Wiener processes with random effects for degradation data

Authors:
Xiao Wang
Affiliations:
Department of Mathematics and Statistics, University of Maryland, 1000 Hilltop Circle, Baltimore, MD 21250, USA
Venue:
Journal of Multivariate Analysis
Year:
2010

Citing 4
Cited 0

Statistical analysis with missing data

Statistical analysis with missing data
The inverse gaussian distribution: theory, methodology, and applications

The inverse gaussian distribution: theory, methodology, and applications
Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution

Technometrics
ML estimation of the multivariate t distribution and the EM algorithm

Journal of Multivariate Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

This article studies the maximum likelihood inference on a class of Wiener processes with random effects for degradation data. Degradation data are special case of functional data with monotone trend. The setting for degradation data is one on which n independent subjects, each with a Wiener process with random drift and diffusion parameters, are observed at possible different times. Unit-to-unit variability is incorporated into the model by these random effects. EM algorithm is used to obtain the maximum likelihood estimators of the unknown parameters. Asymptotic properties such as consistency and convergence rate are established. Bootstrap method is used for assessing the uncertainties of the estimators. Simulations are used to validate the method. The model is fitted to bridge beam data and corresponding goodness-of-fit tests are carried out. Failure time distributions in terms of degradation level passages are calculated and illustrated.