POSTERIOR NORMAL APPROXIMATION OF REAL-TIME DEGRADATION MODELING USING LAPLACE APPROXIMATION
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.