The reliability group of FIGAL team works on probability and statistics applied to dependability. On one hand, we build stochastic models for the processes of failures, repairs and maintenance of various systems. On another hand, we develop statistical methods to analyze failure, degradation and maintenance data, in order to assess and predict the reliability of these systems. Our research ranges from theory to applications. Most of our work is done in close collaboration with industry.
Ageing and maintenance processes
We develop modeling frameworks for the maintenance process of repairable systems, which take into account different types of maintenance: corrective maintenance (CM) alone, CM with preventive maintenance (PM) which can be planned or condition-based. We have proposed several models of imperfect maintenance, expressing their effect by an arithmetic reduction of age (ARA) or intensity (ARI). To express the dependence between PM and CM, we use classical and generalized competing risks models. We study statistical inference issues for some of these models: parametric and semiparametric estimation methods, asymptotic properties of maximum likelihood estimators, Bayesian inference. The simultaneous assessment of system ageing and maintenance efficiency led us to develop an integrated approach of technico-economic optimization of maintenance.
Goodness-of-fit testing in reliability
For any set of reliability data, it is important to choose an appropriate stochastic model. Then, the team studies goodness-of-fit (GOF) tests for reliability models. For non repairable systems, we have performed an extensive comparison study of GOF tests for the exponential and Weibull distributions for complete and censored data, and developed new Weibull GOF tests based on the likelihood and the Laplace transform. For repairable systems, we have proposed GOF tests for Non Homogeneous Poisson Processes and we are developing GOF tests for some imperfect maintenance models.
Accelerated degradation testing
An emerging topic is the development of stochastic models and statistical tools for planning accelerated degradation tests and analyzing their results.
FIGAL is the leader of the ANR project AMMSI (Ageing and Maintenance in reliability - Modelling and Statistical Inference). The other partners are the University of Pau and Pays de l'Adour, the University of Franche-Comté, the University of Technology of Troyes, the University of Toulouse 3, EDF R&D and SNCF. The objective of the AMMSI project is to propose innovative methods and mathematical tools for monitoring the ageing of industrial systems. The project includes the proposal of new models of degradation, failure and maintenance of complex systems. It also includes the development of new statistical methods for analyzing these models and operation data. Finally, it provides decision support tools for the industrial implementation of these methods.
FIGAL and EDF R&D have jointly developed the software tool MARS. MARS (Maintenance Assessment of Repairable Systems) implements the main imperfect maintenance models, and the corresponding statistical inference and maintenance optimization methods. MARS is distributed both in companies (EDF, EADS, HP, SNCF, Dassault Aviation, GDF-Suez, Hydro-Québec, BIBA GmbH, ATEMIC, Visakhapatnam Steel Plant) and University laboratories in France and abroad (Germany, Spain, United Kingdom, Canada, Brazil, India, China, Burma, Taiwan, Algeria, Tunisia). The team is also developing an R package on imperfect maintenance modeling and assessment.
City University of Hong Kong (China), University of Maastricht (Netherlands), Université de Tunis and Université de Carthage (Tunisia), Université de Pau et des Pays de l’Adour, Université de Technologie de Troyes, INSA de Toulouse.