D. Virkler, B. Hillberry, and P. Goel, The Statistical Nature of Fatigue Crack Propagation, Journal of Engineering Materials and Technology, vol.101, issue.2, pp.148-153, 1979.
DOI : 10.1115/1.3443666

W. Wu and C. Ni, Statistical aspects of some fatigue crack growth data, Engineering Fracture Mechanics, vol.74, issue.18, pp.2952-2963, 2007.
DOI : 10.1016/j.engfracmech.2006.08.019

F. Casciati, P. Colombi, and L. Faravelli, Inherent variability of an experimental crack growth curve. Structural Safety, pp.66-76, 2007.

B. Moreno, J. Zapatero, and J. Domínguez, An experimental analysis of fatigue crack growth under random loading, International Journal of Fatigue, vol.25, issue.7, pp.597-608, 2003.
DOI : 10.1016/S0142-1123(03)00018-5

H. Ghonem and S. Dore, Experimental study of the constant-probability crack growth curves under constant amplitude loading, Engineering Fracture Mechanics, vol.27, issue.1, pp.1-25, 1987.
DOI : 10.1016/0013-7944(87)90002-6

T. Righiniotis and M. Chryssanthopoulos, Probabilistic fatigue analysis under constant amplitude loading, Journal of Constructional Steel Research, vol.59, issue.7, pp.867-886, 2003.
DOI : 10.1016/S0143-974X(03)00002-6

J. Mohanty, B. Verma, and P. Ray, Prediction of fatigue crack growth and residual life using an exponential model: Part I (constant amplitude loading), International Journal of Fatigue, vol.31, issue.3, pp.418-424, 2009.
DOI : 10.1016/j.ijfatigue.2008.07.015

S. Sankararaman, Y. Ling, and S. Mahadevan, Uncertainty quantification and model validation of fatigue crack growth prediction, Engineering Fracture Mechanics, vol.78, issue.7, pp.1487-1504, 2011.
DOI : 10.1016/j.engfracmech.2011.02.017

J. Chang and C. Hudson, on Fracture Mechanics Applications ASE. Methods and Models for Predicting Fatigue Crack Growth Under Random Loading, A.S.T.M. STP. ASTM, 1981.

Y. Xiang and Y. Liu, Application of inverse first-order reliability method for probabilistic fatigue life prediction, Probabilistic Engineering Mechanics, vol.26, issue.2, pp.148-156, 2011.
DOI : 10.1016/j.probengmech.2010.11.001

J. Zapatero and J. Domínguez, A statistical approach to fatigue life predictions under random loading, International Journal of Fatigue, vol.12, issue.2, pp.107-114, 1990.
DOI : 10.1016/0142-1123(90)90680-D

F. Mcmaster and D. Smith, Predictions of fatigue crack growth in aluminium alloy 2024???T351 using constraint factors, International Journal of Fatigue, vol.23, pp.93-101, 2001.
DOI : 10.1016/S0142-1123(01)00134-7

W. Wu and C. Ni, A study of stochastic fatigue crack growth modeling through experimental data, Probabilistic Engineering Mechanics, vol.18, issue.2, pp.107-118, 2003.
DOI : 10.1016/S0266-8920(02)00053-X

P. Paris and F. Erdogan, A Critical Analysis of Crack Propagation Laws, Journal of Basic Engineering, vol.85, issue.4, pp.528-533, 1963.
DOI : 10.1115/1.3656900

R. Forman, V. Keary, and R. Eagle, Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures, Journal of Basic Engineering, vol.89, issue.3, pp.459-464, 1967.
DOI : 10.1115/1.3609637

F. Cadini, E. Zio, and A. D. , Monte Carlo-based filtering for fatigue crack growth estimation, Probabilistic Engineering Mechanics, vol.24, issue.3, pp.367-373, 2009.
DOI : 10.1016/j.probengmech.2008.10.002

K. Sobczyk, S. Jr, and B. , Introduction, pp.1-7, 1992.
DOI : 10.1007/978-1-4612-0121-2_1

J. Yang and S. Manning, A simple second order approximation for stochastic crack growth analysis, Engineering Fracture Mechanics, vol.53, issue.5, pp.677-686, 1996.
DOI : 10.1016/0013-7944(95)00130-1

M. Corbetta, C. Sbarufatti, A. Manes, and M. Giglio, Sequential Monte Carlo sampling for crack growth prediction providing for several uncertainties, Proceedings of the 2nd European conference of the prognostics and health management society

M. Skorupa, T. Machniewicz, J. Schijve, and A. Skorupa, Application of the strip-yield model from the NASGRO software to predict fatigue crack growth in aluminium alloys under constant and variable amplitude loading, Engineering Fracture Mechanics, vol.74, issue.3, pp.291-313, 2007.
DOI : 10.1016/j.engfracmech.2006.06.014

A. Beck, S. De, and W. Gomes, Stochastic fracture mechanics using polynomial chaos, Probabilistic Engineering Mechanics, vol.34, pp.26-39, 2013.
DOI : 10.1016/j.probengmech.2013.04.002

C. Mattrand and J. Bourinet, Random load sequences and stochastic crack growth based on measured load data, Engineering Fracture Mechanics, vol.78, issue.17, pp.3030-3048, 2011.
DOI : 10.1016/j.engfracmech.2011.08.022

G. Dhondt, Application of the discrete markov method to crack propagation problems, International Journal of Engineering Science, vol.33, issue.4, pp.457-467, 1995.
DOI : 10.1016/0020-7225(94)00084-0

X. Zou, Statistical moments of fatigue crack growth under random loading. Theoretical and Applied Fracture Mechanics, pp.1-5, 2003.

M. Davis, Piecewise-Deterministic Markov-Processes -A General-Class of Non-Diffusion Stochastic- Models, Journal Of The Royal Statistical Society Series B-Methodological, vol.46, issue.3, pp.353-388, 1984.

J. Chiquet, N. Limnios, and M. Eid, Piecewise deterministic Markov processes applied to fatigue crack growth modelling, Journal of Statistical Planning and Inference, vol.139, issue.5, pp.1657-1667, 2009.
DOI : 10.1016/j.jspi.2008.05.034

X. Guan, A. Giffin, R. Jha, and Y. Liu, Maximum relative entropy-based probabilistic inference in fatigue crack damage prognostics, Probabilistic Engineering Mechanics, vol.29, pp.157-166, 2012.
DOI : 10.1016/j.probengmech.2011.11.006

F. Dufour and Y. Dutuit, Dynamic Reliability: A new model, Proceedings of ?µ13-ESREL02, 2002.

H. Zhang, F. Innal, F. Dufour, and Y. Dutuit, Piecewise Deterministic Markov Processes based approach applied to an offshore oil production system, Reliability Engineering & System Safety, vol.126, pp.126-134, 2014.
DOI : 10.1016/j.ress.2014.01.016
URL : https://hal.archives-ouvertes.fr/hal-00961512

B. De-saporta, F. Dufour, H. Zhang, and C. Elegbede, Optimal stopping for the predictive maintenance of a structure subject to corrosion, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, vol.226, issue.2, pp.169-181, 2012.
DOI : 10.1177/1748006X11413681

M. Beil, S. Luck, F. Fleischer, S. Portet, W. Arendt et al., Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process, Journal of Theoretical Biology, vol.256, issue.4, pp.518-550, 2009.
DOI : 10.1016/j.jtbi.2008.09.044
URL : https://hal.archives-ouvertes.fr/hal-00554513

M. Davis, Markov models and optimization, of Monographs on Statistics and Applied Probability, 1993.
DOI : 10.1007/978-1-4899-4483-2

B. De-saporta and F. Dufour, Numerical method for impulse control of piecewise deterministic Markov processes, Automatica, vol.48, issue.5, pp.779-793, 2012.
DOI : 10.1016/j.automatica.2012.02.031
URL : https://hal.archives-ouvertes.fr/hal-00541413

B. De-saporta, F. Dufour, and K. Gonzalez, Numerical method for optimal stopping of piecewise deterministic Markov processes, The Annals of Applied Probability, vol.20, issue.5, pp.1607-1637
DOI : 10.1214/09-AAP667
URL : https://hal.archives-ouvertes.fr/hal-00367964

A. Brandejsky, B. De-saporta, and F. Dufour, Optimal stopping for partially observed piecewise-deterministic Markov processes. Stochastic Processes and their Applications, pp.3201-3238, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00755119

C. Baysse, D. Bihannic, A. Gégout-petit, M. Prenat, D. Saporta et al., Maintenance Optimisation of Optronic Equipment, Prognostics and System Health Management Conference, pp.709-714, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00906346

V. Fabian, Simulated annealing simulated, Computers & Mathematics with Applications, vol.33, issue.1-2, pp.81-94, 1997.
DOI : 10.1016/S0898-1221(96)00221-0

J. Dréo, Metaheuristics for Hard Optimization: Methods and Case Studies, 2006.

M. Cortie, The irrepressible relationship between the paris law parameters, Engineering Fracture Mechanics, vol.40, issue.3, pp.681-682, 1991.
DOI : 10.1016/0013-7944(91)90160-3

F. Bergner and G. Zouhar, A new approach to the correlation between the coefficient and the exponent in the power law equation of fatigue crack growth, International Journal of Fatigue, vol.22, issue.3, pp.229-268, 2000.
DOI : 10.1016/S0142-1123(99)00123-1

A. Carpinteri and M. Paggi, Are the Paris' law parameters dependent on each other? Frattura ed Integrita Strutturale, pp.10-16, 2007.

A. International, Properties and Selection: Nonferrous Alloys and Special-purpose, Materials. ASM Handbook. ASM International, 1990.

A. International, Fatigue and fracture, 1996.

M. Corbetta, C. Sbarufatti, A. Manes, and M. Giglio, On Dynamic State-Space models for fatigue-induced structural degradation, International Journal of Fatigue, vol.61, pp.202-219, 2014.
DOI : 10.1016/j.ijfatigue.2013.11.008

M. Corbetta, C. Sbarufatti, A. Manes, and M. Giglio, Real-Time Prognosis of Crack Growth Evolution Using Sequential Monte Carlo Methods and Statistical Model Parameters. Reliability, IEEE Transactions on, vol.64, issue.2, pp.736-753, 2015.

F. Perrin, Prise en compte des données expérimentales dans les modèles probabilistes pour la prévision de la durée de vie des structures, 2008.

K. Ortiz and A. Kiremidjian, A Stochastic Model for Fatigue Crack Growth Rate Data, Journal of Engineering for Industry, vol.109, issue.1, pp.13-18, 1987.
DOI : 10.1115/1.3187085