Sequential Binary Decision Diagrams Research Articles

A new ordering method of basic events in dynamic fault tree for sequential binary decision diagram

AbstractDynamic fault tree (DFT) is a reliable method for modeling complex systems with dynamic characteristics. However, evaluating the reliability of such systems can be complex. The sequential binary decision diagram (SBDD) method simplifies this process by reducing computational complexity. This study investigates factors influencing SBDD size and proposes a new method, the complete priority ordering method, for ordering basic events in SBDDs. Results demonstrate the method's effectiveness in comparison to existing approaches.

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.

An adapted component-connection method for building SBDD encoding a dynamic fault tree

Dynamic fault trees (DFTs) are a commonly used tool to analyze the reliability of systems with sequential failure behaviors. A sum of disjoint product (SDP)-based analysis methods are widely accepted as efficient approaches for a DFT, such as dynamic binary decision trees (DBDTs) and sequential binary decision diagrams (SBDDs). However, for a large DFT, the process of obtaining the structure function is error-prone and very time-consuming. In contrast, SBDD built on the improved ite algorithm does not rely on the structure function but is limited to a DFT whose dynamic gates are located at the bottom. This method requires predefined variable ordering for basic events, which greatly influences the computational efficiency, and the caching operation is a problem. In this paper, an enhanced component-connection–based method is proposed to build SBDD encoding a DFT. New component-connection rules are developed to deal with dependent variables having repeated basic events, and several heuristic connection strategies are also developed to reduce the size of the final calculable terms. The proposed method is straightforward and easily implemented. To demonstrate the applications and merits of our method, several case studies are carried out, and the results show the reasonability and effectiveness.

A method for transformation from dynamic fault tree to binary decision diagram

Dynamic fault tree (DFT) is a powerful modeling approach for reliability analysis of complex system with dynamic failure behaviors. In reality, the tree structure may be highly coupled either by shared basic events or by the high-level dynamic gates. Currently, the application of sequential binary decision diagram (SBDD)-based method for quantitative analysis of such highly coupled DFTs is mainly limited to DFTs whose dynamic gates locate in the bottom of the tree. Moreover, there is no efficient way dealing with the dependencies among different nodes of a SBDD 1-path. This paper makes an improvement to the SBDD-based approach. A generation procedure is proposed to directly construct the binary decision diagram (BDD) model for a DFT with arbitrary tree structure. During the construction, the sequential-dependent information of the tree is derived as several BDD nodes, each indicates a binary-sequential event representing the sequence of two occurred basic events. A topological sorting is applied on each 1-path of the resultant BDD to obtain its contained disjoint cut sequences. Based on this, both qualitative and quantitative analysis can be performed on the DFT with no limitations on tree structure, and its minimal cut sequence set (CSS) is obtained as disjoint. Examples are provided for verification and comparison, and the results illustrate the merits of the proposed approach.

Reliability analysis of dynamic fault trees with spare gates using conditional binary decision diagrams

Dynamic fault trees (DFTs) with spare gates have been used extensively in reliability analysis. The traditional approach to DFTs is Markov-based that may suffer from problems like state–space explosion. Algebraic-structure-based methods consume long computation time caused by the inclusive/exclusive formula. Recently, some combinatorial solutions have been applied to DFTs such as sequential binary decision diagrams (SBDD) and algebraic binary decision diagrams (ABDD). They analyze systems by the minimal cut sequence (MCQ) based on sequence-dependence. We propose an analytical method based on conditional binary decision diagrams (CBDD) for combinatorial reliability analysis of non-repairable DFTs with spare gates. A detectable component state is mined to describe the sequence-dependent failure behaviors between components in the spare gate. Minimal cut set (MCS) instead of MCQ is used for qualitative analysis to locate faults via the component state. Compared to Markov-based methods, our method can generate system reliability result with any arbitrary time-to-failure distribution for system components. Different from SBDD and ABDD, specific operation rules are proposed to eliminate inconsistencies and reduce redundancies when building a CBDD. For quantitative analysis, the CBDD simplifies computation via using the sum of disjoint products. Case studies are presented to show the advantage of using our method.

Reliability Modeling of Microgrid System Using Hybrid Methods in Hot Standby Mode

The purpose of this paper is to accomplish the reliability assessment of hot standby microgrid system by using few hybrid methods. This paper has shown relative analysis on failure probability and reliability of microgrid system by means of Markov model, fault tree analysis (FTA) using reduced binary decision diagram (RBDD), and reduced sequential binary decision diagram (RSBDD) approaches. Hot standby mode is usually employed for the enrichment of reliability to prolong the system availability during any catastrophic situation. By analysis, microgrid which falls under the hot standby mode indicates that both the redundant as well as active components have similar failure rates. An inverter dominated photovoltaic system integrated to an IEEE 5-bus microgrid system is designed for which comparative overall system availability is calculated and analyzed in terms of failure probability and reliability by using hybrid approaches. Markov-based models mostly suffer from state-space explosion problems and it needs exponential probability distribution function only. Again, FTA-RBDD and FTA-RSBDD approaches have neither any constraint on time-to-failure distributions nor any computational burden issue. Moreover, FTA-RSBDD-based reliability assessment dealings are reusable with different time-to-failure rates.

Reliability analysis of a cold-standby system considering the development stages and accumulations of failure mechanisms

In this paper we classify failure mechanisms (FMs) into three types based on the triggering loads, including environmental load-triggered (E-type), operating load-triggered (O-type), and combined load-triggered (C-type) FMs. In a cold-standby component, E-type FMs develop when the component does not operate and may develop with different speeds due to changes in the environmental conditions at different stages. O-type FMs are triggered by operational loads. Environmental loads and operating loads are necessary for triggering C-type FMs. Previous studies have often assumed that cold-standby components are not subject to failures or degradation in the standby stage. However, E-type FMs can develop in cold-standby components at the standby stage and contribute to the degradation of the components. In this paper, we propose a hierarchical method based on the sequential binary decision diagram (SBDD) to analyze the reliability of a non-repairable cold-standby system while considering the correlation and development of FMs. In the case study, a reliability analysis is conducted for an example power supply subsystem equipped with an electronic control device, which comprises one primary unit and one cold-standby unit. The results show that the reliability of the cold-standby system is quite different when considering the development of E-type FMs in the cold-standby unit. In addition, the lifetime of the system will decrease when E-type FMs are considered in the simulation.

Negating a Generalized Cut Sequence: Bridging the Gap Between Dynamic Fault Trees Quantification and Sum of Disjoint Products Methods

Dynamic fault trees (DFTs) are powerful tools to model industrial systems having dynamic failure mechanisms, such as sequence- and function-dependent failure behaviors. Yet for large and complex DFTs, their quantitative analyses are still of great challenges. Up to now, many researchers have presented several approaches to deal with this problem, and among which, the sum of disjoint products (SDP) methods, such as dynamic binary decision tree, sequential binary decision diagram (SBDD), and improved SBDD, have proven to be an efficient way. In SDP methods, negating a generalized cut sequence is an unavoidable task. Yet, for a complex cut sequence expression where normal, cold and warm spares basic events coexist, its negating operation is still difficult and needs to be further studied. In this paper, based on De Morgan theorem, improved explicit formulas for negating a generalized cut sequences are presented. The new concept of universal set of basic event and its operating rules are proposed to deduce the simplified expressions of general enforcing occurring cut sequences and warm spares occurring cut sequences. To validate the presented approaches, a typical system DFT is analyzed. The results indicate the reasonability and effectiveness of the improved negating formulas. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamic fault tree analysis using sequential binary decision diagrams

Dynamic fault tree analysis using sequential binary decision diagrams

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.

Quantitative analysis of dynamic fault trees using improved Sequential Binary Decision Diagrams

Dynamic fault trees (DFTs) are powerful in modeling systems with sequence- and function dependent failure behaviors. The key point lies in how to quantify complex DFTs analytically and efficiently. Unfortunately, the existing methods for analyzing DFTs all have their own disadvantages. They either suffer from the problem of combinatorial explosion or need a long computation time to obtain an accurate solution. Sequential Binary Decision Diagrams (SBDDs) are regarded as novel and efficient approaches to deal with DFTs, but their two apparent shortcomings remain to be handled: That is, SBDDs probably generate invalid nodes when given an unpleasant variable index and the scale of the resultant cut sequences greatly relies on the chosen variable index. An improved SBDD method is proposed in this paper to deal with the two mentioned problems. It uses an improved ite (If-Then-Else) algorithm to avoid generating invalid nodes when building SBDDs, and a heuristic variable index to keep the scale of resultant cut sequences as small as possible. To confirm the applicability and merits of the proposed method, several benchmark examples are demonstrated, and the results indicate this approach is efficient as well as reasonable.

Quantification of Highly Coupled Dynamic Fault Tree Using IRVPM and SBDD

Dynamic fault tree (DFT) is a commonly used method to model systems having sequence-dependent and function-dependent failure behaviors. The failure structure function of a DFT can be expressed by logic OR of all minimal cut sequences, that is, minimal cut sequence set (MCSS). The occurrence probability to the top event of a DFT can be calculated using inclusion–exclusion (IE) principle based on enumerating the MCSS. However, the IE-based approach would have exponential evaluation complexity. Then, a sequential binary decision diagram (SBDD)-based method is proposed and successfully applied to analyze simple dynamic systems. This method is more efficient than IE-based method in asymptotic analysis. But this method cannot handle complex systems modeled by different highly coupled dynamic gates. In this paper, we put forward using Independent Random Variable Probabilistic Model-based plus SBDD-based methods to quantify an MCSS to obtain the failure probability of a complex DFT. The results obtained by the proposed method are exactly matched with those obtained by the existing methods. In addition, this method enhances the analyzing ability of the original SBDD and retains the advantage of high computational efficiency. The application and advantage of our proposed method is demonstrated by a case study. Copyright © 2014 John Wiley & Sons, Ltd.

Reliability Analysis of Nonrepairable Cold-Standby Systems Using Sequential Binary Decision Diagrams

Many real-world systems, particularly those with limited power resources, are designed with cold-standby redundancy for achieving fault tolerance and high reliability. Cold-standby units are unpowered and, thus, do not consume any power until needed to replace a faulty online component. Cold-standby redundancy creates sequential dependence between the online component and standby components; in particular, a standby component can start to work and then fail only after the online component has failed. Traditional approaches to handling the cold-standby redundancy are typically state-space-based or simulation-based or inclusion/exclusion-based methods. Those methods, however, have the state-space explosion problem and/or require long computation time particularly when results with a high degree of accuracy are desired. In this paper, we propose an analytical method based on sequential binary decision diagrams (SBDD) for combinatorial reliability analysis of nonrepairable cold-standby systems. Different from the simulation-based methods, the proposed approach can generate exact system reliability results. In addition, the system SBDD model and reliability evaluation expression, once generated, are reusable for the reliability analysis with different component failure parameters. The approach has no limitation on the type of time-to-failure distributions for the system components or on the system structure. Application and advantages of the proposed approach are illustrated through several case studies.

Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures

Many real-life fault-tolerant systems are subjected to sequence-dependent failure behavior, in which the order in which the fault events occur is important to the system reliability. Such systems can be modeled by dynamic fault trees (DFT) with priority-AND (pAND) gates. Existing approaches for the reliability analysis of systems subjected to sequence-dependent failures are typically state-space-based, simulation-based or inclusion–exclusion-based methods. Those methods either suffer from the state-space explosion problem or require long computation time especially when results with high degree of accuracy are desired. In this paper, an analytical method based on sequential binary decision diagrams is proposed. The proposed approach can analyze the exact reliability of non-repairable dynamic systems subjected to the sequence-dependent failure behavior. Also, the proposed approach is combinatorial and is applicable for analyzing systems with any arbitrary component time-to-failure distributions. The application and advantages of the proposed approach are illustrated through analysis of several examples.