An Inverse Gaussian Process Model for Degradation Data

• Published in: Technometrics Vol. 52; no. 2; pp. 188 - 197
• Main Authors: Wang, Xiao, Xu, Dihua
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.05.2010; The American Society for Quality and The American Statistical Association; American Society for Quality and the American Statistical Association; American Society for Quality
• Subjects: Applied sciences; Biodegradation; Bootstrap; Bootstrap resampling; Computer science; control theory; systems; Data models; Data processing. List processing. Character string processing; Degradation data; EM algorithm; Empirical processes; Estimation methods; Exact sciences and technology; Gaussian distributions; Lasers; Material degradation; Mathematics; Maximum likelihood estimation; Memory organisation. Data processing; Modeling; Nonparametric models; Operational research and scientific management; Operational research. Management science; Parametric inference; Probability and statistics; Random effects; Reliability; Reliability theory. Replacement problems; Sciences and techniques of general use; Software; Statistics; Data analysis; Empirical process; Goodness of fit test; Variability; Random effects; Covariate; Empirical processes; Modeling; Bootstrapping; Time distribution; Heterogeneity; Statistical test; Degradation data; Gaussian process; Break up time; Remolded sample; Laser; Gaussian processes; Bootstrap; Random effect; Data models; Maximum likelihood; Reliability; EM algorithm
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/TECH.2009.08197

This paper studies the maximum likelihood estimation of a class of inverse Gaussian process models for degradation data. Both the subject-to-subject heterogeneity and covariate information can be incorporated into the model in a natural way. The EM algorithm is used to obtain the maximum likelihood estimators of the unknown parameters and the bootstrap is used to assess the variability of the maximum likelihood estimators. Simulations are used to validate the method. The model is fitted to laser data and corresponding goodness-of-fit tests are carried out. Failure time distributions in terms of degradation level passages are calculated and illustrated. The supplemental materials for this article are available online.