Probabilistic analysis of safety-critical adaptive systems with temporal dependences

Dynamic adaptation means that components are reconfigured at run time. Consequently, the degree to which a system fulfils its functional and safety requirements depends on the current system configuration at run time. The probability of a violation of functional requirements in combination with an importance factor for each requirement gives us a measure for reliability. In the same way, the degree of violation of safety requirements can be a measure for safety. These measures can easily be derived based on the probabilities of possible system configurations. For this purpose, we are introducing a new probabilistic analysis technique that determines configuration probabilities based on Fault trees, Binary Decision Diagrams (BDDs) and Markov chains. Through our recent work we have been able to determine configuration probabilities of systems but we neglected timing aspects [1]. Timing delays have impact on the adaptation behavior and are necessary to handle cyclic dependences. The contribution of the present article is to extend analysis towards models with timing delays. This technique builds upon the Methodologies and Architectures for Runtime Adaptive Systems (MARS) [2], a modeling concept we use for specifying the adaptation behavior of a system at design time. The results of this paper determine configuration probabilities, that are necessary to quantify the fulfillment of functional and safety requirements by adaptive systems.