Minimal path set importance in complex systems

To find the best mode for system design in reliability optimization, risk engineers around the world use the importance measure as a basic tool. This paper introduces a new importance measure taking into account minimal path sets of the system. It helps to optimize the system designs that occur in many situations. For instance, this importance measure can be used (a) in identifying important components of any complex system and (b) solving constrained redundancy optimization problems. This is illustrated by providing two heuristic algorithms. In the first algorithm, this measure is used to find important components of any complex system ensuring improved system reliability. The second algorithm is used to solve a constrained redundancy optimization problem for any general coherent system giving (near) optimal solutions in 1-neighborhood. The results show that the new importance measure is easily applicable, unlike the classical ones. Hence, it serves as a very useful tool in measuring the important component(s) and solving constrained redundancy optimization problems of complex systems. Thus, it can be considered as a good alternative to the existing importance measures.

Two-terminal Reliability Analysis for Time-evolving and Predictable Delay-tolerant Networks

Background: Several techniques are available to evaluate the two-terminal reliability (2TR) of static networks; however, the advent of dynamic networks in recent past, e.g., Delay Tolerant Networks (DTNs), has made this task extremely challenging due to their peculiar characteristics with an associated disruptive operational environment. Recently, a Cartesian product-based method has been proposed to enumerate time-stamped-minimal path sets (TS-MPS)-a precursor to compute the 2TR of such networks. However, it cannot be used to generate time-stamped-minimal cut sets (TS-MCS). TS-MCS cannot only be used as an alternative to generate 2TR but also to compute other unexplored reliability metrics in DTNs, e.g., the weakest link. Objective: To propose a novel approach to enumerate both TS-MPS and TS-MCS of a dynamic network, thereby computing the 2TR of such networks. Methods: The proposed technique converts the time aggregated graph model of a dynamic network into a Line Graph (LG) while maintaining the time-varying graph’s node reachability information. This LG is used thereafter to generate TS-MCS as well as TS-MPS to compute 2TR of the network. Results: The DTN examples are presented to show the efficacy and salient features of our algorithm to obtain 2TR of such networks. Conclusion: The terminologies and techniques used for studying/analyzing network reliability of static networks can be extended to dynamic networks as well, e.g., the notion of minimal path sets to TS-MPS or minimal cut sets to TS-MCS, to assess their network reliability-a potential area of furthering network reliability research.

Path Sets Combination Method for Reliability Analysis of Phased-Mission Systems Based on Cumulative Exposure Model

The modeling of phased-mission systems is difficult and the solving process is complex because of the relevance of the phase tasks and the sharing of components existing in different phases or between phases. To solve the problem, based on the cumulative exposure model, the path sets combination method of phased-mission systems is proposed. Aiming at the problem of the cross-stage correlation of components and its different failure rate in each phase, the cumulative exposure model considering the historical damage of components is used to solve by obtaining the cumulative damage distribution of each component in each phase. Firstly, a phased-mission systems reliability model is build by mapping phased-mission system fault trees into a Bayesian network. By traversing the Bayesian network, the minimal path sets of each phase are obtained. Secondly, the disjoint formulas introduced by variable elimination method are used to do the disjoint operation of the minimal path sets of each phase and the conditional probability relations of the common components are used to reduce the minimal path sets scale. Finally, the minimum disjoint path sets of each phase are combined and summed according to the component conditional probability relation. The path sets combination method of phased-mission systems avoids the large conditional probability table, large storage and large computation problems caused by the excessive discrete states in the traditional Bayesian method and the problem that the PMS-BDD method has strict requirements for variable ordering and is difficult to solve the system reliability with multiple failure distribution types of components. In the end, a phased-mission systems reliability modeling and solving is carried out for a geosynchronous orbit satellite, and compared with the PMS-BDD method, which verifies the correctness of the method.

ACTIVE REDUNDANCY ALLOCATION FOR COHERENT SYSTEMS WITH INDEPENDENT AND HETEROGENEOUS COMPONENTS

This paper studies the allocation of active redundancies to coherent systems on the context that the base and redundancy components have mutual independent lifetimes. For systems with two symmetric components and systems with one component's minimal cut sets (minimal path sets) covering those of another, we derive sufficient conditions to compare the resultant system lifetimes. Some numerical examples are also presented to illustrate the theoretical results.

A Hierarchical Approach for Fast Calculating Minimal Cut Sets of a Microgrid

Minimal cut sets are the basis of reliability analysis using analytical techniques. At the present stage, minimal cut sets are mainly obtained by dealing with minimal path sets, which involves cumbersome steps and slower operational speed. The speed of reliability analysis is limited by that of calculating minimal cut sets. In consideration of the characteristics of microgrid, a hierarchical approach for fast calculating minimal cut sets is proposed in this paper. Firstly, an equivalent principle is proposed to convert topology structure into network node diagram; then grades of nodes are designated based on their original connection and the breadth-first search approach; afterwards, root-leaf matrices and selected matrix are created to specify the direction and order of the search. Next, all possible combinations of minimal cut sets are vertically traversed out by replacing root nodes with leaf nodes to achieve a more rapid access to minimal cut sets. Finally, taking the electrical structure of type A380 more electric aircraft as an example, mainstream methods are compared to show the correctness and advantage of our proposed method.