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Considerable studies have been done on system reliability estimation under uncertainty. Most of these studies focus on binary-state systems, and the uncertainty source is only admitted in the component reliability estimation. The studies on multistate systems (MSSs) do exist, but these studies either completely ignore the uncertainty in load demand during the system operation period or are restricted to parallel system structures. This paper attempts to extend these previous studies and investigate the effects of uncertainty in both component reliability and load demand on system reliability for general MSSs with any series-parallel structures. Analytical expressions for calculating the expected value and the variance of system reliability considering these two sets of uncertainty factors are derived based on the universal generating function method in an iterative form. The accuracy of the proposed analytical approach is validated through Monte Carlo simulations. Various examples on a complex series-parallel MSS are used to investigate the effects of the two sets of uncertainty factors. The results indicate that these two sets of uncertainty factors affect the expected value and the variance of system reliability for MSSs in different ways.