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

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)

### Software:

bootstrap; SPLIDA
Full Text:

### References:

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