Sensitivity analysis of turbine engine sustainment
In current turbine engine reliability models, the relationship between the MTTF (Mean Time to Failure) and the time to failure (TTF) of individual components is not well understood. Probabilistic sensitivity analysis provides a tool to identify the critical failure modes in an engine. These sensitivity measures reveal any effect of an individual component's uncertainty on the MTTF of the entire system. Using a conservative model, the minimum function, several different methods of identifying these critical failure modes were applied to both a 5-component mock engine model and a 22-component full turbine engine module (Rear Gear Box). Complex variable numerical differentiation methods were applied in order to calculate local probabilistic sensitivities. From this investigation two numerical differentiation methods were developed: direct complex variable Monte Carlo (direct CVMC) and complex variable score function (CVSF). Direct CVMC requires fewer samples but is not robust. CVSF circumvents any discontinuities in the response of interest but inherits a larger variance in the derivatives of interest. While direct CVMC provided first order derivatives, this required an approximation of the minimum function. CVSF, with an additional order of magnitude sampling cost, circumvents discontinuities in the minimum function and provided higher order derivatives. The sensitivities found through complex variable differentiation also provided a means to estimate the MTTF via Taylor series expansion. This eliminates the need to use a computationally expensive nested Monte Carlo loop. The MTTF via Taylor series expansion approximated the MTTF computed through the nested loop in both mock engine and 22-component models.