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A generalized stress-strength interference (SSI) reliability model to consider stochastic loading and strength aging degradation is presented in this paper. This model conforms to previous models for special cases, but also demonstrates the weakness of those models when multiple stochastic elements exist. It can be used for any nonhomogeneous Poisson loading process, and any kind of strength aging degradation model. To solve the SSI reliability equation, a numerical recurrence formula is presented based on the Gauss-Legendre quadrature formula to calculate multiple integrations of a random variable vector. Numerical analysis of three examples shows this SSI reliability model provides accurate results for both homogeneous & nonhomogeneous Poisson loading processes.