Towards the Automated Verification of Weibull Distributions for System Failure Rates

Weibull distributions can be used to accurately model failure behaviours of a wide range of critical systems such as on-orbit satellite subsystems. Markov chains have been used extensively to model reliability and performance of engineering systems or applications. However, the exponentially distributed sojourn time of Continuous-Time Markov Chains (CTMCs) can sometimes be unrealistic for satellite systems that exhibit Weibull failures. In this paper, we develop novel semi-Markov models that characterise failure behaviours, based on Weibull failure modes inferred from realistic data sources. We approximate and encode these new models with CTMCs and use the PRISM probabilistic model checker. The key bene t of this integration is that CTMC-based model checking tools allow us to automatically and e ciently verify reliability properties relevant to industrial critical systems

Lightweight Statistical Model Checking in Nondeterministic Continuous Time

Lightweight scheduler sampling brings statistical model checking to nondeterministic formalisms with undiscounted properties, in constant memory. Its direct application to continuous-time models is rendered ineffective by their dense concrete state spaces and the need to consider continuous input for optimal decisions. In this paper we describe the challenges and state of the art in applying lightweight scheduler sampling to three continuous-time formalisms: After a review of recent work on exploiting discrete abstractions for probabilistic timed automata, we discuss scheduler sampling for Markov automata and apply it on two case studies. We provide further insights into the tradeoffs between scheduler classes for stochastic automata. Throughout, we present extended experiments and new visualisations of the distribution of schedulers.</p

An Effective Heuristic for Adaptive Importance Splitting in Statistical Model Checking

International audienceStatistical model checking avoids the intractable growth of states associated with numerical model checking by estimating the prob-ability of a property from simulations. Rare properties pose a challenge because the relative error of the estimate is unbounded. In [13] we de-scribe how importance splitting may be used with SMC to overcome this problem. The basic idea is to decompose a logical property into nested properties whose probabilities are easier to estimate. To improve perfor-mance it is desirable to decompose the property into many equi-probable levels, but logical decomposition alone may be too coarse. In this article we make use of the notion of a score function to improve the granularity of a logical property. We show that such a score function may take advantage of heuristics, so long as it also rigorously respects certain properties. To demonstrate our importance splitting approach we present an optimal adaptive importance splitting algorithm and an heuristic score function. We give experimental results that demonstrate a significant improvement in performance over alternative approaches

Importance Splitting for Statistical Model Checking Rare Properties

International audienceStatistical model checking avoids the intractable growth of states associated with probabilistic model checking by estimating the probability of a property from simulations. Rare properties are often important, but pose a challenge for simulation-based approaches: the relative error of the estimate is unbounded. A key objective for statistical model checking rare events is thus to reduce the variance of the estimator. Importance splitting achieves this by estimating a sequence of conditional probabilities, whose product is the required result. To apply this idea to model checking it is necessary to define a score function based on logical properties, and a set of levels that delimit the conditional probabilities. In this paper we motivate the use of importance splitting for statistical model checking and describe the necessary and desirable properties of score functions and levels. We illustrate how a score function may be derived from a property and give two importance splitting algorithms: one that uses fixed levels and one that discovers optimal levels adaptively

On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets

Molecular programming is an emerging field concerned with building synthetic biomolecular computing devices at nanoscale, for example from DNA or RNA molecules. Many promising applications have been proposed, ranging from diagnostic biosensors and nanorobots to synthetic biology, but prohibitive complexity and imprecision of experimental observations makes reliability of molecular programs difficult to achieve. This paper advocates the development of design automation methodologies for molecular programming, highlighting the role of quantitative verification in this context. We focus on DNA 'walker' circuits, in which molecules can be programmed to traverse tracks placed on a DNA origami tile, taking appropriate decisions at junctions and reporting the outcome when reaching the end of the track. The behaviour of molecular walkers is inherently probabilistic and thus probabilistic model checking methods are needed for their analysis. We demonstrate how DNA walkers can be modelled using stochastic Petri nets, and apply statistical model checking using the tool Cosmos to analyse the reliability and performance characteristics of the designs. The results are compared and contrasted with those obtained for the PRISM model checker. The paper ends by summarising future research challenges in the field

The 2019 Comparison of Tools for the Analysis of Quantitative Formal Models - (QComp 2019 Competition Report)

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