Subject Ph. D.

The reliability analysis of complex technical and technological systems is among the significant open problems of contemporary reliability engineering. A characteristic feature of these systems is their high complexity, resulting from a large number of mutually interconnected and heterogeneous components, as well as from the dynamics of their operation. A special class is represented by phased-mission systems, in which the system structure, operating conditions, or success criteria of individual phases change during the accomplishment of the mission of the system. Such systems are a typical example of complex systems, since their reliability depends not only on the states of components, but also on the sequence of phases and the mutual dependencies among them. Their complexity significantly limits the applicability of classical reliability approaches based on a static binary-state system model, i.e., on the assumption of an invariant system structure and the existence of only fully functioning or failed states. A more suitable approach to modelling such systems is the use of multi-state models, which allow the representation of a broader spectrum of operational states of both components and the entire system⬔ from a fully operational state, through various levels of partial performance, to complete failure. In the case of phased-mission systems, it is additionally necessary to consider changes in system configuration between individual phases, as well as the accumulation of failures and conditional state transitions. A formal tool for describing the dependence between component states and the system state is the system structure function, which, in the multi-state case, represents a discrete integer-valued function defined over the state space of components. For phased-mission systems, it is necessary to consider a set of structure functions corresponding to individual operational phases, or their suitable composition expressing the successful completion of the overall system mission. In recent years, an extensive methodology for the analysis of multi-state systems has been developed through collaboration between researchers from the Faculty of Management Science and Informatics of the University of Zilina (Zilina, Slovakia) and the Research Center for Automatic Control (CRAN) at the University of Lorraine (Nancy, France). This methodology is based on the principles of multi-valued logic, logical differential calculus, and Hasse diagrams. Despite its theoretical robustness, a fundamental challenge remains the high computational complexity of the applied methods, especially when dealing with large-scale systems involving a high number of components, states, and phases, as is the case with phased-mission systems. The objective of the doctoral thesis is to propose and investigate new methods for the reliability analysis of complex multi-state systems, with a focus on reducing the computational complexity of existing approaches, while particular attention will be paid to the application of the proposed methods to phased- mission systems. The proposed methods will be based on distributed and parallel computing, the application of Hasse diagrams and decision diagrams, logical differential calculus, and the use of principles of modular system decomposition based on the methodology of structure function. The expected outcome of the thesis is an approach enabling efficient, scalable, and methodologically consistent reliability analysis of phased-mission systems under modern computational architectures.

Expected Scientific Contribution:
⬢ new methods for the reliability analysis of phased-mission systems that utilize distributed computing. Recommended Research Methodology: 1. analysis of the current state of the problem, 2. design of algorithms for the reliability analysis of phased-mission systems, 3. development of distributed methods implementing the proposed algorithms, 4. experimental evaluation of the proposed methods.