| Redundancy allocation is an important combinatorial optimization problem that aims to determine an optimal system structure with high reliability and low cost. Although it has been well studied for traditional binary-state systems, its exploration for multi-state systems (MSSs) is still limited. This dissertation focuses on three fundamental issues that are essential to addressing the problem for MSSs.;First, a novel hybrid algorithm, particle swarm optimization with local search (PSO/LS), has been proposed to solve the basic formulation of the optimization problem with heterogeneous redundancy. The algorithm aims to select appropriate components and levels of redundancy so that the built system has a minimum cost while providing desired reliability. Novel local search strategies and a dynamic penalty scheme are proposed to enhance the algorithm's performance. The common assumption appeared in the literature is adopted: true reliabilities of components are ideally known. The universal generating function method is applied to "precisely" calculate the system reliability. PSO/LS is shown superior to the best-known heuristics and meta-heuristics in terms of the improved solution quality.;Second, realizing that component reliabilities are generally estimated based on experimental or operational data, this dissertation argues that the assumption that component reliabilities are precisely known may not be applicable to real-world cases. Statistical uncertainty arises at the component level due to limited experimental or operational data and propagates to the system level. In this dissertation, the uncertainty propagation mechanism is mathematically explained through an iterative derivation. The unbiased estimators of system reliability and the associated variance are obtained. With the help of these estimators, a lower confidence bound is proposed and proved superior to xvii two published bounds. Three importance measures of individual components are also proposed.;Third, the optimization problem formulation is revised to incorporate statistical uncertainty. PSO/LS algorithm is revised to determine the system structure with a minimum cost while providing desired reliability with 95% of confidence. For the same reliability requirement, the solution of the new formulation generally costs more, but the system structure is enhanced, the system reliability is improved, and the solution provides 95% of assurance that the system structure will satisfy the reliability requirement. |
