Graduation Semester and Year

2018

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Shan Sun-Mitchell

Second Advisor

Andrzej Korzeniowski

Third Advisor

Suvra Pal

Fourth Advisor

Yun Jonghyun

Abstract

Preventing failure that can cause delays or catastrophe, has been the focus and motivation for engineers, and other establishments that deals with heavy and light machinery, equipment, and devices. One of the biggest challenges, is accuracy and heavy computations of remaining useful life distribution. In this thesis we will use Laplace Approximations (LA) to avoid relying on complicated numerical computations, in calculating the remaining useful life distribution (RLD). LA is useful method to approximate the posterior distribution of Bayesian formula that incorporates linear degradation model and prior distribution. This proposed approach is applicable to various degradation models composed of univariate and bivariate stochastic parameters that form the models, symmetric and non- symmetric prior believes, and different symmetrical error. Under LA technique, we are able to normally approximate the posterior distribution with its proper parameters, and then implement Bernstein distribution using those parameters to calculate the residual life distribution. In addition, the mean squared error (MSE) of the parameters estimator is considered.

Keywords

Laplace approximation, Mean squared error, Residual life distribution

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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