Mis-specification Analysis Of Degradation Model Based On Exponential Dispersion Process

At present,product quality and its reliability have gradually become the focus of society,and the assessment of product reliability based on relevant information and its research have important practical significance in engineering applications.Compared with the current reliability analysis methods based on product lifetime data,reliability analysis using performance degradation data is superior for products with high reliability,long lifetime and high test costs.Degradation models are the basis for reliability analysis of products with degraded performance,but in practice,the real model applicable to the degraded data set is often unknown.If there is an error in model selection,it will directly affect the calculation of reliability indexes and thus the subsequent product design,use and maintenance processes,etc.The existing degradation models are often selected by some model selection criteria(e.g.,AIC,BIC,etc.)and do not quantitatively give the impact caused by model misuse.Therefore,it is necessary to consider the case of model mis-specification and analyze its possible effects when performing product reliability assessment.In recent years,the exponential dispersion process model has received more and more attention from scholars,which has the advantages of good generalization and wide applicability,and the commonly used Wiener,Gamma,and inverse Gaussian processes are its special cases.Based on this,this thesis selects the exponential dispersion process and quantitatively analyzes the mis-specification problem between it and different degradation models according to White’s model mis-specification related theory,which provides some reference significance for the model selection of performance degradation products in practice.The main research contents of this thesis are as follows:(1)The definition and related properties of three commonly used degradation models are briefly given.According to the characteristics of degradation failure,the definition of exponential dispersion process is introduced.On this basis,the related concepts of Tweedie exponential dispersion process are given.At the same time,the Tweedie exponential dispersion process model with random effect is established,and the related theory introduction and analysis steps of model mis-specification are given.(2)Based on the theory of model mis-specification,this thesis analyzes the mis-specification of exponential dispersion process as Wiener,Gamma and inverse Gaussian processes.Firstly,the evaluation index model is constructed,and then the actual example is substituted to solve the problem.Finally,the influence of mis-specification of evaluation index is analyzed quantitatively.At the same time,the sensitivity of model parameters,the number of test samples and test time are analyzed.(3)Considering the heterogeneity between different products,the random effect is introduced into the exponential dispersion process model.Firstly,an exponential diffusion model with random effects is established and its parameters are estimated.Then,according to these two degradation models,the average lifetime models of their products are established respectively.Based on the theory of model mis-specification,the problem of model mis-specification of exponential dispersion processes with fixed effects and random effects is discussed respectively.In addition,the comparative relationship between the two models is briefly analyzed,and several relevant theorems and proofs are given to lay some foundation for an exhaustive analysis of model mis-specification.Finally,the solution process is described in detail through two different sets of example data,and the influence of parameters,sample number and detection times on the average lifetime evaluation is analyzed by Monte Carlo simulation.