Reliability Analysis of Cold-standby Systems with Subsystems Using Conditional Binary Decision Diagrams

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.

We present DFTSim, a simulation tool for dynamic fault trees (DFT). The simulation is carried out by directly sampling the failure distributions attached to the leaves (called basic events) of the tree and propagating the failure times upwards in the tree.Sampling the distributions of the DFT leaves is however not obvious. To sample from the correct distributions, the analytical expression of the failure distributions of all basic events (BE) must be known. These are indeed known for non-spare BEs; but for spare BEs, they become conditional on the failure of other BEs. Hence, the derivation of the analytical expression of the spares' failure distributions and their sampling is not a trivial task.We evaluate DFTSim by applying it on an extensive benchmark comprised of seven case studies. We compare its results to two other DFT-based reliability tools (namely Galileo and Coral) that, rather than giving simulation-based estimates, compute exact measures.Our simulation-based approach is, in particular for large DFTs, much faster than the existing approaches. In fact, the computation time of the exact solution methods is exponential in the number of DFT leaves, whereas simulation time is linear in the number of leaves. Moreover, DFTSim (and simulation in general) allows to simulate a wide range of distributions and evaluate Markovian as well as non-Markovian models.

It is necessary to make the tape winding system have good reliability. Because the power system usually is a pneumatic or hydraulic system, the static reliability analysis lacks the ability to describe the dynamic state transfer, component fault correlation, and propagation effect of the system; it is difficult to accurately reflect the actual behavior of the complex system. Most of the existing research results lack the situation that the importance of bottom events changes with time; only a single number cannot express the impact of bottom events on top events at different times. Therefore, this study uses the dynamic reliability analysis method to quantitatively analyze the reliability of the tape winding power hydraulic system. Firstly, the dynamic reliability model of hydraulic system is established by using the continuous-time T-S dynamic fault tree to solve the fault rate of the system. Secondly, the results are compared with the traditional Markov chain analysis method of dynamic fault tree. The feasibility and advantages of the continuous-time T-S dynamic fault tree analysis method are verified. Finally, the probability importance and key importance of the system unit are calculated, and the law of importance changing with time is expressed. According to the importance of different time, it can help the regular maintenance and fault diagnosis of equipment.

PurposeThis paper aims to deal with the problems of failure dependence and common cause failure (CCF) that arise in reliability analysis of complex systems.Design/methodology/approachFirstly, a dynamic fault tree (DFT) is used to capture the dynamic failure behaviours and converted into an equivalent generalized stochastic petri net (GSPN) for quantitative analysis. Secondly, an efficient decomposition and aggregation (EDA) theory is combined with GSPN to deal with the CCF problem, which exists in redundant systems. Finally, Birnbaum importance measure (BIM) is calculated based on the EDA approach and GSPN model, and it is used to take decisions for system improvement and fault diagnosis.FindingsIn this paper, a new reliability evaluation method for dynamic systems subject to CCF is presented based on the DFT analysis and the GSPN model. The GSPN model is easy to capture dynamic failure behaviours of complex systems, and the movement of tokens in the GSPN model represent the changes in the state of the systems. The proposed method takes advantage of the GSPN model and incorporates the EDA method into the GSPN, which simplifies the reliability analysis process. Meanwhile, simulation results under different conditions show that CCF has made a considerable impact on reliability analysis for complex systems, which indicates that the CCF should not be ignored in reliability analysis.Originality/valueThe proposed method combines the EDA theory with the GSPN model to improve the efficiency of the reliability analysis.

Reliability analysis of hierarchical computer-based systems subject to common-cause failures

In consideration of some drawbacks of stochastic reliability method in theoretical and practical aspects, as well as the existence of insufficient and vague data in actual equipments design, the possbilistic reliability models of typically general systems are constructed in this paper. Characterizing the systems(components) failure behavior by possibility measures in place of probability measures, treating the systems (components) lifetime as fuzzy variables in the possibility space, and introducing possibilistic approaches into system reliability modeling and analysis, the possibilistic reliability theories are advanced based on possibilistic measurements. By expanding the universe of discourse, the derivation of system reliability models is simplified without loss of the nature of the problems to be solved, and proofs and calculations of possibilistic reliability of typical systems including series, parallel, series-parallel, parallel-series, and cold standby systems are much more straightforward than the traditional ones. The detailed application examples in system reliability analysis verify a possibilistic design framework on the general reliability models background, which provide some technical supports and guarantees for possibilistic reliability design and possibilistic reliability management in the case of limited statistical data.

Fault trees are a key model in reliability analysis. Classical static fault trees (SFT) can best be analysed using binary decision diagrams (BDD). State-based techniques are favorable for the more expressive dynamic fault trees (DFT). This paper combines the best of both worlds by following Dugan’s approach: dynamic sub-trees are analysed via model checking Markov models and replaced by basic events capturing the obtained failure probabilities. The resulting SFT is then analysed via BDDs. We implemented this approach in the Storm model checker. Extensive experiments (a) compare our pure BDD-based analysis of SFTs to various existing SFT analysis tools, (b) indicate the benefits of our efficient calculations for multiple time points and the assessment of the mean-time-to-failure, and (c) show that our implementation of Dugan’s approach significantly outperforms pure Markovian analysis of DFTs. Our implementation Storm-dft is currently the only tool supporting efficient analysis for both SFTs and DFTs.

As the basis for comprehensive integration of the aircraft, AFDX network has been widely used in avionics network. AFDX’s reliability analysis and verification is particularly important according to the requirements of airworthiness. The transmission process, components and functional contact between components of AFDX network is analyzed in this paper. Dynamic fault tree (DFT) is used to model AFDX network reliability according to network fault characteristics. This analysis process has two contributions for network reliability analysis. Firstly, the analysis of AFDX network failures is implemented to device-level, which is facilitated to quantitative calculations in engineering. Secondly, end system and switch system, the core subsystem in transmission of AFDX, are analyzed and modeled, besides fault of redundant network.

For a dynamic fault tree (DFT) that models dynamic system, the occurrence of top event depends on not only the combination of basic events, but also on the occurrence order of basic events. Cut sequence is a set of basic events that fail in a particular order that can induce top event. Cut sequence set (CSS) model uses cut sequences to analyze the dynamic behaviors of dynamic systems, and if includes two parts: the generation and the quantification of CSS. Since the known CSS model has to face large complexity, the paper provided several simplification methods so as to decrease the computational complexity. The simplification methods include the modularization of individual sub-frees, simplifying the equation of the top event probability, ignoring the cut sequences that contain many basic events. An example is used to illustrate the applications of the simplification methods.

An extended HAZOP analysis approach with dynamic fault tree

Enhancing the ability to perform diagnostics on a system that has failed can significantly impact maintenance and repair costs. A good diagnostic tool enables a user to analyze a failed system and identify the failed components. While the field of diagnostics is not a modern one, the way in which system diagnostics are performed is continuously changing. The automatic diagnosis based on reliability analysis (ADORA) methodology utilizes reliability information developed during the design phase to build a diagnostic map. Previous work on ADORA demonstrated how a diagnostics procedure can be performed on a system that has been analyzed using a static reliability model, particularly a fault tree (Assaf and Dugan, 2003). In this article, we extend the ADORA methodology to utilize reliability analysis of dynamic fault trees (DFTs), which are reliability models that capture sequences and combinations of component failures that induce system failure. DFTs are particularly well suited for analyzing computer-based systems.As an example the common rail fuel injection system is discussed.

Cold standby technique is one of the most commonly applied techniques to achieve high reliability requirement of modern products. This paper studies a 1-out-of-n cold standby system, where scheduled backups are performed to ensure that a standby component can take over the task effectively when the online component fails. Since a component may fail during switching from the cold standby state to the online state, effect of imperfect switch is also considered. Lifetimes of components in the considered system can follow arbitrary distributions and are not necessarily identical. Backup intervals are deterministic but can be non-identical. A multivalued decision diagram (MDD)-based analytical approach is proposed to evaluate reliability of 1-out-of-n cold standby systems subject to scheduled backups. Illustrative examples are provided. Correctness of the proposed method is verified usi ng Monte Carlo simulations.

The reliability analysis of critical systems is often performed using fault tree analysis. Fault trees are analyzed using analytic approaches or Monte Carlo simulation. The usage of the analytic approaches is limited in few models and certain kinds of parameter distributions. In contrast to the analytic approaches, Monte Carlo simulation can be broadly used. However, Monte Carlo simulation is time-consuming because of the intensive computation. In this paper, a new model is presented which is called time-to-failure tree. Static and dynamic fault trees can be easily transformed into time-to-failure trees. In fact, each time-to-failure tree is a digital circuit, which can be synthesized to a field programmable gate array (FPGA). Therefore, Monte Carlo simulation can be significantly accelerated using FPGAs.

ABSTRACTAn alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.

This paper considers the reliability analysis of a two‐component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensity λ > 0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.