신뢰성 해석을 위한 바이모달 결합분포함수의 통계모델링

Abstract

For reliability analysis or system reliability analysis, statistical model such as joint cumulative distribution function is required. Statistical models for bimodal data or correlated data in engineering application have been considered. However, statistical modelling for correlated data that have bimodal marginal distributions has been rarely studied for reliability analysis of mechanical system. Gaussian mixture model is a widely used multivariate distribution that consists of a mixture of one or more multivariate normal distribution components to describe multimodal correlated data. However, in Gaussian mixture model, only combination of normal distributions can be used. In this paper, copula is employed to model joint distribution function. By increasing the number of parameters in copula and using finite mixture models to deal with bimodal marginal distributions, statistical modelling procedure of bimodal joint distribution functions for reliability analysis is developed and some mathematical examples are performed.