Reliability analysis of non repairable systems using stochastic Petri nets (original) (raw)
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Dynamic Fault Tree Analysis Based on Petri Nets
—In traditional Dynamical Fault Tree analysis, it is necessary to modularize DFT tree firstly so as to obtain static subtrees and dynamic subtrees. Generally, Binary Decision Diagram (BDD) and Markov chains are utilized in the DFT to process static and dynamic subtrees, respectively. However, due to the possibility of state combinatorial explosion problem in Markov chain, it is difficult to analyze system with DFT in some cases. This paper investigated Petri net method in DFT in order to solve this problem. An example of processor system is analyzed with the proposed Petri net based DFT, which contains many dynamic logic gates in two classes. The analysis results show that the proposed method can overcome the state combinatorial explosion problem and guarantee high accuracy.
IEEE Transactions on …, 2003
In order to cope efficiently with the dependability analysis of redundant systems with replicated units, a new, more compact fault-tree formalism, called Parametric Fault Tree (PFT), is defined. In a PFT formalism, replicated units are folded and indexed so that only one representative of the similar replicas is included in the model. From the PFT, a list of parametric cut sets can be derived, where only the relevant patterns leading to the system failure are evidenced regardless of the actual identity of the component in the cut set. The paper provides an algorithm to convert a PFT into a class of High-Level Petri Nets, called SWN. The purpose of this conversion is twofold: to exploit the modeling power and flexibility of the SWN formalism, allowing the analyst to include statistical dependencies that could not have been accommodated into the corresponding PFT; to exploit the capability of the SWN formalism to generate a lumped Markov chain, thus alleviating the state explosion problem. The search for the minimal cut sets (qualitative analysis) can be often performed by a structural T-invariant analysis on the generated SWN. The advantages that can be obtained from the translation of a PFT into a SWN are investigated considering a fault-tolerant multiprocessor system example.
Failure scenarios analysis constitutes one of the cornerstones of risk assessment and availability analysis. After a detailed review of available methods, this paper identified two distinct formalisms to analyze failure scenarios and systems' availability: generalized stochastic Petri nets (GSPN) and Fault tree driven Markov processes (FTDMP). The FTDMP formalism is a combination of the Markov process and the fault tree. This aims to overcome fault tree limitations while maintaining the use of deductive logic. The GSPN is a Petri net with probabilistic analysis using Monte Carlo simulation. The effectiveness of both methods is studied through an emergency flare system including a knockout drum. It is observed that GSPN provides a robust and reliable mechanism for accident scenario analysis. It provides additional information such as events' frequencies at operating and failing modes and expected occurrence timing and durations resulting from different complex sequences. Even for multi-state variables which could be used to design a safety management system. Although FTDMP is a powerful formalism, it provides limited information.
Equivalence of Fault Trees and Stochastic Petri Nets in Reliability Modelling
DOAJ (DOAJ: Directory of Open Access Journals), 2020
Modeling of reliability of the complex systems (machines, large networks, human body) is an important area of recent research. There are two main approaches applied: i) fault trees, ii) Petri nets. For the probabilistic study of a system is vital to know its minimal cut/minimal path sets. Both for fault trees and Petri Nets it is an NP-hard problem. Liu and Chiou (1997) described the equivalence of both representations for a given system. Furthermore, they found a top-down matrix algorithm to find critical cuts and minimal paths of the Petri net of the system. They claim without proof that their algorithm is more efficient than the ones for fault trees. We present both representations of a system. The algorithm is illustrated on a simple example of a three-masted vessel and a more complex "three-motor" system by Vesely et al. (1981).
Petri Nets and …, 2001
The case-study presented in this paper is aimed at assessing the dependability of a Programmable Logic Controller (PLC) devoted to safety functions. This case study has been brought to our attention by a national environmental agency and has been partially abstracted and anonymized to protect proprietary information. The PLC consists of a triplicated channel with a (2 : 3) majority voting logic and is modeled by means of a recently proposed extension of the classical Fault Tree (FT) formalism called Parametric Fault Tree (PFT). In the PFT replicated units are folded and parameterized so that only one representative of the various similar replicas is explicitly included in the model. The quantitative analysis of the PFT assumes s-independence among components and is based on combinatorial formulas. In order to include dependencies both in the failure and repair process, the PFT is directly converted into a particular class of High Level Petri Nets, called SWN. The paper illustrates the PFT formalism and the automatic conversion algorithm from a PFT into a SWN. Moreover, it is shown how various kind of dependencies can be accommodated in the obtained SWN model.
2009
Binary decision diagrams (BDDs) are a well-known alternative to the minimal cutsets (MCS) approach to assess Boolean reliability models. While the application of fault tree analysis can be considered to be consolidated, its application to the event trees involved in the probabilistic safety assessment (PSA) studies of the nuclear industry require extended efforts. For many real PSA models the full conversion procedure remains out of reach in terms of computational resources owing to their size, non-coherency, redundancy, and complexity. A potential solution to improve the quality of assessment methods is to design hybrid algorithms that combine the information derived from the calculation of MCS with the BDD methodology.
A Hybrid Modular Approach for Dynamic Fault Tree Analysis
IEEE Access
Over 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. INDEX TERMS Reliability analysis, fault tree analysis, dynamic fault trees, modularisation, petri nets.
Combining various solution techniques for dynamic fault tree analysis of computer systems
Proceedings Third IEEE International High-Assurance Systems Engineering Symposium (Cat. No.98EX231)
Fault trees provide a conceptually simple modeling framework to represent system-level reliability in terms of interactions between component reliabilities. DIFtree [1] effectively combines the best static fault tree solution technique (Binary Decision Diagrams) with Markov solution techniques for dynamic fault trees. DIFtree includes advanced techniques for modeling coverage; coverage modeling has been shown to be critical to the analysis of fault tolerant computer systems. DIFtree is based on a divideand-conquer technique for modularizing the system level fault tree into independent sub-trees; different solution techniques can be used for sub-trees. In this paper we extend the DIFtree analysis capability to model several different distributions of time to failure, including fixed probabilities (no time component), exponential (constant hazard rate), Weibull (time varying hazard rate), and log normal. Our approach extends both the BDD and Markov analytical approaches and incorporates simulation as well.
Fault Trees, Decision Trees, And Binary Decision Diagrams: A Systematic Comparison
Proceedings of the 31st European Safety and Reliability Conference (ESREL 2021), 2021
In reliability engineering, we need to understand system dependencies, cause-effect relations, identify critical components, and analyze how they trigger failures. Three prominent graph models commonly used for these purposes are fault trees (FTs), decision trees (DTs), and binary decision diagrams (BDDs). These models are popular because they are easy to interpret, serve as a communication tool between stakeholders of various backgrounds, and support decision-making processes. Moreover, these models help to understand real-world problems by computing reliability metrics, minimum cut sets, logic rules, and displaying dependencies. Nevertheless, it is unclear how these graph models compare. Thus, the goal of this paper is to understand the similarities and differences through a systematic comparison based on their (i) purpose and application, (ii) structural representation, (iii) analysis methods, (iv) construction, and (v) benefits & limitations. Furthermore, we use a running example based on a Container Seal Design to showcase the models in practice. Our results show that, given that FTs, DTs and BDDs have different purposes and application domains, they adopt different structural representations and analysis methodologies that entail a variety of benefits and limitations, the latter can be addressed via conversion methods or extensions. Specific remarks are that BDDs can be considered as a compact representation of binary DTs, since the former allow sub-node sharing, which makes BDDs more efficient at representing logical rules than binary DTs. It is possible to obtain cut sets from BDDs and DTs and construct a FT using the (con/dis)junctive normal form, although this may result in a sub-optimal FT structure.