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This paper proposes an algorithm for the reliability analysis of multi-state systems with multiple dependent trigger components subject to competing failure propagation and failure isolation events. Propagated failure from a system component causes failures of other system components. However, the effect of a propagated failure is not deterministic in systems with functional dependence behavior. Failure from a component (referred to as trigger component) can isolate propagated failures from other components (referred to as dependent components) when the trigger component fails before any propagated failure originating from the dependent components happens. For systems with multiple functional dependence groups, reliability analysis is more complex since the failure order of trigger components also affects the system behavior. In this paper, a combinatorial and analytical algorithm is proposed to analyze the reliability of multi-state systems with multiple dependent trigger components. An example of memory systems is analyzed to demonstrate the application of the proposed algorithm.