The design of energy systems is inevitably affected by uncertainty. Sources of uncertainty include user demands, system components and system operating conditions. Ignoring these uncertainties and developing deterministic designs can render such designs suboptimal and result in system failure. To optimize design under conditions of uncertainty necessitates the quantification of its effects. Monte Carlo Simulation is commonly used to this end because it is simple and easy to understand. However, for complex non-linear systems, it is difficult to directly apply Monte Carlo Simulation due to its high computational cost. Through the study of an innovative gas turbine (an adaptive cycle engine), this paper presents a method for the rapid quantification of uncertainty based on a linear substitute model. There are two basic types of linear substitute model: one based upon the Taylor series method; the other upon the least squares method. Out of the two, the least squares method offers better accuracy at an affordable computational cost. Using this method, it takes 500 s to estimate the means and standard deviation of a system's performance. This is substantially less than the 100,000 s needed for direct Monte Carlo Simulation. The approximation error is typically less than 1% for the standard deviation and less than 5% for the mean under most conditions, far less than a comparable use of the Taylor series method. The same approach can also be adopted for the uncertainty analysis of other complex non-linear energy systems.