近年來故障樹的理論被廣泛地使用著，因為它俱有能夠簡單且具體地呈現出普遍電腦容錯系統在運作時可能產生的錯誤行為的能力。但傳統的故障樹理論在進行分析某些有著自動從錯誤中回復的系統設計時，會因為無法正確描述這種含有順序相性的動態的錯誤行為，而造成分析的評估結果不準確。但我們仍就可以透過使用行為分解(Behavioral Decomposition)這一類的理論來解決這個問題。在行為分解這一類的理論前提下，一個系統將被劃分為許多動態和靜態的子模組，每個子模組再依照其類型為動態或是靜態的分類，而分別使用二元決定圖(Binary Decision Diagram)或馬可夫鏈(Markov Chains)這兩種理論來進行模組可靠度與敏感度的後續分析與求值。在這篇論文中，我們將提出一種新的分解(Decomposition)的方法，這種分解方法可以從一個動態子模組中，更深一層地嘗試去辨斷且標示出錯誤行為上獨立的子樹，再藉由階層式的解算法求出模組可靠度與模組內各元件的敏感度，這種方法在原理上是利用化簡馬可夫模型的狀態空間(state space)來節省馬可夫鏈矩陣運算時所花費的計算時間，同時產生的元件敏感度誤差也是在可調整的控制範圍內。最後將介紹我們以這個方法為理論基礎所開發出來的一套動態故障樹分析自動化軟體套件: DyFA (Dynamic Fault-trees Analyzer)。

Fault trees theories have been used in years because they can easily provide a concise representation of failure behavior of general non-repairable fault-tolerant systems. But the defect of traditional fault trees is lack of accuracy when modeling sequence-dependent dynamic failure behavior of certain systems with fault-recovery process. A solution to this problem is called behavioral decomposition. A system will be divided into several dynamic or static modules, and each module can be further analyzed using BDD or Markov Chains separately. In this paper, we will show a decomposition scheme that independent subtrees of a dynamic module are detected and solved hierarchically for saving computation time of solving Markov Chains by reducing the state space of Markov model but without losing unacceptable accuracy when assessing components sensitivities. In the end, we present our analyzing software toolkit: DyFA (Dynamic Fault-trees Analyzer) which implements our enhanced methodology.

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