| Dependent failures can have significant effects in system reliability and must be given adequate treatment so as to estimate the reliability accurately. However, dependent failures are usually hard to define and model. Current reliability analysis approaches often make the assumption of independence among events to simplify the modeling and analysis procedures or only consider simple dependent relationships among events. The often-made assumption of independent failures and lack of dependent failure modeling and analysis capability limit the applicability of current reliability approaches to real systems.; In general reliability analysis approaches are based on either combinatorial models, such as binary decision diagram (BDD), or Markov models. Markov models are more comprehensive and flexible than combinatorial models in dependent failure modeling, but combinatorial models are usually much more efficient as Markov models suffer from the state explosion problem when the number of components becomes large.; Beginning with the analysis of a phased mission system (PMS) with multimode failures, we propose a combinatorial model-based dependence-BDD (DEP-BDD) approach for the analysis of systems with components subject to two types of dependent failures at the same time. The DEP-BDD approach consists of the DEP-BDD operation, which is applied to convert system fault tree models into DEP-BDD models, and the DEP-BDD evaluation, which is used to calculate the system reliability including the effect of dependent failures. Both the DEP-BDD operation and evaluation are supported by the dependence algebra, which is derived in our work to handle the complicated dependencies among Boolean variables.; The DEP-BDD approach can be applied to a variety of systems with various dependent failures. In this dissertation, we investigate its applications in the analysis of PMS with multi-state components, PMS with coverage modeling, and incorporating common cause failure (CCF) analysis into the DEP-BDD approach.; The dependence algebra and DEP-BDD approach expand and enrich the applications of combinatorial models in the reliability analysis of systems with complicated dependencies by breaking the restriction of independence assumption. Due to the nature of combinatorial models, the DEP-BDD approach is very efficient compared to Markov model based solutions. |
