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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Jawad, Mahmoud Ali, "POSTERIOR NORMAL APPROXIMATION OF REAL-TIME DEGRADATION MODELING USING LAPLACE APPROXIMATION" (2018). Mathematics Dissertations. 246.
https://mavmatrix.uta.edu/math_dissertations/246
Comments
Degree granted by The University of Texas at Arlington