Incomplete component information may lead to wide system reliability bounds, which make it difficult to make decisions during the system design stage. The missing information is often the component dependence, which is a crucial source for the exact system reliability estimation. Component dependence exists due to the shared environment and operation conditions. But it is difficult for system designers to model component dependence because they may not have access to detailed component design information if the components are designed and manufactured by outside suppliers. This research intends to produce narrow system reliability bounds with a new way for system designers to consider the component dependence implicitly and automatically without knowing component design details. The proposed method is applicable for a wide range of applications where the time-dependent system stochastic load is shared by components of the system. Simulation is used to obtain the extreme value of the system load for a given period of time, and optimization is employed to estimate the system reliability interval. As a result, the system reliability can be estimated within a narrower interval than that obtained from the traditional method with independent component assumption and completely dependent component assumption. Examples are given to demonstrate the proposed method.