Inference for accelerated test models based on failures or degradation data from cumulative damage processes

This dissertation investigates some statistical problems in reliability theory. First, based on a discrete cumulative damage approach with a gamma process describing "initial damage" for a fibrous composite specimen, a new statistical model for the strength of such composites is developed. The model is an accelerated inverse Gaussian-type distribution and is shown to fit carbon composite strength data better than previous models. Asymptotic lower confidence bounds for percentiles of the strength distribution are obtained based on Bonferroni's inequality and the Fisher information. Simulation results indicate that the asymptotic Bonferroni lower bounds are quite conservative, and bootstrap methods for improving the bounds are considered. Then an example for observed tensile strengths of carbon micro-composites is presented.;Approximate lower confidence bounds on percentiles of the Weibull and the Birnbaum-Saunders distributions are investigated next. Asymptotic bounds based on Bonferroni's inequality and Fisher information are discussed, and parametric bootstrap methods are proposed to provide better bounds. Since the percentile bootstrap method typically does not perform well for confidence bounds on quantiles, other bootstrap procedures are studied via computer simulations. Results of the simulations indicate that the bootstrap methods generally give sharper lower bounds than the Bonferroni bounds but with coverages still near the nominal confidence level. Illustrative examples are given for carbon micro-composite specimen strength data and for cycles-to-failure data.;An important problem in reliability and survival analysis is that of modeling degradation together with any observed failures in a life test. Based on a continuous cumulative damage approach with a Gaussian process describing degradation, a general accelerated test model is presented in which failure times and degradation measures can be combined for inference about system lifetime. Some specific models when the drift of the Gaussian process depends on the acceleration variable are discussed in detail. Examples using simulated data as well as real data on degradation of carbon-film resistors are presented.;Finally, preliminary results on Bayesian estimation are given, and topics for future research are discussed.