| The research objective is to develop models for system reliability estimation and optimization considering component reliability estimation uncertainty. To accomplish these tasks, the dissertation investigates two primary research topics: system reliability estimations for series-parallel, complex, and network systems; and system reliability optimization with single and multiple objectives.; Estimation of system reliability is generally based on a system structure and component reliability estimates. However, the component reliability estimates are often uncertain due to insufficient failure data or limited testing schedules, and thus, the associated system reliability estimate exhibits uncertainty as well. The variance is often used to quantify the uncertainty of system reliability estimates. Based on moments of component reliability estimates, generating function (GF) and linear-quadratic (LQ) models are proposed respectively for series-parallel and network systems to approximate the system reliability estimate and the associated variance. They are also applicable for components with small sample sizes through Bayesian statistics. Most importantly, GF and LQ models offer distinct advantages because systems are allowed to have statistically dependent component reliability estimates. Existing methods do not satisfactorily address this design problem. Simulations and numerical examples have demonstrated that GF and LQ models are theoretically sound and mathematically accurate.; Based on system reliability estimates such as GF and LQ models, various optimization algorithms are proposed to solve several related testing and design problems under cost and weight constraints. For single objective problems, gradient-based non-linear programming methods are used to minimize the variance of the system reliability estimates. Multi-criteria optimization problems are also developed for redundancy allocation such that system reliability is maximized while the variance is minimized. The weighted objectives method, solution space reduction procedure (SSRP) and branch and bound (B&B) are used to identify Pareto optimal solution sets.; The research shows that the consideration of the component reliability estimation uncertainty is essential to risk-averse system design, though very few researchers have sufficiently addressed this problem. This dissertation explores the impact of component reliability estimation uncertainties on system reliability estimation and optimization. It provides a systematic tool to design highly reliable systems with minimum risk. |
