Subject Area



For degradation data in reliability analysis, estimation of the first-passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571-590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this thesis, we propose improved techniques based on saddlepoint approximation, which enhance upon their suggested methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible solutions to such are proposed.

Then, we proposed different semiparametric and nonparametric methods to estimate the FPT distribution of dependence bivariate degradation data. The saddlepoint approximation and bootstrap methods are used to estimate the marginal FPT distributions empirically and the empirical copula is used to estimate the joint distribution of two dependence degradation processes nonparametrically. A Monte Carlo simulation study is used to demonstrate the effectiveness of the proposed semiparametric and nonparametric approaches.

Next, we considered nonlinear degradation modeling using trend-renewal-process (TRP)-type models. In TRP-type models, a proper trend function is used to transform the degradation data so that the Lévy process approach can be applied. We proposed several parametric and semiparametric models and approaches to estimate the FPT distribution and mean-time-to-failure for the nonlinear degradation data. A Monte Carlo simulation and numerical example on lithium-ion battery degradation data are applied to illustrate performance and validity of the proposed models.

Degree Date

Summer 5-16-2020

Document Type


Degree Name



Statistical Science


Dr. Hon Keung Tony Ng

Second Advisor

Dr. Ronald W. Butler

Third Advisor

Dr. Lynne S. Stokes

Fourth Advisor

Dr. Narayanaswamy Balakrishnan

Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License