Binary Decision Diagram Method Research Articles

A hybrid approach of partially applying BDD for seismic PSA quantification

The binary decision diagram (BDD) method provides a means to calculate the exact probability of a fault tree, but cannot solve large fault trees for nuclear power plant PSAs. However, the BDD method can be used as a supplementary means to increase the accuracy of PSA quantification, especially for a seismic PSA which includes many non-rare events.Since it is difficult to solve a large PSA model using BDD method, several approaches have been developed that partially apply the BDD technique to small-sized branches of a large PSA model. This paper proposes an approach of partially applying BDD technique to large-sized branches. The results from the pilot application to a seismic PSA model shows that the partial BDD approach of this paper provides a relatively accurate way to quantify each sequence as well as the overall core damage in a seismic PSA model.

Analytical Calculation and Rapid Simulation of Survival Signatures in Dynamic Fault Trees With Priority-AND Gates

Many practical systems are often involved in sequence-dependent failure behaviors. The efficiency of analyzing these dynamic systems is limited by addressing sequential failure events (SFEs). The survival signature method has the potential to address this issue. However, the survival signature cannot be applied directly due to the existence of SFEs. In this article, the adapted survival signature-based methods are developed for the rapid analysis of dynamic systems modeled by dynamic fault trees with priority- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</small> gates. First, we deduce the probabilistic expressions of SFEs under the survival signature paradigm using conditional probability. Second, an analytical method for accurately computing the survival signatures of dynamic systems is proposed. Third, for large-scale and highly coupled dynamic systems, a semianalytical method is proposed to obtain the survival signature through simulating the Boolean states of SFEs under given components’ state. Several numerical and practical engineering cases are examined to highlight the superiority of the proposed methods compared with the sequential binary decision diagram method and coarse Monte Carlo simulation.

Reliability and Service Life Analysis of Airbag Systems

Airbag systems are important to a car’s safety protection system. To further improve the reliability of the system, this paper analyzes the failure mechanism of automotive airbag systems and establishes a dynamic fault tree model. The dynamic fault tree model is transformed into a continuous-time Bayesian network by introducing a unit step function and an impulse function, from which the failure probability of the system is calculated. Finally, the system reliability and average life are calculated and analyzed and compared with the sequential binary decision diagram method. The results show that the method can obtain more accurate system reliability and effectively identify the weak parts of the automotive airbag system, to a certain extent compensating for the lack of computational complexity of dynamic Bayesian networks in solving system reliability problems with continuous failure processes.

Improved MDD Algorithm for Mission Reliability Estimation of an Escort Formation

An escort formation is a phased mission system of systems (PMSoS), which is composed of multiple ships with different functions. The configuration of the formation and success criteria for a mission may vary in different phases. Reliability estimation for PMSoS is complicated due to the strong phase dependence of multiple systems. This paper proposes an improved multiple-valued decision diagram (MDD) algorithm to perform reliability estimation of a nonrepairable escort formation. First, a phased fault tree is established to describe the failure mode of an escort formation throughout a mission, which is simplified according to the common failure basic mission (module) (CFBM). Bottom events are sorted based on the CFBM, and the case method is adopted to generate an MDD from the simplified fault tree model. On this basis, the MDD method is adopted to estimate mission reliability. The performance of the improved MDD method is compared with that of a binary decision diagram (BDD) method and a general MDD method. The results show that the improved MDD method can offer lower computational complexity as well as a simpler model construction over the BDD method and general MDD method. A case study of an escort formation PMSoS is analyzed to illustrate the proposed MDD method, and the sensitivity and composite importance measure (CIM) of each system are evaluated.

A Failure Mechanism Cumulative Model for Reliability Evaluation of a k-Out-of-n System With Load Sharing Effect

In this paper, we propose a failure mechanism cumulative model that considers the loading history of the load sharing effect in a k-out-of-n system. Three types of failure mechanisms are considered, continuous degradation, compound point degradation, and sudden failure due to shock. By constructing a logic diagram with functional dependence gate, the load-sharing effect can be explained from the failure mechanism point of view using a mechanism-acceleration gate that shows that when one component fails, the failure mechanisms of the other surviving components will be accelerated. By deriving the total damage equation and a constructing failure behavior model, the system reliability of a k-out-of-n system with different types of failure mechanisms were evaluated. A voltage stabilizing system that contains a 1-out-of-2 subsystem, or a 2-out-of 3 subsystem was used to illustrate the practical applicability of the proposed approach. A combined Monte Carlo and binary decision diagram method was used in the numerical simulation process.

Binary decision diagram quantitative analysis method based on fuzzy set theory

A binary decision diagram (BDD) is a data structure that is used to represent a Boolean function. Converting fault tree into BDD can effectively simplify counting processes and improve the accuracy and effectiveness of the results. However, due to various types of uncertainties in reliability data, we cannot obtain precise failure probabilities. In order to accurately quantify the certainties and obtain much more reliable results, we use BDD method based on fuzzy set theory for reliability quantitative analysis. In this regard, we take W-axis feeding system of heavy-duty computer numerical control (CNC) machine as a project example and adopt fuzzy BDD quantitative analysis method to analyze its reliability. The analysis results (aided by computer calculation) illustrate the effectiveness of the method proposed in this paper.

Reliability analysis of complex dynamic fault trees based on an adapted K.D. Heidtmann algorithm

Dynamic fault tree as a powerful analyzing tool is used to model systems having sequence- and function-dependent failure behaviors. The problem is how to quantify a complex dynamic fault tree where different dynamic gates coexist and are highly coupled. Existing analytical methods for analyzing dynamic fault trees are mainly Markov-based, inclusion–exclusion-based and sequential binary decision diagram–based approaches. Unfortunately, all these methods have their own shortcomings. As to the Markov-based method, it is frequently subjected to the problem of state-space explosion and only applicable for systems having components with exponential time-to-failure distributions. For the inclusion–exclusion-based method, it is often vulnerable to the problem of combinatorial explosion. As to the sequential binary decision diagram method, it cannot be directly applied to a complex dynamic fault tree where dynamic gates are highly coupled together, and its computational efficiency greatly depends on the chosen variable index. In this article, we put forward using an adapted K.D. Heidtmann algorithm to analyze the reliability of a complex dynamic fault tree. To improve the computational efficiency of our proposed method, products are ordered according to their lengths and compositions. To illustrate the applicability and advantages of the proposed method, a case study is analyzed. The results show the proposed method is reasonable and efficient.

Multi-objective offshore safety system design optimization

The objective of this paper is to present a multi-objective approach to the design optimization process applied to systems that require a high likelihood of functioning on demand. In the real world it is common that there are several objectives to be met, not just maximising the system availability, and hence an approach is required to deal with these issues. A method is presented that integrates the latest advantages of the fault tree analysis technique and the binary decision diagram method to model the availability issue, along with a multi-objective optimization approach (the Improved Strength Pareto Evolutionary Approach) to cater for meeting the multiple criteria of assessment. The end product is a mechanism to yield the best design option. The paper presents the principles of the method and a case study to illustrate how the method is applied, along with the results produced. The case study relates to a high integrity protection system of an offshore platform. The optimization criteria involves unavailability, cost, spurious trip frequency and maintenance down time. Several enhancements to the optimization strategy to improve the efficiency of the approach are discussed.

Safety system design optimisation using a multi-objective genetic algorithm

This paper describes a design optimisation process applied to systems that require a high likelihood of functioning on demand. It is imperative that the best use of the available resources is made and an optimal rather than just an adequate system design is produced. The contribution of this research is in the development of an integrated approach which not only considers the primary system objective, availability of the system, but caters for all critical factors imperative to obtain an optimal system design. This research therefore combines the latest advantages of the fault tree analysis technique and the binary decision diagram method along with a multi-objective optimisation approach. The application area is a High Integrity Protection System of an offshore platform. The optimisation criteria involves unavailability, cost, spurious trip frequency and maintenance down time. The results produced using this method are compared to those obtained by exhaustive search.

A Graphic Computerised Maintenance Management System for Fault Detection, Supervision and Safety of the Railway Infrastructure

Fault Detection and Diagnostic (FDD) is usually employed for maintenance management. This paper presents an intelligent system applied to FDD. The method is based on a dynamic B-spline approximation. In case that the fault is verified, then the probability of failure is calculated by employing the Fault Tree Analysis (FTA) technique. A Binary Decision Diagram (BDD) is used to provide an alternative to the traditional cutest-based methods for FTA. The BDD method does not analyse the FTA directly, but converts the tree to a BDD that represents the Boolean equation for the top event.

An efficient real‐time method of analysis for non‐coherent fault trees

AbstractFault tree analysis is commonly used to assess the reliability of potentially hazardous industrial systems. The type of logic is usually restricted to AND and OR gates, which makes the fault tree structure coherent. In non‐coherent structures not only components' failures but also components' working states contribute to the failure of the system. The qualitative and quantitative analyses of such fault trees can present additional difficulties when compared with the coherent versions. It is shown that the binary decision diagram (BDD) method can overcome some of the difficulties in the analysis of non‐coherent fault trees. This paper presents the conversion process of non‐coherent fault trees to BDDs. A fault tree is converted to a BDD that represents the system structure function (SFBDD). An SFBDD can then be used to quantify the system failure parameters but is not suitable for the qualitative analysis. Established methods, such as the meta‐products BDD method, the zero‐suppressed BDD (ZBDD) method and the labelled BDD (L‐BDD) method, require an additional BDD that contains all prime implicant sets. The process using some of the methods can be time consuming and is not very efficient. In addition, in real‐time applications the conversion process is less important and the requirement is to provide an efficient analysis. Recent uses of the BDD method are for real‐time system prognosis. In such situations as events happen, or failures occur, the prediction of mission success is updated and used in the decision‐making process. Both qualitative and quantitative assessments are required for the decision making. Under these conditions fast processing and small storage requirements are essential. Fast processing is a feature of the BDD method. It would be advantageous if a single BDD structure could be used for both the qualitative and quantitative analyses. Therefore, a new method, the ternary decision diagram (TDD) method, is presented in this paper, where a fault tree is converted to a TDD that allows both qualitative and quantitative analyses and no additional BDDs are required. The efficiency of the four methods is compared using an example fault tree library. Copyright © 2008 John Wiley &amp; Sons, Ltd.

A binary decision diagram method for phased mission analysis of non-repairable systems

Phased mission analysis is carried out to predict the reliability of systems which undergo a series of phases, each with differing requirements for success, with the mission objective being achieved only on the successful completion of all phases. Many systems from a range of industries experience such missions. The methods used for phased mission analysis are dependent upon the repairability of the system during the phases. If the system is non-repairable, fault-tree-based methods offer an efficient solution. For repairable systems, Markov approaches can be used. This paper is concerned with the analysis of non-repairable systems. When the phased mission failure causes are represented using fault trees, it is shown that the binary decision diagram (BDD) method of analysis offers advantages in the solution process. A new way in which BDD models can be efficiently developed for phased mission analysis is proposed. The paper presents a methodology by which the phased mission models can be developed and analysed to produce the phase failure modes and the phase failure likelihoods.

Searching for feasible splitting strategies of controlled system islanding

Controlled system islanding, also called system splitting, can effectively prevent blackouts of power systems. The splitting strategy determining how to split a power network into islands should be given in real time. Previous papers proposed an ordered binary decision diagram method to search for the splitting strategies satisfying necessary steady-state constraints, e.g. generation–load balance and transmission-line capacity constraint, and also showed that, without any other corrective controls, the splitting strategies may produce unstable islands according to a further simulation study. A modified method to find feasible splitting strategies in real time for large power network is presented. Each feasible splitting strategy not only satisfies necessary steady-state constraints but also easily produces stable islands to prevent a blackout. The method also introduces new techniques into strategy searching to increase its efficiency and practicality, e.g. network partitioning and parallel processing, generator classifying, deriving splitting strategies from cut-set splitting strategies, etc. Simulations on the IEEE 118-bus system show that the real-time portion of the modified method finds feasible splitting strategies in less than one second.

Cause–consequence analysis of non-repairable phased missions

Many systems can be modelled as a mission made up of a sequence of discrete phases. Each phase has a different requirement for successful completion and mission failure will result if any phase is unsuccessful. Fault tree analysis and Markov techniques have been used previously to model this type of system for non-repairable and repairable systems, respectively. Cause–consequence analysis is an alternative assessment technique capable of modelling all system outcomes on one logic diagram. The structure of the diagram has been shown to have advantageous features in both its representation of the system failure logic and its subsequent quantification, which could be applied to phased mission analysis. This paper outlines the use of the cause–consequence diagram method for systems undergoing non-repairable phased missions. Methods for construction of the cause–consequence diagram are first considered. The disjoint nature of the resulting diagram structure can be utilised in the later quantification process. The similarity with the Binary Decision Diagram method enables the use of efficient and accurate solution routines.

A branching search approach to safety system design optimisation

Abstract Safety systems are designed to prevent or mitigate the consequences of potentially hazardous events. In many industries the failure of such systems can result in fatalities. Current design practice is usually to produce a safety system which meets a target level of performance that is deemed acceptable by the regulators. However, when the system failure will result in fatalities it is desirable for the system to achieve an optimal rather than adequate level of performance given the limitations placed on available resources. The unavailability of safety systems can be predicted using fault tree analysis methods. Formulating an optimisation problem for the system design has features which make standard mathematical optimisation techniques inappropriate. The form of the objective function is itself a function of the design variables, the design variables are mainly integers and the constraint forms can be implicit or non-linear. This paper presents a Branching Search algorithm which exploits characteristics common to many safety systems to explore the potential design space and deliver an optimal design. Efficiency in the method is maintained by performing the system unavailability evaluations using the Binary Decision Diagram method of fault tree solution. Limitations are placed on resources such as cost, maintenance down-time and spurious trip frequency. Its application is demonstrated on a High Integrity Protection System.

Improved efficiency in qualitative fault tree analysis

The fault tree diagram itself is an excellent way of deriving the failure logic for a system and representing it in a form which is ideal for communication to managers, designers, operators, etc. Since the method was first conceived, algorithms to derive the minimal cut sets have worked directly with the fault tree diagram using either bottom-up or top-down approaches. These conventional techniques have several disadvantages when it comes to analysing the fault tree. For complex systems an analysis may produce hundreds of thousands of minimal cut sets, the determination of which can be a very time-consuming process. Also, for large fault trees it may not be possible to evaluate all minimal cut sets, so methods to identify those event combinations which provide the most significant contributions to the system failure are evoked. Such methods include probabilistic or order culling to reduce the problem to a practical size, but they can also create considerable inaccuracies when it comes to evaluating top event probability parameters This paper describes how the binary decision diagram method can be employed to evaluate the minimal cut sets of a fault tree efficiently and without the need to use approximations such as order culling. © 1997 John Wiley & Sons, Ltd.

Improved accuracy in quantitative fault tree analysis

The fault tree diagram defines the causes of the system failure mode or 'top event' in terms of the component failures and human errors, represented by basic events. By providing information which enables the basic event probability to be calculated, the fault tree can then be quantified to yield reliability parameters for the system. Fault tree quantification enables the probability of the top event to be calculated and in addition its failure rate and expected number of occurrences. Importance measures which signify the contribution each basic event makes to system failure can also be determined. Owing to the large number of failure combinations (minimal cut sets) which generally result from a fault tree study, it is not possible using conventional techniques to calculate these parameters exactly and approximations are required. The approximations usually rely on the basic events having a small likelihood of occurrence. When this condition is not met, it can result in large inaccuracies. These problems can be overcome by employing the binary decision diagram (BDD) approach. This method converts the fault tree diagram into a format which encodes Shannon's decomposition and allows the exact failure probability to be determined in a very efficient calculation procedure. This paper describes how the BDD method can be employed in fault tree quantification.

Improved accuracy in quantitative fault tree analysis

The fault tree diagram defines the causes of the system failure mode or ‘top event’ in terms of the component failures and human errors, represented by basic events. By providing information which enables the basic event probability to be calculated, the fault tree can then be quantified to yield reliability parameters for the system. Fault tree quantification enables the probability of the top event to be calculated and in addition its failure rate and expected number of occurrences. Importance measures which signify the contribution each basic event makes to system failure can also be determined. Owing to the large number of failure combinations (minimal cut sets) which generally result from a fault tree study, it is not possible using conventional techniques to calculate these parameters exactly and approximations are required. The approximations usually rely on the basic events having a small likelihood of occurrence. When this condition is not met, it can result in large inaccuracies. These problems can be overcome by employing the binary decision diagram (BDD) approach. This method converts the fault tree diagram into a format which encodes Shannon's decomposition and allows the exact failure probability to be determined in a very efficient calculation procedure. This paper describes how the BDD method can be employed in fault tree quantification. © 1997 John Wiley & Sons, Ltd.