Reliability Analysis of Systems with Dynamic Dependencies (original) (raw)

Probabilistic Algebraic Analysis of Fault Trees With Priority Dynamic Gates and Repeated Events

IEEE Transactions on Reliability, 2000

This paper focuses on a sub-class of Dynamic Fault Trees (DFTs), called Priority Dynamic Fault Trees (PDFTs), containing only static gates, and Priority Dynamic Gates (Priority-AND, and Functional Dependency) for which a priority relation among the input nodes completely determines the output behavior. We define events as temporal variables, and we show that, by adding to the usual Boolean operators new temporal operators denoted BEFORE and SIMULTANEOUS, it is possible to derive the structure function of the Top Event with any cascade of Priority Dynamic Gates, and repetition of basic events. A set of theorems are provided to express the structure function in a sum-of-product canonical form, where each product represents a set of cut sequences for the system. We finally show through some examples that the canonical form can be exploited to determine directly and algebraically the failure probability of the Top Event of the PDFT without resorting to the corresponding Markov model. The advantage of the approach is that it provides a complete qualitative description of the system, and that any failure distribution can be accommodated.

A Static Analysis of Dynamic Fault Trees with Priority-AND Gates

2013 Sixth Latin-American Symposium on Dependable Computing, 2013

A PAND gate is a special AND gate of Dynamic Fault Trees (DFTs) where the input events must occur in a specific order for the occurrence of its output event. We present a transformation from a PAND gate to an AND gate with some dependent conditioning events, called CAND gate, provided that the dynamic behavior of the system can be modeled by a (semi-)Markov process. With the transformation, a DFT with only static Boolean logic gates and PAND gates can be transformed into a static fault tree, which opens up the way to employ efficient combinatorial analysis for the DFT. In addition, the PAND gate cannot model the priority relations between the events whose occurrences are not necessary for the output event. The inability has not been addressed before and it can be overcome by the proposed CAND gate. 2013 6th Latin-American Symposium on Dependable Computing 978-0-7695-4962-0/13 $26.00

Quantitative Analysis of Dynamic Fault Trees Based on the Structure Function

Quality and Reliability Engineering International, 2014

This paper presents a probabilistic model of dynamic gates which allows to perform the quantitative analysis of any dynamic fault tree (DFT) from its structure function. Both these probabilistic models and the quantitative analysis which can be performed thanks to them can accommodate any failure distribution of basic events. We illustrate our approach on a DFT example from the literature.

A compositional semantics for dynamic fault trees in terms of interactive Markov chains

AUTOMATED TECHNOLOGY FOR VERIFICATION AND ANALYSIS PROCEEDINGSBook Series Lecture Notes in Computer Science, 2007

Dynamic fault trees (DFTs) are a versatile and common formalism to model and analyze the reliability of computer-based systems. This paper presents a formal semantics of DFTs in terms of input/output interactive Markov chains (I/O-IMCs), which extend continuous-time Markov chains with discrete input, output and internal actions. This semantics provides a rigorous basis for the analysis of DFTs. Our semantics is fully compositional, that is, the semantics of a DFT is expressed in terms of the semantics of its elements (i.e. basic events and gates). This enables an efficient analysis of DFTs through compositional aggregation, which helps to alleviate the state-space explosion problem by incrementally building the DFT state space. We have implemented our methodology by developing a tool, and showed, through four case studies, the feasibility of our approach and its effectiveness in reducing the state space to be analyzed.

Dynamic Model-based Safety Analysis: From State Machines to Temporal Fault Trees

Finite state transition models such as State Machines (SMs) have become a prevalent paradigm for the description of dynamic systems. Such models are well-suited to modelling the behaviour of complex systems, including in conditions of failure, and where the order in which failures and fault events occur can affect the overall outcome (e.g. total failure of the system). For the safety assessment though, the SM failure behavioural models need to be converted to analysis models like Generalised Stochastic Petri Nets (GSPNs), Markov Chains (MCs) or Fault Trees (FTs). This is particularly important if the transformed models are supported by safety analysis tools.

Algebraic expression of the structure function of a subclass of dynamic fault trees

2nd IFAC Workshop on Dependable Control of Discrete Systems (2009), 2009

This paper focuses on a subclass of Dynamic Fault Trees (DFTs), called Priority Dynamic Fault Trees (PDFTs), containing only static gates and Priority Dynamic Gates (PAND and FDEP) for which a priority relation among the input nodes completely determines the output behavior. We define events as temporal variables and we show that, by adding to the usual Boolean operators new temporal operators denoted BEFORE and SIMULTANEOUS, it is possible to derive the structure function of the Top Event with any cascade of Priority Dynamic Gates and repetition of basic events. A set of theorems are provided to express the structure function in a sum-of-product canonical form. We finally show through an example that the canonical form can be exploited in order to determine directly and algebraically the failure probability of the Top Event of the PDFT without resorting to the corresponding Markov model. The advantage of this approach is that it provides a complete qualitative description of the system and that any failure distribution can be accommodated.

DBNet, a tool to convert Dynamic Fault Trees into Dynamic

The unreliability evaluation of a system including dependencies involving the state of components or the failure events, can be performed by modelling the system as a Dynamic Fault Tree (DFT). The combinatorial technique used to solve standard Fault Trees is not suitable for the analysis of a DFT. The conversion into a Dynamic Bayesian Network (DBN) is a way to analyze a DFT. This paper presents a software tool allowing the automatic analysis of a DFT exploiting its conversion to a DBN. First, the architecture of the tool is described, together with the rules implemented in the tool, to convert dynamic gates in DBNs. Then, the tool is tested on a case of system: its DFT model and the corresponding DBN are provided and analyzed by means of the tool. The obtained unreliability results are compared with those returned by other tools, in order to verify their correctness. Moreover, the use of DBNs allows to compute further results on the model, such as diagnostic and sensitivity indices.

Reliability analysis of non repairable systems using stochastic Petri nets

[1988] The Eighteenth International Symposium on Fault-Tolerant Computing. Digest of Papers

Many real-life systems are typically involved in sequence-dependent failure behaviors. Such systems can be modeled by dynamic fault trees (DFTs) with priority AND gates, in which the occurrence of the top events depends on not only combinations of basic events but also their failure sequences. To the author's knowledge, the existing methods for reliability assessment of DFTs with priority AND gates are mainly Markov-state-space-based, inclusion-exclusion-based, Monte Carlo simulation-based, or sequential binary decision diagram-based approaches. Unfortunately, all these methods have their shortcomings. They either suffer the problem of state space explosion or are restricted to exponential components time-to-failure distributions or need a long computation time to obtain a solution with a high accuracy. In this article, a novel method based on dynamic binary decision tree (DBDT) is first proposed. To build the DBDT model of a given DFT, we present an adapted format of the traditional Shannon's decomposition theorem. Considering that the chosen variable index has a great effect on the final scale of disjoint calculable cut sequences generated from a built DBDT, which to some extent determines the computational efficiency of the proposed method, some heuristic branching rules are presented. To validate our proposed method, a case study is analyzed. The results indicate that the proposed method is reasonable and efficient.

Analytical Calculation of Failure Probabilities in Dynamic Fault Trees including Spare Gates

This paper focuses on one of the dynamic gates which are used in Dynamic Fault Trees (DFT): the Spare gate. We provide an algebraic model which allows to determine the structure function of DFTs with Spare gates from which qualitative analysis can be performed directly. We also provide a probabilistic model allowing to determine the failure probability of Spare gates without any restriction on the failure distribution for basic events.

A translation of State Machines to temporal fault trees

2010

State Machines (SMs) are increasingly being used to gain a better understanding of the failure behaviour of safety-critical systems. In dependability analysis, SMs are translated to other models, such as Generalized Stochastic Petri Nets (GSPNs) or combinatorial fault trees. The former does not enable qualitative analysis, whereas the second allows it but can lead to inaccurate or erroneous results, because combinatorial fault trees do not capture the temporal semantics expressed by SMs. In this paper, we discuss the problem and propose a translation of SMs to temporal fault trees using Pandora, a recent technique for introducing temporal logic to fault trees, thus preserving the significance of the temporal sequencing of faults and allowing full qualitative analysis. Since dependability models inform the design of condition monitoring and failure prevention measures, improving the representation and analysis of dynamic effects in such models can have a positive impact on proactive failure avoidance.