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

Quantification of temporal fault trees based on fuzzy set theory

© Springer International Publishing Switzerland 2014. Fault tree analysis (FTA) has been modified in different ways to make it capable of performing quantitative and qualitative safety analysis with temporal gates, thereby overcoming its limitation in capturing sequential failure behaviour. However, for many systems, it is often very difficult to have exact failure rates of components due to increased complexity of systems, scarcity of necessary statistical data etc. To overcome this problem, this paper presents a methodology based on fuzzy set theory to quantify temporal fault trees. This makes the imprecision in available failure data more explicit and helps to obtain a range of most probable values for the top event probability

Reliability analysis of dynamic systems by translating temporal fault trees into Bayesian networks

Classical combinatorial fault trees can be used to assess combinations of failures but are unable to capture sequences of faults, which are important in complex dynamic systems. A number of proposed techniques extend fault tree analysis for dynamic systems. One of such technique, Pandora, introduces temporal gates to capture the sequencing of events and allows qualitative analysis of temporal fault trees. Pandora can be easily integrated in model-based design and analysis techniques. It is, therefore, useful to explore the possible avenues for quantitative analysis of Pandora temporal fault trees, and we identify Bayesian Networks as a possible framework for such analysis. We describe how Pandora fault trees can be translated to Bayesian Networks for dynamic dependability analysis and demonstrate the process on a simplified fuel system model. The conversion facilitates predictive reliability analysis of Pandora fault trees, but also opens the way for post-hoc diagnostic analysis of failures

Qualitative temporal analysis: Towards a full implementation of the Fault Tree Handbook

The Fault tree handbook has become the de facto standard for fault tree analysis (FTA), defining the notation and mathematical foundation of this widely used safety analysis technique. The Handbook recognises that classical combinatorial fault trees employing only Boolean gates cannot capture the potentially critical significance of the temporal ordering of failure events in a system. Although the Handbook proposes two dynamic gates that could remedy this, a Priority-AND and an Exclusive-OR gate, these gates were never accurately defined. This paper proposes extensions to the logical foundation of fault trees that enable use of these dynamic gates in an extended and more powerful FTA. The benefits of this approach are demonstrated on a generic triple-module standby redundant system exhibiting dynamic behaviour

Compositional synthesis of temporal fault trees from state machines

Dependability analysis of a dynamic system which is embedded with several complex interrelated components raises two main problems. First, it is difficult to represent in a single coherent and complete picture how the system and its constituent parts behave in conditions of failure. Second, the analysis can be unmanageable due to a considerable number of failure events, which increases with the number of components involved. To remedy this problem, in this paper we outline an analysis approach that converts failure behavioural models (state machines) to temporal fault trees (TFTs), which can then be analysed using Pandora -- a recent technique for introducing temporal logic to fault trees. The approach is compositional and potentially more scalable, as it relies on the synthesis of large system TFTs from smaller component TFTs. We show, by using a Generic Triple Redundant (GTR) system, how the approach enables a more accurate and full analysis of an increasingly complex system

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

Model-based dependability analysis : state-of-the-art, challenges and future outlook

Abstract: Over the past two decades, the study of model-based dependability analysis has gathered significant research interest. Different approaches have been developed to automate and address various limitations of classical dependability techniques to contend with the increasing complexity and challenges of modern safety-critical system. Two leading paradigms have emerged, one which constructs predictive system failure models from component failure models compositionally using the topology of the system. The other utilizes design models - typically state automata - to explore system behaviour through fault injection. This paper reviews a number of prominent techniques under these two paradigms, and provides an insight into their working mechanism, applicability, strengths and challenges, as well as recent developments within these fields. We also discuss the emerging trends on integrated approaches and advanced analysis capabilities. Lastly, we outline the future outlook for model-based dependability analysis

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

Quantification of Simultaneous-AND Gates in Temporal Fault Trees

Fault Tree Analysis has been a cornerstone of safety-critical systems for many years. It has seen various extensions to enable it to analyse dynamic behaviours exhibited by modern systems with redundant components. However, none of these extended FTA approaches provide much support for modelling situations where events have to be "nearly simultaneous", i.e., where events must occur within a certain interval to cause a failure. Although one such extension, Pandora, is unique in providing a "Simultaneous-AND" gate, it does not allow such intervals to be represented. In this work, we extend the Simultaneous-AND gate to include a parameterized interval - referred to as pSAND - such that the output event occurs if the input events occur within a defined period of time. This work then derives an expression for the exact quantification of pSAND for exponentially distributed events and provides an approximation using Monte Carlo simulation which can be used for other distributions

Quantitative analysis of dynamic safety-critical systems using temporal fault trees

Emerging technological systems present complexities that pose new risks and hazards. Some of these systems, called safety-critical systems, can have very disastrous effects on human life and the environment if they fail. For this reason, such systems may feature multiple modes of operation, which may make use of redundant components, parallel architectures, and the ability to fall back to a degraded state of operation without failing completely. However, the introduction of such features poses new challenges for systems analysts, who need to understand how such systems behave and estimate how reliable and safe they really are.Fault Trees Analysis (FTA) is a technique widely accepted and employed for analysing the reliability of safety-critical systems. With FTA, analysts can perform both qualitative and quantitative analyses on safety-critical systems. Unfortunately, traditional FTA is unable to efficiently capture some of the dynamic features of modern systems. This problem is not new; various efforts have been made to develop techniques to solve it. Pandora is one such technique to enhance FTA. It uses new 'temporal' logic gates, in addition to some existing ones, to model dynamic sequences of events and eventually produce combinations of basic events necessary and sufficient to cause a system failure. Until now, Pandora was not able to quantitatively evaluate the probability of a system failure. This is the motivation for this thesis.This thesis proposes and evaluates various techniques for the probabilistic evaluation of the temporal gates in Pandora, enabling quantitative temporal fault tree analysis. It also introduces a new logical gate called the 'parameterised Simultaneous-AND' (pSAND) gate. The proposed techniques include both analytical and simulation-based approaches. The analytical solution supports only component failures with exponential distribution whilst the simulation approach is not restricted to any specific component failure distribution. Other techniques for evaluating higher order component combinations, which are results of the propagation of individual gates towards a system failure, have also been formulated. These mathematical expressions for the evaluation of individual gates and combinations of components have enabled the evaluation of a total system failure and importance measures, which are of great interest to system analysts