Designers should try to design systems that are resilient to adverse conditions during a system’s lifetime. The resilience of a system under time-dependent adverse conditions can be assessed by modeling the degradation and recovery of the system’s components. Decision makers in a firm should attempt to find the optimal design to make the system resilient to the various adverse conditions. A risk-neutral firm maximizes the expected profit gained from fielding the system, but a risk-averse firm may sacrifice some profit in order to avoid failure from these adverse conditions. The uniqueness of this paper lies in its model of a design firm’s risk aversion with a utility function or Value-at-Risk (VAR) and its use of that model to identify the optimal resilient design for the risk-averse firm. These risk-averse decision-making methods are applied to a design firm determining the resilience of a new engineered system. This paper significantly advances the engineering design discipline by modeling the firm’s appetite for risk within the context of designing a system that can fail due to degradation in the presence of adverse events and can respond to and recover from failure. Since the optimization model requires a complex Monte Carlo simulation to evaluate the objective function, we use a ranking and selection method and Bayesian optimization to find the optimal design. This paper incorporates the design of the wind turbine and the reliability and restoration of the turbine’s components for both risk-neutral and risk-averse decision makers. The results show that in order to make the system more resilient, risk-averse firms should pay a larger design cost to prevent catastrophic costs of failure. In this case, the system is less likely to fail due to the high resilience of its physical components.