Statistical modeling and reliability analysis for multi-component systems with dependent failures

Reliability analysis of systems based on component reliability models has drawn the great interest of many researchers so far, as one of the fundamental aspects of reliability assessment issues. In particular, reliability analysis considering dependent failure occurrences of system components is important because the components may fail mutually due to sharing workloads such as heat, tasks and so on. In such a situation, we are liable to incorrectly estimate the reliability of the system unless we consider the possibility of the dependent failure occurrence phenomena. Thus, there are many publications about this topic in the literature. Most of the existing studies deal with the dependent failure between any two components in a multi-component system since its mathematical formulation is comparatively easy. However, the dependent failure may occur among two or more components in actual cases.In this thesis, we aim at developing reliability analysis techniques when several components of a system break down dependently. First, we newly formulate a reliability model of systems with the dependent failure by using a multivariate Farlie-Gumbel-Morgenstern (FGM) copula. Based on the model, we investigate the effect of the dependent failure occurrence on the system\u27s reliability. Secondly, we deal with the parameter estimation for the model in order to evaluate the dependence among the components by using their failure times. To do so, we propose a useful estimation algorithm for the multivariate FGM copula. In addition, we theoretically reveal the asymptotic normality of the proposed estimators and numerically investigate the estimation accuracy. Finally, we present a new method for the detection of the dependent failure occurrence in an n-component parallel system. These results are helpful to both quantitative and qualitative reliability assessment of the system under the possibility of the dependent failure occurrences. Also, our estimation method is especially applicable not only the reliability analysis but also other research fields.博士(工学)法政大学 (Hosei University