Graduation Year

2022

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Lu Lu, Ph.D.

Committee Member

Li Mingyang, Ph.D.

Committee Member

Kandethody Ramachandran

Committee Member

Getachew Dagne, Ph.D.

Keywords

Accelerated Degradation Test, Cox Partial Log Likelihood, Multivariate Degradation, Pareto Front, Variable selection, Weibull Test Plan

Abstract

This dissertation develops several statistical methods to advance the techniques and applications in the fields of reliability test planning and data analysis as well as statistical modeling and analysis in survival analysis.

The first project focuses on developing new demonstration test plans for lifetime data based on considering multiple objectives. Reliability demonstration tests have been broadly used for assuring reliability performance at the desired confidence level. We consider lifetime data that follows a Weibull distribution which has been broadly used for modeling a variety of shapes of lifetime distributions. When planning a demonstration test, there are often multiple aspects to be considered including the consumer's risk, the producer's risk, the acceptance probability, and the cost. The natural trade-offs between these objectives require a careful evaluation of their interrelationship with the planning parameters and a systematic approach to making a tailored decision. We propose a Pareto front optimization approach for balancing the multiple objectives and offer a set of graphical and numerical tools for comparing solutions and selecting the best test plan to match different users' priorities.

The second project focuses on advancing the statistical modeling and analysis of accelerated degradation test (ADT) data with interdependent multiple degradation measures. In some ADTs, to assess and understand the different aspects of reliability performance, multiple characteristics of how the product degrade are measured, which are often interdependent within individual test units. A nonlinear multivariate general path model with random effects and covariates was developed to capture the variation in the individual degradation paths from unit-to-unit while allowing to model the interdependence among the multiple degradation measurements and also capture the correlation between the initial degradation condition and the degradation rate. A full Bayesian approach for estimation and inferential analysis is demonstrated. The method is evaluated and compared to the stage-of-art practices via a simulation study and is also illustrated using synthetic optical media ADT data from ISO [3].

The third project focuses on advancing the use of penalized regression based on Cox Proportional Hazard models in survival analysis. It is a common challenge in the field of reliability and survival analysis to select a subset of key variables for accurate estimation and prediction of the reliability or survival experience when there are small data with a large number of predictor variables. Penalized Regression models work well for effective variable selection and reduce the complexity of the model. A new penalized regression model based on the Cox partial likelihood and a modified minimax concave penalty is proposed. The performance of the proposed penalized regression model compared with existing methods is demonstrated through a simulation study and its application is illustrated via two real-world examples for analyzing the heart failure data and the NKI breast cancer data.

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