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Bayesian gamma processes for optimizing condition‐based maintenance under uncertainty
Author(s) -
Bousquet N.,
Fouladirad M.,
Grall A.,
Paroissin C.
Publication year - 2014
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2076
Subject(s) - bayesian probability , computer science , estimator , bayesian experimental design , bayes' theorem , bayes estimator , bayesian hierarchical modeling , bayesian average , machine learning , data mining , econometrics , artificial intelligence , statistics , mathematics
The aim of this article is twofold: (i) modeling partially observed crack growth of industrial components using gamma processes and (ii) providing estimators of the best maintenance time in a statistical Bayesian framework. The choice of a Bayesian framework is motivated by the small size of data, the availability of expert knowledge about the crack propagation, and more generally, the concern about the integration of parametrical uncertainties when optimizing a maintenance action. The article answers to the methodological question of Bayesian prior elicitation by adopting a strategy based on virtual data information and defines optimal replacement times as posterior Bayes estimators minimizing appropriate cost functions. More precisely, the industrial data are described, and two different levels of available information are considered. Then, the Bayesian parameter estimation procedure in each case is thoroughly explained, by conducting MCMC runs. Different criteria for maintenance optimization, taking account all uncertainties, are considered and discussed. The overall procedure is tested on simulated data and applied over a real dataset. Copyright © 2014 John Wiley & Sons, Ltd.