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We present a software architecture-based approach to compositional estimation of system's reliability. Our approach is applicable to early stages of development when the implementation artifacts are not yet available, and exact execution profile is unknown. The uncertainty of the execution profile is modeled using stochastic processes with unknown parameters. The compositional approach calculates overall reliability of the system as a function of the reliability of its constituent components and their (complex) interactions. Sensitivity analysis to identify critical components and interactions will be provided.