•A survival signature-based reliability approach for the multi-state system with both dependence and imprecision is developed.•The survival function is derived through a structural reliability treatment.•Two numerical algorithms are developed to address the efficient computation of the survival function.•A numerical case and a real application example are demonstrated for validation and to illustrate the benefits of our approach. Reliability evaluation of a multi-state system (MSS) with dependent components makes much practical sense because the independent identical assumption (i.i.d.) assumption between different components is sometimes impractical in the context of real engineering cases. The task becomes more challenging if imprecision gets involved due to the pervasive uncertainty. The loss of monotony resulting from the introduction of imprecise parameters makes many analytical reliability methods not applied. To address this challenge, in this paper, we develop a survival signature-based reliability framework for an MSS taking into account both dependence and uncertainty. In our framework, the survival function is derived through some unique structural reliability treatments. Vine copula and imprecise probability are integrated and embedded within the framework to address the case that dependence and imprecision simultaneously appear. Implementation-wise, two numerical simulation algorithms are developed to address some complicated cases in which the analytical solution is not available. For demonstration and validation, both the numerical case and application examples are presented. The results show the superiority of the proposed method and its potential in real engineering use.