival analysis, and evolutionary game theory. The dynamic hybrid fault modeling (i) transforms hybrid fault models into time- and covariate-dependent models; (ii) makes real-time prediction of reliability more realistic, and allows for real-time prediction of fault-tolerance; (iii) sets the foundation for integrating hybrid fault models with reliability and survivability analyses by integrating them with evolutionary game modeling; and (iv) extends evolutionary game theory by stochastically modeling the survival (or fitness) and behavior of `game players.' To analyse survivability, we extend dynamic hybrid fault modeling with a third-layer, operational level modeling, to develop the three-layer survivability analysis approach (dynamic hybrid fault modeling constitutes the tactical and strategic levels). From the perspective of evolutionary game modeling, the two mathematical fields, i.e., survival analysis and agreement algorithms, which we applied for developing dynamic hybrid fault modeling, can also be utilized to extend the power of evolutionary game theory in modeling complex engineering, biological (ecological), and social systems. Indeed, a common property of the areas where our extensions to evolutionary game theory can be advantageous is that the risk analysis and management are a core issue. Survival analysis (including competing risks analysis, and multivariate survival analysis) offers powerful modeling tools to analyse time-, space-, and/or covariate-dependent uncertainty, vulnerability, and/or frailty which `game players' may experience. The agreement algorithms, which are not limited to the agreement algorithms from distributed computing, when applied to extend evolutionary game modeling, can be any problem (game system) specific rules (algorithms or models) that can be utilized to dynamically check the consensus among game players. We expect that the modeling architecture and approaches discussed in the study should be implemented as a software environment to deal with the necessary sophistication. Evolutionary computing should be particularly convenient to serve as the core optimization engine, and should simplify the implementation. Accordingly, a brief discussion on the software architecture is presented.