This paper presents an approach to assess the effects of common cause failures (CCF) on dependability of digital systems. Independent failures of system components and partial or lethal shocks are considered in a global CCF model, the Atwood model. The Coloured Petri nets (CPN) are used to modelize the digital system and the common cause failures. Based on the CPN, the parameters of Atwood model are estimated analytically and by Monte-Carlo simulation. Thereafter, the Atwood model of CCF is modified in order to represent the dominant failures propagation on some system components in the case of partial shocks. The assessment of system dependability, in the presence of CCF failures, becomes possible. This approach is applied to a representative instrumentation and control system of a nuclear power plant. The system is large with a high level of redundancy.