A methodology is developed and applied that determines the sensitivities of the probability-of-fracture of a gas turbine disk fatigue analysis with respect to the parameters of the probability distributions describing the random variables. The disk material is subject to initial anomalies, in either low-or high-frequency quantities, such that commonly used materials (titanium, nickel, powder nickel) and common damage mechanisms (inherent defects or surface damage) can be considered. The derivation is developed for Monte Carlo sampling such that the existing failure samples are used and the sensitivities are obtained with minimal additional computational time. Variance estimates and confidence bounds of the sensitivity estimates are developed. The methodology is demonstrated and verified using a multizone probabilistic fatigue analysis of a gas turbine compressor disk analysis considering stress scatter, crack growth propagation scatter, and initial crack size as random variables.

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Traditionally, probabilistic design codes are developed for a particular field of application such as aerospace, nuclear and offshore structures. These codes contain specific mechanics models and random variables. Also, the probabilistic methods implemented are specific and highly optimized for the particular problem. Over a period of time these codes may need to be enhanced and certain variables that were once considered deterministic need to be made random. In addition, the source code may not be available. In such a scenario, the generalized conditional expectation method is implemented to enhance the probabilistic design code and add new random variables without changing the source code. This methodology can also be used to assist the developer in evaluating the enhancement of code, before changing the source code. In this paper, the generalized conditional expectation methodology is used to enhance a probabilistic fatigue code by adding more random variables to the existing code without changing the source code. Also, new features such as estimating the sensitivities of the probability of failure to the parameters of random variables are demonstrated. A numerical example is solved to demonstrate the methodology.

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