Wiener processes with random effects for degradation data. (English) Zbl 1178.62091

Wang, Xiao

J. Multivariate Anal. 101, No. 2, 340-351 (2010).

Summary: This article studies the maximum likelihood inference of a class of Wiener processes with random effects for degradation data. Degradation data are a 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. The EM algorithm is used to obtain the maximum likelihood estimators of the unknown parameters. Asymptotic properties such as consistency and convergence rate are established. The 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.

MSC:

62M05	Markov processes: estimation; hidden Markov models
62N05	Reliability and life testing
62F12	Asymptotic properties of parametric estimators
62N02	Estimation in survival analysis and censored data
62G20	Asymptotic properties of nonparametric inference
65C60	Computational problems in statistics (MSC2010)

Keywords:

bootstrap; degradation; EM algorithm; empirical processes; random effects; reliability; Wiener process; bridge beam data

Software:

bootstrap; SPLIDA

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