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

On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula

In this paper we consider an extension to the classical compound Poisson risk model in which we introduce a dependence structure between the claim amounts and the interclaim time. This structure is embedded via a generalized Farlie-Gumbel-Morgenstern copula. In this framework, we derive the Laplace transform of the Gerber-Shiu discounted penalty function. An explicit expression for the Laplace transform of the time of ruin is given for exponential claim sizes.Compound Poisson risk model Copula Generalized Farlie-Gumbel-Morgenstern copulas Ruin theory Dependence models Gerber-Shiu discounted penalty function

Laplace copulas of multifactor gamma distributions are new generalized Farlie-Gumbel-Morgenstern copulas

This paper provides bifactor gamma distribution, trivariate gamma distribution and two copula families on [0, 1] n obtained from the Laplace transforms of the multivariate gamma distribution and the multi-factor gamma distribution given by [P (θ)] −λ and [P (θ)] −λ n i=1 (1 + piθi) −(λ i −λ) respectively, where P is an affine polynomial with respect to the n variables θ1,. .. , θn. These copulas are new generalized Farlie-Gumbel-Morgenstern copulas and allow in particular to obtain multivariate gamma distributions for which the cumulative distribution functions and the probability distribution functions are known

Various measures of dependence of a new asymmetric generalized Farlie-Gumbel-Morgenstern copulas

In this paper, we discuss an asymmetric extension of Farlie-Gumbel-Morgenstern copulas studied by several authors and obtain the range of the parameter. We derive an expression for regression function and the properties of these copulas are studied in detail. Also, explicit expressions for various measures of association are obtained. These measures are numerically compared for some particular parametric values of the copulas