Analysis Methods of Multi-state Systems Partially Having Dependent Components Using Multiple-Valued Decision Diagrams

Abstract

Abstract-In a large system, such as a water, gas, or electrical distribution system, degraded performance due to failures of components can be modeled as a set of discrete states interconnected by edges with weights that represent conditional probabilities. To establish such a model, we compute the conditional probabilities with multi-valued decision diagrams (MDDs). Since a typical decision diagram is large, the computation time is also large. In this paper, we propose an edge-valued MDD (EVMDD) based method to avoid unnecessary path traversals. The proposed method is a hybrid method of a path traversal method and a bottomup method that visits each node only once. By effectively combining both methods, we achieve a speed-up of the analysis by about 2.3 times for large systems compared to an existing method.Keywords-Multi-state systems with multi-state components; structure functions; system analysis based on decision diagrams; system analysis using conditional probabilities; EVMDDs.

Edge Reduction for EVMDDs to Speed Up Analysis of Multi-state Systems

“…To show the efficiency of the proposed edge reduction technique, we used the same analysis algorithms and the same structure functions as [13], [14]. The methods are implemented on our private EVMDD package, and run on the following computer environment: CPU: Intel Core2 Quad Q6600 2.4GHz, memory: 4GB, OS: CentOS 5.7, and C-compiler: gcc -O3 (version 4.1.2).…”

“…Since edge reduction is a fundamental technique, it can be used along with the hybrid analysis method [14] that is used for analysis of systems having dependent components.…”

“…Since analysis time of MSSs depends on the number of edges in an EVMDD, the proposed edge reduction rule can also reduce analysis time. The proposed technique can be applied to a wide range of analyses including steady-state analysis, transient analysis, and analysis of systems having dependent components [14]. This is because the proposed technique is a fundamental one.…”