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In this paper, a bottom-up architecture-based reliability estimation framework for component based software systems is presented. The approach takes the component composition mechanisms and the utilization frequency of each component into account, and it is general for different architecture styles. We first propose five basic component composition mechanisms and their reliability representation methods. Then we show how to estimate the reliability of heterogeneous architectures using these basic component composition mechanisms through an iterative process. Finally a case study of a stock trading system is used to illustrate the application of our approach.