Marginal and joint reliability importance based on survival signature

•New results on importance measures for systems with multiple types of components.•Includes dependence of failure times of components of different types.•Includes marginal and joint importance measures.•New results for black-box systems.•Novel application of the concept of survival signature enabling use for large systems. Marginal and joint reliability importance measures have been found to be useful in optimal system design. Various importance measures have been defined and studied for a variety of system models. The results in the literature are mostly based on the assumption that the components within the system are independent or identical. The present paper is concerned with computation of marginal and joint reliability importance for a coherent system that consists of multiple types of dependent components. In particular, by utilizing the concept of survival signature, expressions for marginal and joint reliability importance measures are presented. We also introduce reliability importance for a system of which only the survival signature is known, which therefore can be regarded to be a black box system.