A hybrid Finite Element-Statistical Energy Analysis (FE-SEA) method has been developed and improved over the past fifteen years to analyse complex vibro-acoustic built-up systems, comprised by both deterministic and statistical components, and the FE-SEA equations have been derived considering that the power input to the structure is due to prescribed forces applied to the degrees of freedom of either the deterministic and/or the statistical components. In this paper, it is presented a generalised set of FE-SEA equations to estimate the response of a system when prescribed displacements contribute to the power input to the complex system. It was found that the equations are not necessarily reversible, meaning that if a set of displacements estimated from the hybrid approach with prescribed forces are used as input to the same randomised structure, the response will be altered due to its statistical nature. The generalised set of FE-SEA equations is validated against numerical data of FE Monte Carlo simulations of two complex built-up structures, where the input is given to the statistical system and to a deterministic resonant structure, respectively.