Reliable systems: fault tree analysis via Markov reward automata

Today’s society is characterised by the ubiquitousness of hardware and software systems on which we rely on day in, day out. They reach from transportation systems like cars, trains and planes over medical devices at a hospital to nuclear power plants. Moreover, we can observe a trend of automation and data exchange in today’s society and economy, including among others the integration of cyber-physical systems, internet of things, and cloud computing. All theses systems have one common denominator: they have to operate safe and reliable. But how can we trust that they operate safe and reliable? Model checking is a technique to check if a system fulfils a given requirement. To check if the requirements hold, a model of the system has to be created, while the requirements are stated in terms of some logic formula w.r.t. the model. Then, the model and formula are given to a model checker, which checks if the formula holds on the model. If this is the case the model checker provides a positive answer, otherwise a counterexample is provided. Note that model checking can be used to verify hardware as well as software systems and has been successfully applied to a wide range of different applications like aerospace systems, or biological systems. Reliability engineering is a well-established field with the purpose of developing methods and tools to ensure reliability, availability, maintainability and safety (RAMS) of complex systems, as well as to support engineers during the development, production, and maintenance to maintain these characteristics. However, with the advancements and ubiquitousness of new hardware and software systems in our daily life, also methods and tools for reliability engineering have to be adapted. This thesis contributes to the realm of model checking as well as reliability engineering. On the one hand we introduce a reward extension to Markov automata and present algorithms for different reward properties. On the other hand we extend fault trees with maintenance procedures. In the first half of the thesis, we introduce Markov reward automata (MRAs), supporting non-deterministic choices, discrete as well as continuous probability distributions and timed as well as instantaneous rewards. Moreover we introduce algorithms for reachability objectives for MRAs. In particular we define expected reward objectives for goal and time bounded rewards as well as for long-run average rewards. In the second half of the thesis we introduce fault maintenance trees (FMTs). They extend dynamic fault trees (DFTs) with corrective and preventive main-