Wiener processes with random effects for degradation data

• Published in: Journal of multivariate analysis Vol. 101; no. 2; pp. 340 - 351
• Main Author: Wang, Xiao
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier Inc 01.02.2010; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: 62G20; 62G20 62M05 62N05 Bootstrap Degradation EM algorithm Empirical processes Random effects Reliability Wiener process; 62M05; 62N05; Acceleration of convergence; Bootstrap; Bootstrap method; Degradation; Distribution theory; EM algorithm; Empirical processes; Exact sciences and technology; Mathematics; Maximum likelihood method; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Optimization algorithms; Parameter estimation; Parametric inference; Probability and statistics; Random effects; Reliability; Sciences and techniques of general use; Simulation; Statistics; Stochastic models; Studies; Wiener process; Degradation; 62M05; 62N05; 62G20; Bootstrap; Random effects; Wiener process; Empirical processes; Reliability; EM algorithm; Empirical process; Statistical distribution; Multivariate analysis; Stochastic process; Asymptotic convergence; Industry; Hypothesis test; Engineering; Statistical test; Model matching; Convergence rate; Random effect; Jackknife method; Approximation theory; Convergence acceleration; Goodness of fit test; Asymptotic behavior; Statistical estimation; Life test; Functional; Statistical method; Survival analysis; Time distribution; Numerical analysis; Simulation; Trend analysis; Failure time; Maximum likelihood; Resampling method
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2008.12.007

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.