Yuchang Mo

A Multiple-Valued Decision Diagram Based Method for Efficient Reliability Analysis of Non-Repairable Phased-Mission Systems

Many practical systems are phased-mission systems (PMSs), where the mission consists of multiple, consecutive, and non-overlapping phases of operation. An accurate reliability analysis of a PMS must consider statistical dependence of component states across phases, as well as dynamics in system configurations, success criteria, and component behavior. This paper proposes a new method based on multiple-valued decision diagrams (MDDs) for the reliability analysis of a non-repairable binary-state PMS. Due to its multi-valued logic nature, the MDD model has recently been applied to the reliability analysis of multistate systems. In this work, we present a novel way to adapt MDDs for the reliability analysis of systems with multiple phases. Examples show how the MDD models are generated and evaluated to obtain the mission reliability measures. Performance of the MDD-based method is compared with an existing binary decision diagram (BDD)-based method for PMS analysis. Empirical results show that the MDD-based method can offer lower computational complexity as well as a simpler model construction and improved evaluation algorithms over those used in the BDD-based method.

Efficient analysis of multi-state k-out-of-n systems

Many practical systems are multi-state k-out-of-n systems with independent, non-identical components, where the system and its components have multiple performance levels and maybe multiple failure modes. Furthermore the system may have different requirements on the number of working components (i.e., value of k) for different system state levels. This paper proposes a new analytical method based on multi-valued decision diagrams (MDDs) for the reliability analysis of such multi-state k-out-of-n systems. MDDs have recently been applied to the reliability analysis of general multi-state systems (MSS). In this work, we make the new contribution by proposing a novel and efficient algorithm for constructing the system MDD that is designed to fully make use of the well-defined k-out-of-n structure. Examples show how the MDD models are generated using the proposed algorithm, and are then evaluated to obtain the system reliability measures. Performance of the MDD-based method is compared with that of an existing recursive algorithm through a comprehensive benchmark study. Empirical results show that the proposed MDD-based method can offer lower computational complexity than the recursive algorithms, and it can be effectively applied to large practical cases for multi-state k-out-of-n systems.

MDD-Based Method for Efficient Analysis on Phased-Mission Systems With Multimode Failures

Many practical systems are phased-mission systems with multimode failures (MFPMSs) where the mission consists of multiple nonoverlapping phases of operation, and the system components may assume more than one failure mode. In MFPMSs, dependence arises among different phases and among different failure modes of the same component, which makes the reliability analysis of MFPMSs difficult. This paper proposes a new analytical method based on multivalued decision diagrams (MDDs) for the reliability analysis of nonrepairable MFPMSs. MDDs have recently been applied to the reliability analysis of single-phase systems with multiple component states. In this paper, we make the new contribution by proposing a novel way to adapt MDDs for the reliability analysis of systems with multiple phases and multimode failures. Examples show how the MDD models are generated and evaluated to obtain the mission reliability measures. Performance of the MDD-based method is compared with an existing binary decision diagram (BDD)-based method for MFPMS analysis through several examples and a comprehensive benchmark study. Empirical results show that the proposed MDD-based method can offer lower computational complexity and simpler model construction and evaluation algorithms than the BDD-based method, and it can be effectively applied to large practical cases.

A Multiple-Valued Decision-Diagram-Based Approach to Solve Dynamic Fault Trees

Dynamic fault trees (DFTs) have been used for many years because they can easily provide a concise representation of the dynamic failure behaviors of general non-repairable fault tolerant systems. However, when repeated failure events appear in real-life DFT models, the traditional modularization-based DFT analysis process can still generate large dynamic subtrees, the modeling of which can lead to a state explosion problem. Examples of these kinds of large dynamic subtrees abound in models of real-world dynamic software and embedded computing systems integrating with various multi-function components. This paper proposes an efficient, multiple-valued decision-diagram (MDD)-based DFT analysis approach for computing the reliability of large dynamic subtrees. Unlike the traditional modularization methods where the whole dynamic subtree must be solved using state-space methods, the proposed approach restricts the state-space method only to components associated with dynamic failure behaviors within the dynamic subtree. By using multiple-valued variables to encode the dynamic gates, a single compact MDD can be generated to model the failure behavior of the overall system. The combination of MDD and state-space methods applied at the component or gate level helps relieve the state explosion problem of the traditional modularization method, for the problems we explore. Applications and advantages of the proposed approach are illustrated through detailed analyses of an example DFT, and through two case studies.

New Insights Into the BDD-Based Reliability Analysis of Phased-Mission Systems

We present a generalized analysis methodology for binary decision diagram-based fault tree analysis of a wide range of phased-mission systems, with various mission requirements, and structure characteristics. This methodology includes 1) four alternative variable ordering schemes: forward/backward phased dependent operations, and forward/backward concatenation; 2) a strategy to choose an adequate ordering scheme to process a new phased-mission system instance depending on its phase and mission configuration; and 3) efficient generation and evaluation algorithms for generalized phased-mission system binary decision diagrams adopting any arbitrary ordering scheme. The advantages of this methodology are in the low computational complexity, broad applicability, and easy implementation.

Efficient Ordering Heuristics in Binary Decision Diagram–based Fault Tree Analysis

In binary decision diagram–based fault tree analysis, the size of binary decision diagram encoding fault trees heavily depends on the chosen ordering. Heuristics are often used to obtain good orderings. The most important heuristics are depth-first leftmost (DFLM) and its variants weighting DFLM (WDFLM) and repeated-event-priority DFLM (RDFLM). Although having been used widely, their performance is still only vaguely understood, and not much formal work has been done. This article firstly identifies some basic requirements for a reliable benchmark and gives a benchmark generation method. Then, using the generated benchmark, the performance of DFLM and its variants is studied. Both the experimental results and some interesting findings for our research questions are proposed. This article also presents a new weighting DFLM (NWDFLM) heuristic and the underlying basic ideas and gives both the experimental results and conclusions on the performance comparison. As a final synthesis of all previous results, a practical suggestion of the order of heuristic selection to process a large fault tree is NWDFLM < WDFLM < RDFLM. Copyright

MDD-based performability analysis of multi-state linear consecutive-k-out-of-n: F systems

A multi-state linear consecutive-k-out-of-n: F system, MLC(k,n) consists of n components ordered in a line, which fails if at least k consecutive components have failed. It abounds in real-world applications such as wireless sensor networks, microwave station networks, and oil pipeline systems. Performability of an MLC(k,n) system is concerned with probability that the system performs at a performance state characterized in terms of the largest number of consecutive failed components. This paper proposes a multi-valued decision diagram (MDD)-based approach to model and evaluate performability of an MLC(k,n) system with heterogeneous components following arbitrary lifetime distributions. The proposed approach encompasses a novel and efficient MDD model generation procedure. Both complexity analysis and illustrative examples are provided to show efficiency of the proposed MDD approach. As demonstrated through examples, the proposed MDD approach is also applicable to MLC(k,n) systems with non-identical reparable components and component importance analysis.

Choosing a heuristic and root node for edge ordering in BDD-based network reliability analysis

In the Binary Decision Diagram (BDD)-based network reliability analysis, heuristics have been widely used to obtain a reasonably good ordering of edge variables. Orderings generated using different heuristics can lead to dramatically different sizes of BDDs, and thus dramatically different running times and memory usages for the analysis of the same network. Unfortunately, due to the nature of the ordering problem (i.e., being an NP-complete problem) no formal guidelines or rules are available for choosing a good heuristic or for choosing a high-performance root node to perform edge searching using a particular heuristic. In this work, we make novel contributions by proposing heuristic and root node selection methods based on the concept of boundary sets for the BDD-based network reliability analysis. Empirical studies show that the proposed selection methods can help to generate high-performance edge ordering for most of studied cases, enabling the efficient BDD-based reliability analysis of large-scale networks. The proposed methods are demonstrated on different types of networks, including square lattice networks, torus lattice networks and de Bruijn networks.

Reliability Evaluation of Network Systems with Dependent Propagated Failures Using Decision Diagrams

In a network system, a propagated failure (PF) is a failure originating from a network component that can cause extensive damages to other network components or even the failure of the entire system. Existing works on PFs have mostly assumed the deterministic effect from a component PF, i.e., a fixed subset of system components is affected whenever the PF occurs. However, in many real-world systems, the components may have different levels of protection, and the effect of damage from a component PF can be dependent upon the status of other components within the same system or the occurrence order of component failures. This paper proposes a new analytical method based on multi-valued decision diagrams (MDDs) for the reliability analysis of network systems with dependent propagation effects. Particularly, new MDD modeling procedures are proposed for considering different types of dependent PF effects introduced by different protection levels. After the system MDD is generated using a new MDD combination algorithm to efficiently handle the dependent PF effects, methods for computing the network reliability and component importance measures are presented. The detailed analysis of an example network system subjected to dependent PFs is presented to illustrate the basics and application of the proposed method. It is shown that the proposed MDD-based method generates smaller model size and thus presents lower computational complexity in the model generation and evaluation than the existing Markov method and separable method.

A new reliability evaluation method for networks with imperfect vertices using BDD

As an efficient data structure for representation and manipulation of Boolean functions, binary decision diagrams (BDDs) have been applied to network reliability analysis. However, most of the existing BDD methods on network reliability analysis have assumed perfectly reliable vertices, which is often not true for real-world networks where the vertices can fail because of factors such as limited resources (eg, power and memory) or harsh operating environments. Extensions have been made to the existing BDD methods (particularly, edge expansion diagram and boundary set–based methods) to address imperfect vertices. But these extended methods have various constraints leading to problems in accuracy or space efficiency. To overcome these constraints, in this paper, we propose a new BDD-based algorithm called ordered BDD dependency test for K-terminal network reliability analysis considering both edge and vertex failures. Based on a newly defined concept “dependency set”, the proposed algorithm can accurately compute the reliability of networks with imperfect vertices. In addition, the proposed algorithm has no restrictions on the starting vertex for the BDD model construction. Comprehensive examples and experiments are provided to show effectiveness of the proposed approach.