The Studies On Change-point Problem In Stochastic Processes And Spatial Ordinal Data

The significant advances in material sciences and manufacturing technologies prolong the lifetimes of the product.Thus the lifetimes of the products can be extrapolated from the degradation path patterns.Nowadays,a variety of degradation models have been proposed by the researchers.However,we found that some display devices,such as plasma display panels(PDPs)and organic light-emitting diodes(OLEDs),exhibit two-phase degradation patterns.Thus the change-point problems becomes a very promising research direction.Considering the characteristics of the degradation pattern,we adopted the Wiener process with the drift function being a two-phase linear function of time.In this thesis,we also considered another special type of data,the spatial ordinal data.The spatial ordinal data is collected from the engineering,clinical science,business,electronics and social science fields.Because it is easy to be collected and save storage.We propose the maximum composite likelihood method to estimate the spatial probit model,which improves the computational efficiency at the loss of statistical efficiency.The content of this thesis is as follows.(1)We fit the two-phase degradation data by the change-point Wiener process model Under the Bayesian framework,we propose the change-point Wiener process to fit the degradation data with two-phase pattern.Considering the different degradation behaviors between the units,we assume that the degradation rate and the change-point are unit-specific.Thus we use the hierarchical Bayesian method to estimate the parameters in the proposed model.For the purpose of comparison,we also develop the maximum likelihood method.The simulation study verifies that the hierarchical Bayesian method outperforms the maximum likelihood method.The analysis of the OLED degradation data shows that the proposed model is superior to other existing models(2)We propose the change-point Wiener process with measurement error.The Wiener process only incorporates the inherent randomness of the system.However,the imperfect instrument and environment may result in the measurement errors for the degradation data.Thus,we incorporate the measurement error into the change-point Wiener process model.Based on the proposed model,we provide the closed form of the distributions of the failure-time and the remaining useful life,the mean time to failure and the mean residual life function.We also show the predictive power of the proposed model through the simulation example and the OLED data set.(3)We study the compound Poisson process with change-point.We model the frequency and the magnitude of the earthquake data concurrently by the compound process process.We also adopt the hierarchical Bayesian method to estimate the parameters in this model.The model is superior to the quadratic linear regression model for the earthquake data.(4)We infer the spatial ordinal probit model by the composite likelihood method.We propose the spatial probit model according the speciality of the spatial ordinal data The spatial correlation is established by the Matern family.The parameters in this model is obtain via the composite likelihood method,which improves the computa-tion efficiency.The simulation study verify the good performance of the proposed method.The analysis of the periodontal disease data illustrates the applicability of the proposed model.