This proposal aims to study semiparametric likelihood inference of some nonhomogeneous Levy processes for degradation data. In some studies where the subjects are put on test at time zero, these subjects degrade over time. Failure is defined as the time when the amount of degradation reaches a pre-specified critical level. Data of this type are called degradation data. The setting for observed data is one on which n independent units, each with a nonhomogeneous Levy process with common shape function and scale parameter, are observed at several possibly different times during the study. The difficulty is that unknown parameters of these processes include a monotone function and a finite dimensional parameter and also the data themselves are correlated. The investigator studies the maximum likelihood estimator (MLE) and maximum pseudo-likelihood estimator (MPLE) of the unknown parameters and develops efficient algorithms to compute both the MLE and the MPLE. Asymptotic properties of these estimators including consistency, convergence rate and asymptotic distribution are established. Related problems, including semiparametric inference of models with random effects and/or time-independent covariates, joint modeling of failure time data and degradation data, and a variation of the Neyman-Scott problem on variance estimation are also investigated.
Traditional analysis in reliability focuses on collecting and modeling failure time data. This poses difficulties in high-reliability applications where there are few failures. Advances in sensing technologies are making it possible to collect extensive amount of data on degradation associated with systems and components. The degradation modeling allows the manufactures to obtain the reliability information required in a timely manner such that they can make effective business decisions regarding warranty periods or demonstrate that the product meets the customer's reliability specifications. The proposed work develops a class of flexible models to analyze the degradation data and has direct applications in industrial engineering and AIDS patients' immune system study, as it formulates real degradation data. The investigator develops numerical software in the forms of R and/or MATLAB for degradation analysis for public use through the internet.
