Quantitative Verification: Formal Guarantees for Timeliness, Reliability and Performance

Computerised systems appear in almost all aspects of our daily lives, often in safety-critical scenarios such as embedded control systems in cars and aircraft or medical devices such as pacemakers and sensors. We are thus increasingly reliant on these systems working correctly, despite often operating in unpredictable or unreliable environments. Designers of such devices need ways to guarantee that they will operate in a reliable and efficient manner. Quantitative verification is a technique for analysing quantitative aspects of a system's design, such as timeliness, reliability or performance. It applies formal methods, based on a rigorous analysis of a mathematical model of the system, to automatically prove certain precisely specified properties, e.g. ``the airbag will always deploy within 20 milliseconds after a crash'' or ``the probability of both sensors failing simultaneously is less than 0.001''. The ability to formally guarantee quantitative properties of this kind is beneficial across a wide range of application domains. For example, in safety-critical systems, it may be essential to establish credible bounds on the probability with which certain failures or combinations of failures can occur. In embedded control systems, it is often important to comply with strict constraints on timing or resources. More generally, being able to derive guarantees on precisely specified levels of performance or efficiency is a valuable tool in the design of, for example, wireless networking protocols, robotic systems or power management algorithms, to name but a few. This report gives a short introduction to quantitative verification, focusing in particular on a widely used technique called model checking, and its generalisation to the analysis of quantitative aspects of a system such as timing, probabilistic behaviour or resource usage. The intended audience is industrial designers and developers of systems such as those highlighted above who could benefit from the application of quantitative verification,but lack expertise in formal verification or modelling

A synthesis of logic and bio-inspired techniques in the design of dependable systems

Much of the development of model-based design and dependability analysis in the design of dependable systems, including software intensive systems, can be attributed to the application of advances in formal logic and its application to fault forecasting and verification of systems. In parallel, work on bio-inspired technologies has shown potential for the evolutionary design of engineering systems via automated exploration of potentially large design spaces. We have not yet seen the emergence of a design paradigm that effectively combines these two techniques, schematically founded on the two pillars of formal logic and biology, from the early stages of, and throughout, the design lifecycle. Such a design paradigm would apply these techniques synergistically and systematically to enable optimal refinement of new designs which can be driven effectively by dependability requirements. The paper sketches such a model-centric paradigm for the design of dependable systems, presented in the scope of the HiP-HOPS tool and technique, that brings these technologies together to realise their combined potential benefits. The paper begins by identifying current challenges in model-based safety assessment and then overviews the use of meta-heuristics at various stages of the design lifecycle covering topics that span from allocation of dependability requirements, through dependability analysis, to multi-objective optimisation of system architectures and maintenance schedules

Quantitative evaluation of Pandora Temporal Fault Trees via Petri Nets

© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Using classical combinatorial fault trees, analysts are able to assess the effects of combinations of failures on system behaviour but are unable to capture sequence dependent dynamic behaviour. Pandora introduces temporal gates and temporal laws to fault trees to allow sequence-dependent dynamic analysis of events. Pandora can be easily integrated in model-based design and analysis techniques; however, the combinatorial quantification techniques used to solve classical fault trees cannot be applied to temporal fault trees. Temporal fault trees capture state and therefore require a state space solution for quantification of probability. In this paper, we identify Petri Nets as a possible framework for quantifying temporal trees. We describe how Pandora fault trees can be mapped to Petri Nets for dynamic dependability analysis and demonstrate the process on a fault tolerant fuel distribution system model

FAULT TREES AND BELIEF NETWORKS IN RISK MODELLING: A COMPARATIVE ANALYSIS

Nowadays, an ever-growing complexity of technical systems can be observed worldwide, problems of rational use of nature resources and diminution in negative impact on the environment are not completely settled yet, and international competition in different areas is strengthening. All the above tendencies cause an increase of different risks: technical, ecological, political, military and financial. Due to their nature, most of the risks are caused by a set of factors with commonly unknown relationships. Therefore, the need to use risk modelling methods that enable visual representation of the sets of cause-risk relationships becomes evident. This paper briefly examines two widely used techniques of modelling risky situations: fault trees and belief networks, and provides their comparative analysis

A review of applications of fuzzy sets to safety and reliability engineering

Safety and reliability are rigorously assessed during the design of dependable systems. Probabilistic risk assessment (PRA) processes are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). In conventional PRA, failure data about components is required for the purposes of quantitative analysis. In practice, it is not always possible to fully obtain this data due to unavailability of primary observations and consequent scarcity of statistical data about the failure of components. To handle such situations, fuzzy set theory has been successfully used in novel PRA approaches for safety and reliability evaluation under conditions of uncertainty. This paper presents a review of fuzzy set theory based methodologies applied to safety and reliability engineering, which include fuzzy FTA, fuzzy FMEA, fuzzy ETA, fuzzy Bayesian networks, fuzzy Markov chains, and fuzzy Petri nets. Firstly, we describe relevant fundamentals of fuzzy set theory and then we review applications of fuzzy set theory to system safety and reliability analysis. The review shows the context in which each technique may be more appropriate and highlights the overall potential usefulness of fuzzy set theory in addressing uncertainty in safety and reliability engineering

Supporting group maintenance through prognostics-enhanced dynamic dependability prediction

Condition-based maintenance strategies adapt maintenance planning through the integration of online condition monitoring of assets. The accuracy and cost-effectiveness of these strategies can be improved by integrating prognostics predictions and grouping maintenance actions respectively. In complex industrial systems, however, effective condition-based maintenance is intricate. Such systems are comprised of repairable assets which can fail in different ways, with various effects, and typically governed by dynamics which include time-dependent and conditional events. In this context, system reliability prediction is complex and effective maintenance planning is virtually impossible prior to system deployment and hard even in the case of condition-based maintenance. Addressing these issues, this paper presents an online system maintenance method that takes into account the system dynamics. The method employs an online predictive diagnosis algorithm to distinguish between critical and non-critical assets. A prognostics-updated method for predicting the system health is then employed to yield well-informed, more accurate, condition-based suggestions for the maintenance of critical assets and for the group-based reactive repair of non-critical assets. The cost-effectiveness of the approach is discussed in a case study from the power industry

Abstractions of stochastic hybrid systems

Many control systems have large, infinite state space that can not be easily abstracted. One method to analyse and verify these systems is reachability analysis. It is frequently used for air traffic control and power plants. Because of lack of complete information about the environment or unpredicted changes, the stochastic approach is a viable alternative. In this paper, different ways of introducing rechability under uncertainty are presented. A new concept of stochastic bisimulation is introduced and its connection with the reachability analysis is established. The work is mainly motivated by safety critical situations in air traffic control (like collision detection and avoidance) and formal tools are based on stochastic analysis

A hybrid modular approach for dynamic fault tree analysis

YesOver the years, several approaches have been developed for the quantitative analysis of dynamic fault trees (DFTs). These approaches have strong theoretical and mathematical foundations; however, they appear to suffer from the state-space explosion and high computational requirements, compromising their efficacy. Modularisation techniques have been developed to address these issues by identifying and quantifying static and dynamic modules of the fault tree separately by using binary decision diagrams and Markov models. Although these approaches appear effective in reducing computational effort and avoiding state-space explosion, the reliance of the Markov chain on exponentially distributed data of system components can limit their widespread industrial applications. In this paper, we propose a hybrid modularisation scheme where independent sub-trees of a DFT are identified and quantified in a hierarchical order. A hybrid framework with the combination of algebraic solution, Petri Nets, and Monte Carlo simulation is used to increase the efficiency of the solution. The proposed approach uses the advantages of each existing approach in the right place (independent module). We have experimented the proposed approach on five independent hypothetical and industrial examples in which the experiments show the capabilities of the proposed approach facing repeated basic events and non-exponential failure distributions. The proposed approach could provide an approximate solution to DFTs without unacceptable loss of accuracy. Moreover, the use of modularised or hierarchical Petri nets makes this approach more generally applicable by allowing quantitative evaluation of DFTs with a wide range of failure rate distributions for basic events of the tree.This work was supported in part by the Dependability Engineering Innovation for Cyber Physical Systems (CPS) (DEIS) H2020 Project under Grant 732242, and in part by the LIVEBIO: Light-weight Verification for Synthetic Biology Project under Grant EPSRC EP/R043787/1