In this paper, the effect of the staggered test scheme, in which component tests in a surveillance test are performed in a staggered way, is justified by a time-dependent failure model. The staggered test scheme is well known in the nuclear industry in that it can reduce the risk of core damage due to common-cause failures (CCFs) in redundant standby safety-related trains. CCFs largely contribute core damage risks in the internal level 1 probabilistic risk assessment, so the staggered test scheme is ideal for improving nuclear plant safety. However, its validity to tests with arbitrary component test intervals is still unclear since its mathematical justification is based on a number of demands. To address this issue, the mathematical justification of the staggered test scheme should be generalized to account for tests with arbitrary component test intervals. Hence, the new concept of a generalized staggered test scheme, where component test intervals are arbitrary, is introduced. The mathematical model for the generalized staggered test scheme is justified by the time-dependent failure model. It is shown that the current demand-based model of the staggered test scheme underestimates the CCF risks in redundant standby trains. Applications of the generalized staggered test scheme to single-unit and multiunit probabilistic risk assessment are also demonstrated.