The Selection Of Copula Function And Its Application In The Dual Degradation Model

In many areas, with the development of science and technology,it is more and more important to study long-life products’ reliability.In order to avoid the lack of long-life product life prediction information, in recent years, a growing number of scientists use the reliability analysis method of product performance degradation. Currently, the research is only limited to a single performance characteristic, or some independent performance characteristics, or multivariate normal reliability analysis in the case. However, in fact, a product often has multiple interrelated performance characteristics which may not follow the multivariate normal distribution. In this case, copula function just gives a new idea to the degradation joint distribution. This method can be divided into two steps, that is, construction of the marginal distribution and selection of copula function. At the same time, the study of the copula function selection is not perfect.This paper mainly discusses copula function selection method and its application in the reliability study of the dual degradation data. The main work is as follows:First,based on the existing literature,copula selection method is proposed three principle of copula function selection.Then we caculate the accuracy of copula function selection.Second,because the product has two related performance characteristics, we use copula function to describe the correlation between the two degradation failure processes,and thus give the model based on the copula and the Wiener process.Third,it is applied to the degradation process modeling of fatigue crack that the proposed selection method of the copula function combined with binary degradation modeling method based on Wiener process.