| This research focuses on systems' reliability analysis using analytical methods and Monte Carlo simulation combined to produce a novel analysis technique for complex systems with dependency structures.; The method starts by exploring the design space in order to reduce the model to a less number of design factors using methods like PCA and Cholesky factorization. This in turn accelerates further analysis and facilitates design optimization by transforming the design into the orthogonal space, hence decoupling of the design parameters.; For complex systems that incorporate many components, we model each component's failure mechanism and fit a canonical and close form equation to the data using a hybrid genetic algorithm that uses libraries and mathematical equation simplification such as Groebner bases to accelerate the algorithm and aid its convergence. A closed form for the limit state function can be very helpful when performing sensitivity analysis where many design changes need to be assessed.; Finally, after all components' failure mechanisms are modeled by their limit state functions, the method uses Monte Carlo simulation to generate the different scenarios that a system will experience and assess the propagation of the component failures over time and their effect on other components in the system in a semi analytical way that uses the limit state functions of the component in a varying system environment.; This research contributes new methods to the system's reliability analysis arena by incorporating damage accumulation into the limit state function as the components degrade over time; it also addresses the interaction between the different components by incorporating changes in the environment into the limit state functions of the components themselves. Therefore, this method will accelerate the development process of complex designs without sacrificing the reliability of such designs due to lack of testing, it will also reduce the cost of development by conducting cheaper but very thorough analyses on the fly. |
