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Failure mode and effects analysis (FMEA) is a technique to reason about possible system hazards that result from system or system component failures. Traditionally, FMEA does not take the probabilities with which these failures may occur into account. Recently, this shortcoming was addressed by integrating stochastic model checking techniques into the FMEA process. A further improvement is the integration of techniques for the generation of counterexamples for stochastic models, which we propose in this paper. Counterexamples facilitate the redesign of a potentially unsafe system by providing information which components contribute most to the failure of the entire system. The usefulness of this novel approach to the FMEA process is illustrated by applying it to the case study of an airbag system provided by our industrial partner, the TRW Automotive GmbH.

Abstract. The inability to provide counterexamples for the violation of timed probabilistic reachability properties constrains the practical use of CSL model checking for continuous time Markov chains (CTMCs). Counterexamples are essential tools in determining the causes of property violations and are required during debugging. We propose the use of explicit state model checking to determine runs leading into property offending states. Since we are interested in finding paths that carry large amounts of probability mass we employ directed explicit state model checking technology to find such runs using a variety of heuristics guided search algorithms, such as Best First search and Z*. The estimates used in computing the heuristics rely on a uniformisation of the CTMC. We apply our approach to a probabilistic model of the SCSI-2 protocol.

Current numerical model checkers for stochastic systems can efficiently analyse stochastic models. However, the fact that they are unable to provide debugging information constrains their practical use. In precursory work we proposed a method to select diagnostic traces, in the parlance of functional model checking commonly referred to as failure traces or counterexamples, for probabilistic timed reachability properties on discrete-time and continuous-time Markov chains. We applied directed explicit-state search algorithms, like Z * , to determine a diagnostic trace which carries large amount of probability. In this work we extend this approach to determining sets of traces that carry large probability mass, since properties of stochastic systems are typically not violated by single traces, but by collections of those. To this end we extend existing heuristics guided search algorithms so that they select sets of traces. The result is provided in the form of a Markov chain. Such diagnostic Markov chains are not just essential tools for diagnostics and debugging but, they also allow the solution of timed reachability probability to be approximated from below. In particular cases, they also provide real counterexamples which can be used to show the violation of the given property. Our algorithms have been implemented in the stochastic model checker PRISM. We illustrate the applicability of our approach using a number of case studies.