Exponential Dispersion Process For Degradation Analysis

Degradation tests are widely used to assess the lifetime information of high reliability product in engineering field.It is a core problem to establish the mathematical model for the degradation characteristics of high reliability product in degradation analysis.The common methods for analyzing degradation data are usually based on a special models.However,this may result in a large bias to estimate the reliability of the product when the assumed model is wrong.In this paper,a new stochastic process,called exponential dispersion process,is developed to describe the degradation path of the product's physical or chemical characteristics.Exponential dispersion process includes the most used degradation models(Wiener process,gamma process,inverse Gaussian process and compound Poisson process)as special cases.Thus,it is useful for suggesting an appropriate degradation model for a special dataset.In section 2,we investigate the exponential dispersion model with nonlinear degradation path,and use approximated maximum likelihood method and bootstrap method to obtain the point estimation and interval estimation of the unknown model parameters.Furthermore,an exponential dispersion process with acceleration factors is also explored.The simula tion study and real data analysis are carried out in the remainder of this chapter.In section 3,we explore the bayesian analysis of exponential disper sion model briefly.According to the form of the kernel function of the parameters in exponential dispersion model,setting an appropriate prior for every parameter.Especially for setting of the prior distribution of parameterd,which can make parameters estimation and model selection simultaneously.The simulation study are carried out in the remainder of this chapter.