Reliability of an engineering system depends on two reliability metrics: the mechanical reliability, considering component failures, that a functional system topology is maintained and the performance reliability of adequate system performance in each functional configuration. Component degradation explains not only the component aging processes leading to failure in function, but also system performance change over time. Multiple competing failure modes for systems with degrading components in terms of system functionality and system performance are considered in this paper with the assumption that system functionality is not independent of system performance. To reduce errors in system reliability prediction, this paper tries to extend system performance reliability prediction methods in open literature through combining system mechanical reliability from component reliabilities and system performance reliability. The extended reliability prediction method provides a useful way to compare designs as well as to determine effective maintenance policy for efficient reliability growth. Application of the method to an electro-mechanical system, as an illustrative example, is explained in detail, and the prediction results are discussed. Both mechanical reliability and performance reliability are compared to total system reliability in terms of reliability prediction errors.