Enabling more than one function in an entity provides a new cost-effective way to develop a highly reliable system. In this dissertation, we study the reliability of systems containing multi-functional entities. We derive the expressions for reliability of one-shot systems and reliability of each function. A step further, a redundancy allocation problem (RAP) with the objective of maximizing system reliability is formulated. Unlike constructing a system with only single-functional entities, the number of copies of a specific function to be included in each multi-functional entity (i.e., functional redundancy) needs to be determined as part of the design. Moreover, a start-up strategy for turning on specific functions in these components must be decided prior to system operation. We develop a heuristic algorithm and include it in a two-stage Genetic Algorithm (GA) to solve the new RAP. We also apply a modified Tabu search (TS) method for solving such NP-hard problems. Our numerical studies illustrate that the two-stage GA and the TS method are quite effective in searching for high quality solutions. The concept of multi-functional entities can be also applied in probabilistic site selection problem (PSSP). Unlike traditional PSSP with failures either at nodes or on edges, we consider a more general problem, in which both nodes and edges could fail and the edge-level redundancy is included. We formulate the problem as an integer programming optimization problem. To reduce the searching space, two corresponding simplified models formulated as integer linear programming problems are solved for providing a lower bound to the primal problem. Finally, a big challenge in reliability analysis is how to determine the failure distribution of components. This is especially significant for multi-functional entities as more levels of redundancy are considered. We provide an automated model-selection method to construct the best phase-type (PH) distribution for a given data set in terms of the model complexity and the adequacy of statistical fitting. To efficiently utilize the Akaike Information Criterion for balancing the likelihood value and the number of free parameters, the proposed method is carried out in two stages. The detailed subproblems and the related solution procedures are developed and illustrated through numerical studies. The results verify the effectiveness of the proposed model-selection method in constructing PH distributions.