This paper presents a new system design platform and approaches leading to the development of resilient engineered systems through integrating design of system functions and prognosis of function failures in a unified design framework. Failure prognosis plays an increasingly important role in complex engineered systems since it detects, diagnoses, and predicts the system-wide effects of adverse events, therefore enables a proactive approach to deal with system failures at the life cycle use phase. However, prognosis of system functional failures has been largely neglected in the past at early system design stage, mainly because quantitative analysis of failure prognosis in the early system design stage is far more challenging than these activities themselves that have been mainly carried out at the use phase of a system life cycle. In this paper, a generic mathematical formula of resilience and predictive resilience analysis will be introduced, which offers a unique way to consider lifecycle use phase failure prognosis in the early system design stage and to systematically analyze their costs and benefits, so that it can be integrated with system function designs concurrently to generate better overall system designs. Engineering design case studies will be used to demonstrate the proposed design for resilience methodology.