Mathematical Reliability Modeling of Cyber-Physical Systems: From Classical Failure Theory to Multilayer Predictive Indices

Cyber-physical systems (CPS) require a reliability theory that is broader than the classical probability of failure-free operation of a technical component. In CPSs, failure can be caused by deterioration, sensor error, delay in communication, software malfunction, control problems, cyber vulnerabilities, human interaction, and stress due to environment. This paper offers a mathematical approach to CPS reliability that brings together classical theories of reliability with multilayer, state-dependent, logical, Bayesian, and predictive approaches. The result is an integrated model in which the exponential and Weibull life distributions, structural reliability approaches, Markov models of state transitions, fault trees, Bayesian inference, normalization, and multilayer integral approach to reliability are combined into one coherent methodology. The paper presents some extended concepts of reliability, such as availability, maintainability, resilience, recoverability, data integrity, and CPS safety. The proposed approach makes possible theoretical work and practical decisions, since it connects layer-by-layer indicators with layer indices, layer indices with system reliability, and system reliability with failure probability prediction.