The survival signature has been introduced to simplify quantification of reliability of systems which consist of components of different types, with multiple components of at least one of these types. The survival signature generalizes the system signature, which has attracted much interest in the theoretical reliability literature but has limited practical value as it can only be used for systems with a single type of components. The key property for uncertainty quantification of the survival signature, in line with the signature, is full separation of aspects of the system structure and failure times of the system components. This is particularly useful for statistical inference on the system reliability based on component failure times.This paper provides a brief overview of the survival signature and its use for statistical inference for system reliability. We show the application of generalized Bayesian methods and nonparametric predictive inference, both these inference methods use imprecise probabilities to quantify uncertainty, where imprecision reflects the amount of information available. The paper ends with a discussion of related research challenges.