Multi-state systems are widely used in engineering field, which usually contain complex internal structures and variable external environmental stresses. Discussing the reliability of such system has theoretical significance and application values. In this paper, a new stress–strength model for multi-state system consisting of multi-type multi-state components is introduced with copulas. Each type of components has two dependent strengths, which is suffered from two dependent stresses in working environment, while the strengths and stresses are independent. We discuss inferential procedures for stress–strength reliability of the multi-state system using the proposed improved generalized survival signature in the case of all types of components exposed to common pair of dependent stresses.