This research proposes comprehensive models for analyzing common cause failures (CCF) due to cumulative shocks and to assess system reliability under the CCF. The proposed cumulative shock models are based on the binomial failure rate (BFR) model. Six kinds of models are proposed so as to explain diverse cumulative shock phenomena. The models are composed of the initial failure probability, shape parameter, and the total shock number. Some parameters of the proposed models can not be explicitly estimated, so we adopt the Expectation-maximization (EM) algorithm in order to obtain the maximum likelihood estimator (MLE) for the parameters. By estimating the parameters for the cumulative shock models, the system reliability with CCF can be assessed sequentially according to the number of cumulative shocks. The result can be utilizes in dynamic probabilistic safety assessment (PSA), aging studies, or risk management for nuclear power plants. Replacement or maintenance policies can also be developed based on the proposed model.