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Mathematical Problems in Engineering
Volume 2015, Article ID 908742, 8 pages
Research Article

Generalized Accelerated Failure Time Frailty Model for Systems Subject to Imperfect Preventive Maintenance

1Department of Electrical & Information Engineering, CDHK, Tongji University, Shanghai 200092, China
2Department of Mathematics, Tongji University, Siping Road 1239, Shanghai 200092, China
3School of Electrical & Information Engineering, Tongji University, Shanghai 200092, China

Received 14 August 2014; Revised 13 October 2014; Accepted 13 October 2014

Academic Editor: Gang Li

Copyright © 2015 Huilin Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Imperfect preventive maintenance (PM) activities are very common in industrial systems. For condition-based maintenance (CBM), it is necessary to model the failure likelihood of systems subject to imperfect PM activities. In this paper, the models in the field of survival analysis are introduced into CBM. Namely, the generalized accelerated failure time (AFT) frailty model is investigated to model the failure likelihood of industrial systems. Further, on the basis of the traditional maximum likelihood (ML) estimation and expectation maximization (EM) algorithm, the hybrid ML-EM algorithm is investigated for the estimation of parameters. The hybrid iterative estimation procedure is analyzed in detail. In the evaluation experiment, the generated data of a typical degradation model are verified to be appropriate for the real industrial processes with imperfect PM activities. The estimates of the model parameters are calculated using the training data. Then, the performance of the model is analyzed through the prediction of remaining useful life (RUL) using the testing data. Finally, comparison between the results of the proposed model and the existing model verifies the effectiveness of the generalized AFT frailty model.