1,720,981 research outputs found
Reduced ZBDD Construction Algorithms for Large Fault Trees Analysis
No full textThe determination of the small set of Significant Minimal Cut Sets (SMCS) is currently the unique mode for analysing complex trees. The set of SMCS is made up by failure combinations having probability greater than and / or order less than pre-established probabilistic and logical thresholds. Rules for constructing a Reduced ZBDD (RZBDD) embedding all SMCS satisfying the cut-off conditions was proposed by Jung et al. for coherent fault trees. This paper describes an improved implementation of the Jung method and a new set of rules for the construction of an RZBDD for non-coherent fault trees. The proposed method is based on a Labelled BDD (LBDD) in which the information about the variable type is dynamically associated to the nodes. Test results of the application of the RZBDD algorithms implemented in the JRC ASTRA fault tree analyser will be provided to show the efficiency of the proposed methods.JRC.DG.G.7 - Traceability and vulnerability assessmen
On the efficiency of functional decomposition in fault tree analysis
No full textRecently the functional decomposition method for the analysis of complex fault trees was proposed by the authors. A fault tree is recursively decomposed into a set of mutually exclusive simpler fault trees up to their dimensions are compatible with the available working memory size. Then, the analysis results of simpler trees are composed to obtain the results for the original un-decomposed fault tree. Since a fault tree is decomposed with respect to a small subset S of the vector x of basic events, the efficiency of the decomposition process is highly dependent on this subset. Hence the problem is how to select the events of S in order to minimise the fault tree analysis time. This paper describes and compares four different methods to construct S with the aim of identifying the one for which the decomposition procedure requires the least computational resources. Due to the heuristic nature of this problem it was necessary to experimentally test all criteria on a number of fault trees in order to draw useful indications on the relatively “best” method(s).JRC.G.5 - Security technology assessmen
ASTRA 3.0: Test Case Report
Get PDFIn the context of activities related to the application of system analysis to safety and security of critical installations a new logical and probabilistic fault tree analysis procedure was developed and implemented in the software package ASTRA, version 3.0. This report contains the results of the logical and probabilistic analysis for a limited, but significant, subset of test cases considered during the test campaign performed at the JRC. Most of the described test cases come from the open literature, for which results are available to the reader. For more complex test cases ASTRA 3.0 was compared with other available tools, such as ASTRA 2.0 and XS-MKA, a Markovian analysis package. The experience gained with the testing activity also allowed the identification of a set of recommendations for future improvements.JRC.DG.G.7 - Traceability and vulnerability assessmen
ASTRA 3.0: Logical and Probabilistic Analysis Methods
Get PDFThis report contains the description of the main methods, implemented in ASTRA 3.0, to analyse coherent and non-coherent fault trees. ASTRA 3.0 is fully based on the Binary Decision Diagrams (BDD) approach. In case of non-coherent fault trees ASTRA 3.0 dynamically assigns to each node of the graph a label that identifies the type of the associated variable in order to drive the application of the most suitable analysis algorithms. The resulting BDD is referred to as Labelled BDD (LBDD). Exact values of the unavailability, expected number of failure and repair are calculated; the unreliability upper bound is automatically determined under given conditions. Five different importance measures of basic events are also provided. From the LBDD a ZBDD embedding all the MCS is obtained from which a subset of Significant Minimal Cut Sets (SMCS) is determined through the application of the cut-off techniques.
With very complex trees it may happen that the working memory is not sufficient to store the large LBDD structure. In these cases ASTRA 3.0 completes the analysis by constructing a Reduced ZBDD embedding the SMCS - using cut-off techniques - thus by-passing the construction of the LBDD.
The report also contains few tutorials on the usefulness of non-coherent fault trees, on the BDD approach, and on the determination of failure and repair frequencies.JRC.DG.G.7 - Traceability and vulnerability assessmen
A new method for evaluation of the qualitative importance measures
No full textThe importance measures are utilized in the probabilistic safety analysis (PSA) to assess the impact of risk contributors on the selected risk measure. The particular risk measure can be safety system unavailability, the core melt frequency, expected latent fatalities or some other measure of system unreliability or plant risk. The importance measures are divided into quantitative and qualitative. The qualitative importance measures are derived for the qualitative, logic structure of the PSA. The logic structure of the PSA includes the fault tree and event tree models, the failure combinations causing undesired events and the success paths preventing undesired events. The exact logic expression of the selected risk measure is required input for assessment of the qualitative importance measures. The assessment of the exact logic expression is complex even for a small system. A new method of assessment of the qualitative importance of the events in the fault tree is developed and presented in this paper. The qualitative importance of the events is assessed with new qualitative importance measures. The new measures are obtained from the Birnbaum importance measure and application of the min cut upper bound approximation. The minimal cut sets of the analyzed system, as standard qualitative result, are required input for the assessment of the new measures. The developed method is applied on test systems. The ranking of the events based on new qualitative importance measure is compared to the ranking based on structural measure of importance. The structural measure of importance of the events is assessed with application of the binary decision diagram. Obtained results show that ranking of the events based on the new qualitative importance measure is comparable to the ranking obtained by structural importance measure. Utilization of the new qualitative importance measures together with quantitative importance measures for classification of the systems, structures and components is discussed.JRC.G.10 - Knowledge for Nuclear Security and Safet
Analysis of large fault trees based on functional decomposition
No full textWith the advent of the Binary Decision Diagrams (BDD) approach in fault tree analysis a significant enhancement has been achieved, with respect to previous approaches, both in terms of efficiency and accuracy of the overall outcome of the analysis. However, the exponential increase of the number of nodes with the complexity of the fault tree may prevent the construction of the BDD. In these cases the only way to complete the analysis is to reduce the complexity of the BDD by applying the truncation technique, which nevertheless implies the problem of estimating the truncation error or upper and lower bounds of the top event unavailability.
This paper describes a new method to analyse large coherent fault trees which can be advantageously applied when the working memory is not sufficient to perform the analysis with current methods. It is based on the decomposition of the fault tree into simpler disjoint functions containing a lower number of variables. The number and complexity of these functions depend on the dimensions of the available working memory, i.e. the smaller is the working memory the greater is the number of functions and vice versa. The analysis of each simple function is performed by using all the computational resources. The results from the analysis of all simpler functions are re-combined to obtain the results for the original fault tree.
Two decomposition methods are herewith described: the first aims at determining the minimal cut sets (MCS) and the upper and lower bounds of the top-event unavailability; the second can be applied to determine the exact value of the top-event unavailability. Potentialities, limitations and possible variations of these methods will be discussed with reference to the results of their application to some complex fault trees.JRC.DG.G.7 - Traceability and vulnerability assessmen
ASTRA Plus User Manual
Get PDFThis report describes the user interface and the main commands to perform system dependability analysis by means of ASTRA Plus. This package implements the analysis methods developed at the Institute for the Protection and Security of the Citizen from mid-2008. ASTRA Plus is composed of the Fault Tree Analysis (FTA) module and of the Concurrent Importance and Sensitivity Analysis (CISA) module.
The FTA module contains three different methods for solving a fault tree; all are based on the state of the art approach of Binary Decision Diagrams (BDD). These three methods allow the user to analyse fault trees of increasing complexity (i.e. increasing number of basic events and gates). In particular the third method, which is based on functional decomposition, allow performing the analysis of fault trees of very high complexity.
The CISA module is based on a new methodology for system design improvement. The key operation is the calculation of Global Importance Measures of basic events considering all system fault trees. This allows identifying the weakest part of the system with reference to all top-events. Then the on-line sensitivity analysis allows the user to rapidly identify the set of suitable design improvements from which the best cost-effective one can be selected.JRC.G.6 - Security technology assessmen
Components' IMportance Measures for Initiating and Enabling events in Fault Tree Analysis
Get PDFThis report deals with the problem of determining the exact values of the importance indexes of basic events in case of both unavailability and frequency analysis of coherent and non-coherent fault trees. In particular a new method is described for determining the importance of enabling events in case of frequency analysis. Insights are given into the importance analysis implemented in the new software ASTRA 3.0 based on the Binary Decision Diagram approach with Labelled variables (LBDD). The analysis methods are also described with reference to modularised fault trees. Simple numerical examples are provided to clarify how the methods work. Proofs of the implemented equations are provided in Appendixes.JRC.DG.G.7 - Traceability and vulnerability assessmen
Impact of different minimal path set selection methods on the efficiency of fault tree decomposition
No full textIn recent papers a new method to analyse complex fault trees was proposed. The fault tree is decomposed into a set of mutually exclusive simpler fault trees up to their dimensions are compatible with the available computational resources. Then, the results of the exact analysis of all simpler trees are composed to obtain the exact results for the original un-decomposed fault tree. The decomposition is based on the events making up a Minimal Path Set (MPS). An MPS is a set of components such that if they are all working the Top event is not verified (i.e. any minimal cut set (MCS) contains at least one event of the MPS). This means that it is possible to partition all MCSs into a given number of sets. In general, complex tree can be decomposed in as many ways as the number of its MPSs. The efficiency of the decomposition method is sensitive to the composition of the MPS. Hence, the problem is the determination of the MPS that minimises the time needed for decomposition based analysis of fault tree. Due to the heuristic nature of this problem it is necessary to experimentally test a number of MPS selection algorithms in order to draw indications on the relatively “best” method(s).JRC.G.6 - Security technology assessmen
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