Branching Transitions for Semi-Markov Processes with Application to Safety-Critical Systems

Abstract

When developing safety-critical systems, performing dependability analyses such as computing the reliability is of utmost importance. In the safety standard IEC61508, Markov processes are suggested for quantifying the reliability. However, real-world systems can not always be accurately modeled as a Markov process. Semi-Markov Processes (SMPs) generalizes Markov processes to allow for more accurate models. It has been previously suggested that a intuitive modeling approach of semi-Markov processes is to assign a timer to each possible transition. These timers race to first reach zero which triggers the corresponding transition. However, some situations such as non-perfect diagnostic procedures cannot be modeled with these transition timers. As the first, and main contribution, the theory of modeling SMPs with transition timers is extended with branching transitions, i.e. transitions with several possible output states. The second contribution is tool support for dependability analyses of SMPs modeled with branching transitions. A use case example of an automotive steering system modeled as an SMP with transition timers and with branching transitions is considered and analyzed.