Thesis (Ph.D.)--University of Oklahoma, 1991. / Includes bibliographical references (leaves 148-153).

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

Reliability characteristics of new devices are usually demonstrated by life testing. When lifetime data are sparse, as is often the case with highly reliable devices, expensive devices, and devices for which accelerated life testing is not feasible, reliability models that are based on a combination of degradation and lifetime data represent an important practical approach. This thesis presents reliability models based on the combination of degradation and lifetime data or degradation data alone, with and without the presence of covariates. Statistical inference methods associated with the models are also developed. / The degradation process is assumed to follow a Wiener process. Failure is defined as the first passage of this process to a fixed barrier. The degradation data of a surviving item are described by a truncated Wiener process and lifetimes follow an inverse Gaussian distribution. Models are developed for three types of data structures that are often encountered in reliability studies, terminal point data (a combination of degradation and lifetime data) and mixed data (an extended case of terminal point data); conditional degradation data; and covariate data. / Maximum likelihood estimators (MLEs) are derived for the parameters of each model. Inferences about the parameters are based on asymptotic properties of the MLEs and on the likelihood ratio method. An analysis of deviance is presented and approximate pivotal quantities are derived for the drift and variance parameters. Predictive density functions for the lifetime and the future degradation level of either a surviving item or a new item are obtained using empirical Bayes methods. Case examples are given to illustrate the applications of the models.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 438-442).

Thesis (M.Sc.). / Written for the Dept. of Mathematics and Statistics. Title from title page of PDF (viewed 2008/12/07). Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 126-131).

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 257-261).

No description available.

A reliability model to study the behavior of an electronic component subject to several failure mechanisms ls developed. The mechanisms considered for the analysis are of degradation type where the number of defects for a mechanism increases with time, eventually causing the failure of the component. The failure pattern of the component subject to a single mechanism · with given initial and final number of defects is modelled as a pure birth process. Failure time for this mechanism is expressed as the first passage time of the birth process to state k from initial state l. First passage time distribution is derived for different forms of transition rates. When the initial and final states of the process are considered as random, the failure time is expressed as the mixture distribution obtained from the conditional first passage time distributions. The mixture distributions are well represented by a Weibull distribution. A computer program is developed to compute the parameters of the Weibull distribution iteratively by the method of matching moments. The approximation results are statistically validated. The results for a single mechanism are extended to the case of multiple mechanisms. Extreme·value theory and competing risk theory are applied to analyze the simultaneous effects of multiple mechanisms. lt is shown that the aggregate failure time distribution has a Weibull form for both the theories. The model explains the influence of physical and chemical properties of the component and the operating conditions on the failure times. It can be used for accelerated testing and for lncorporating reliability at product design stage. / Ph. D.

This work develops a marginal screening test to detect the presence of significant predictors for a right-censored time-to-event outcome under a high-dimensional accelerated failure time (AFT) model. Establishing a rigorous screening test in this setting is challenging, not only because of the right censoring, but also due to the post-selection inference. The oracle property in such situations fails to ensure adequate control of the family-wise error rate, and this raises questions about the applicability of standard inferential methods. McKeague and Qian (2015) constructed an adaptive resampling test to circumvent this problem under ordinary linear regression. To accommodate right censoring, we develop a test statistic based on a maximally selected Koul--Susarla--Van Ryzin estimator from a marginal AFT model. A regularized bootstrap method is used to calibrate the test. Our test is more powerful and less conservative than the Bonferroni correction and other competing methods. This proposed method is evaluated in simulation studies and applied to two real data sets.