| Traditional methods in survival, reliability, actuarial science, risk, and other event-history applications are based on the analysis of time-to-occurrence of some event of interest, generically called "failure". In the presence of high-degrees of censoring, however, it is difficult to make inference about the underlying failure distribution using failure time data. Moreover, such data are not very useful in predicting failures of specific systems, a problem of interest when dealing with expensive or critical systems. As an alternative, there is an increasing trend towards collecting and analyzing richer types of data related to the states and performance of systems or subjects under study. These include data on multistate and degradation processes. This dissertation makes several contributions to the analysis of multistate and degradation data.;The first part of the dissertation deals with parametric inference for multistate processes with panel data. These include interval, right, and left censoring, which arise naturally as the processes are not observed continuously. Most of the literature in this area deal with Markov models, for which inference with censored data can be handled without too much difficulty. The dissertation considers progressive semi-Markov models and develops methods and algorithms for general parametric inference. A combination of Markov Chain Monte Carlo techniques and stochastic approximation methods are used. A second topic deals with the comparison of the traditional method and the process method for inference about the time-to-failure distribution in the presence of multistate data. Here, time-to-failure is the time when the process enters an absorbing state. There is limited literature in this area. The gains in both estimation and prediction efficiency are quantified for various parametric models of interest.;The second part of the dissertation deals with the analysis of data on continuous measures of performance and degradation with missing data. In this case, time-to-failure is the time at which the degradation measure exceeds a certain threshold or performance level goes below some threshold. Inference problems about the mean and variance of the degradation and the imputation of the missing are studied under different settings. |
