M. Zelen, Statistical theory of reliability : proceedings of an advanced seminar, p.80, 1963.

A. Alhouaij, Contribution à l'optimisation de la maintenance dans un contexte distribué, Thèse de Doctorat, 2010.

P. Ribot, Vers l'intégration diagnostic-pronostic pour la maintenance des systèmes complexes, Thèse de Doctorat, 2009.

J. F. Lawless, Statistical models and methods for lifetime data Wiley series in probability and mathematical statistics, pp.10-24, 1982.

H. Bertholon, Une modélisation du vieillissement, Thèse de Doctorat, 2001.

W. A. Thompson, On the Foundations of Reliability, Technometrics, vol.5, issue.4, pp.1-13, 1981.
DOI : 10.2307/1266340

N. R. Mann, R. E. Schafer, and N. D. Singpurwalla, Methods for statistical analysis of reliability and life data, p.16, 1974.

H. Procaccia, E. Ferton, and M. Procaccia, Fiabilite et maintenance des materiels industriels reparables et non reparables, Tec et Doc, p.16, 2011.

A. Lannoy and H. Procaccia, Livre Evaluation et maîtrise du vieillissement industriel, Lavoisier, p.16, 2005.

A. Lannoy and H. Procaccia, Evaluation de la fiabilité prévisionnelle, Lavoisier, p.16, 2006.

J. F. Lawless, Statistical Methods in Reliability, Technometrics, vol.3, issue.4, pp.305-316, 1983.
DOI : 10.2307/1266475

G. Saporta, Probabilités : analyse des données et statistique, Technip, vol.20, issue.36, p.136, 1990.

J. I. Mccool, Inference on Weibull Percentiles and Shape Parameter from Maximum Likelihood Estimates, IEEE Transactions on Reliability, vol.19, issue.1, pp.2-9, 1970.
DOI : 10.1109/TR.1970.5216370

D. Markovic, D. Jukic, and M. Bensic, Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, Journal of Computational and Applied Mathematics, vol.228, issue.1, pp.304-312, 2009.
DOI : 10.1016/j.cam.2008.09.025

D. Cousineau, Fitting the three-parameter weibull distribution: review and evaluation of existing and new methods, IEEE Transactions on Dielectrics and Electrical Insulation, vol.16, issue.1, pp.281-288, 2009.
DOI : 10.1109/TDEI.2009.4784578

B. Abbasi, H. Abdol, J. Eshragh, J. Arkat, and M. Hosseinkouchack, Estimating the parameters of Weibull distribution using simulated annealing algorithm, Applied Mathematics and Computation, vol.183, issue.1, pp.85-93, 2006.
DOI : 10.1016/j.amc.2006.05.063

H. Qiao and C. P. Tsokos, Parameter estimation of the Weibull probability distribution, Mathematics and Computers in Simulation, vol.37, issue.1, pp.47-55, 1994.
DOI : 10.1016/0378-4754(94)90058-2

H. Qiao and C. P. Tsokos, Estimation of the three parameter Weibull probability distribution, Mathematics and Computers in Simulation, vol.39, issue.1-2, pp.173-185, 1995.
DOI : 10.1016/0378-4754(95)95213-5

A. Fortin, Analyse numéique pour ingénieurs, p.137, 2008.

D. Markovic and D. Jukic, On nonlinear weighted total least squares parameter estimation problem for the three-parameter Weibull density, Applied Mathematical Modelling, vol.34, issue.7, pp.1839-1848, 2010.
DOI : 10.1016/j.apm.2009.10.001

D. Jukic and D. Markovic, On nonlinear weighted errors-in-variables parameter estimation problem in the three-parameter Weibull model, Applied Mathematics and Computation, vol.215, issue.10, pp.3599-3609, 2010.
DOI : 10.1016/j.amc.2009.10.056

T. Bucar, M. Nagode, and M. Fajdiga, Reliability approximation using finite Weibull mixture distributions, Reliability Engineering & System Safety, vol.84, issue.3, pp.241-251, 2004.
DOI : 10.1016/j.ress.2003.11.008

B. Veber, M. Nagode, and M. Fajdiga, Generalized renewal process for repairable systems based on finite Weibull mixture, Reliability Engineering & System Safety, vol.93, issue.10, pp.1461-1472, 2008.
DOI : 10.1016/j.ress.2007.10.003

G. J. Mclachlan and T. Krishnan, The EM algorithm and extensions, p.24, 1997.

D. Foata and A. Fuchs, Calcul des probabilités : cours et exercices corrigés, p.25, 1996.

M. Krifa, A mixed Weibull model for size reduction of particulate and fibrous materials, Powder Technology, vol.194, issue.3, pp.233-238, 2009.
DOI : 10.1016/j.powtec.2009.04.011

B. Kleine and B. Bertsche, Estimating parameters of mixed weibull distributions using genetic algorithms. Reliability Risk and safety Ale Papazoglou&Zio, pp.861-867, 2010.

J. J. Droesbeke, B. Fichet, and P. Tassi, Analyse statistique des durées de vie : modélisation des données censurées, Économica, vol.26, p.27, 1989.

D. R. Cox, Regression Models and Life-Tables, Journal of the Royal Statistical Society. Series B (Methodological), vol.34, issue.2, pp.187-220, 1972.
DOI : 10.1007/978-1-4612-4380-9_37

A. Zuashkiani, D. Banjevic, and A. K. Jardine, Estimating parameters of proportional hazards model based on expert knowledge and statistical data, Journal of the Operational Research Society, vol.47, issue.12, pp.1621-1636, 2008.
DOI : 10.1016/S0377-2217(96)00318-9

A. K. Jardine and A. H. Tsang, Maintenance, replacement, and reliability : theory and applications, p.80, 2006.

Y. P. Mack, Rate of strong uniform convergence of k-NN density estimates, Journal of Statistical Planning and Inference, vol.8, issue.2, pp.185-192, 1983.
DOI : 10.1016/0378-3758(83)90037-X

D. Bosq and J. P. Lecoutre, Theorie de l'estimation fonctionnelle, Economica, vol.28, issue.51, pp.31-39, 1987.

Y. P. Mack and M. Rosenblatt, Multivariate k-nearest neighbor density estimates, Journal of Multivariate Analysis, vol.9, issue.1, pp.1-15, 1979.
DOI : 10.1016/0047-259X(79)90065-4

P. Hall, On near neighbour estimates of a multivariate density, Journal of Multivariate Analysis, vol.13, issue.1, pp.24-39, 1983.
DOI : 10.1016/0047-259X(83)90003-9

G. S. Watson, Density Estimation by Orthogonal Series, The Annals of Mathematical Statistics, vol.40, issue.4, pp.1496-1498, 1969.
DOI : 10.1214/aoms/1177697523

URL : http://doi.org/10.1214/aoms/1177697523

A. A. Farag and R. M. Mohamed, classification of multispectral data using support vector machines approach for density estimation, p.31, 2003.

R. M. Mohamed and A. A. Farag, Mean field theory for density estimation using support vector, pp.495-501, 2004.

P. Hominal and P. Deheuvels, Estimation non paramétrique de la densité comptetenu d'informations sur le support, Revue de statistique appliquee, vol.29, issue.47, pp.47-68, 1979.

S. Saoudi, F. Ghorbel, and A. Hillion, Some statistical properties of the kernel???diffeomorphism estimator, Applied Stochastic Models and Data Analysis, vol.13, issue.1, pp.39-58, 1997.
DOI : 10.1002/(SICI)1099-0747(199703)13:1<39::AID-ASM292>3.0.CO;2-J

B. W. Silverman, Density Estimation for Statistics and Data Analysis, pp.51-52, 1986.
DOI : 10.1007/978-1-4899-3324-9

M. C. Jones, Simple boundary correction for kernel density estimation, Statistics and Computing, vol.86, issue.3, pp.135-146, 1993.
DOI : 10.1007/978-1-4899-3324-9

J. S. Marron and D. Ruppert, Transformations to reduce boundary bias in kernel density estimation, Journal of the Royal Statistical Society. Series BMethodological), vol.56, issue.51, pp.653-671, 1994.

A. Cowling and P. Hall, On pseudodata methods for removing boundary effects in kernel density estimation, Journal of the Royal Statistical Society. Series B (Methodological ), vol.58, issue.47, pp.551-563, 1996.

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

E. Parzen, Nonparametric Statistical Data Modeling, Journal of the American Statistical Association, vol.55, issue.365, pp.105-121, 1979.
DOI : 10.1007/BF00535694

M. Samiuddin and G. M. , On nonparametric kernel density estimates, Biometrika, vol.77, issue.4, pp.865-874, 1990.
DOI : 10.1093/biomet/77.4.865

D. B. Cline, Admissibile Kernel Estimators of a Multivariate Density, The Annals of Statistics, vol.16, issue.4, pp.1421-1427, 1988.
DOI : 10.1214/aos/1176351046

P. Deheuvels, Estimation non paramétrique de la densité par histogrammes généralisés, pp.5-42, 1977.

S. Adjabi and M. Cherfaoui, Bootstrap dans l'estimation de la densité par la méthode du noyau, p.42, 2010.

L. Devroye, The equivalence of weak, strong and complete convergence in l1 for kernel density, pp.896-904, 1983.

L. Devroye, On the non-consistency of the L2-cross-validated kernel density estimate, Statistics & Probability Letters, vol.8, issue.5, pp.425-433, 1989.
DOI : 10.1016/0167-7152(89)90022-9

L. Devroye, A universal lower bound for the kernel estimate, Statistics & Probability Letters, vol.8, issue.5, pp.419-423, 1989.
DOI : 10.1016/0167-7152(89)90021-7

M. C. Jones and P. J. Foster, A simple nonnegative boundary correction method for kernel density estimation, Statistica Sinica, vol.6, issue.47, pp.1005-1013, 1996.

S. X. Chen, Probability Density Function Estimation Using Gamma Kernels, Annals of the Institute of Statistical Mathematics, vol.52, issue.3, pp.471-480, 2000.
DOI : 10.1023/A:1004165218295

S. X. Chen, Beta kernel estimators for density functions, Computational Statistics & Data Analysis, vol.31, issue.2, pp.131-145, 1999.
DOI : 10.1016/S0167-9473(99)00010-9

S. Adjabi, K. Lagha, and M. Hassani, Méthode du noyau dans l'évaluation de performances des systèmes d'attente, p.48, 2009.

T. Bouezmarni and J. M. Rolin, Consistency of the beta kernel density function estimator, Canadian Journal of Statistics, vol.27, issue.1, pp.89-98, 2003.
DOI : 10.2307/3315905

M. P. Wand and L. Devroye, How easy is a given density to estimate?, Computational Statistics & Data Analysis, vol.16, issue.3, pp.311-323, 1993.
DOI : 10.1016/0167-9473(93)90132-D

R. J. Karunamuni and T. Alberts, On boundary correction in kernel density estimation, Statistical Methodology, vol.2, issue.3, pp.191-212, 2005.
DOI : 10.1016/j.stamet.2005.04.001

R. P. Duin, On the choice of smoothing parameters for parzen estimators of probability density functions. Computers, pp.25-1175, 1976.

S. Kullback and R. A. Leibler, On information and sufficiency. The Annals of, Mathematical Statistics, vol.22, issue.1, pp.76-86, 1951.

P. Hall and M. P. Wand, Minimizing L1 distance in nonparametric density estimation, Journal of Multivariate Analysis, vol.26, issue.1, pp.59-88, 1988.
DOI : 10.1016/0047-259X(88)90073-5

C. J. Stones, An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates, The Annals of Statistics, vol.12, issue.4, pp.1285-1297, 1984.
DOI : 10.1214/aos/1176346792

A. W. Bowman, An alternative method of cross-validation for the smoothing of density estimates, Biometrika, vol.71, issue.2, pp.353-360, 1984.
DOI : 10.1093/biomet/71.2.353

J. S. Marron, Comments on a data based bandwidth selector, Computational Statistics & Data Analysis, vol.8, issue.2, pp.155-170, 1989.
DOI : 10.1016/0167-9473(89)90003-0

P. Hall and J. S. Marron, On the Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator, The Annals of Statistics, vol.15, issue.1, pp.163-181, 1987.
DOI : 10.1214/aos/1176350259

W. Feluch and J. Koronacki, A note on modified cross-validation in density estimation, Computational Statistics & Data Analysis, vol.13, issue.2, pp.143-151, 1992.
DOI : 10.1016/0167-9473(92)90002-W

D. W. Scott and G. R. Terrell, Biased and Unbiased Cross-Validation in Density Estimation, Journal of the American Statistical Association, vol.9, issue.400, pp.1131-1146, 1987.
DOI : 10.1214/aoms/1177696810

S. J. Sheather, Density Estimation, Statistical Science, vol.19, issue.4, pp.588-597, 2004.
DOI : 10.1214/088342304000000297

B. U. Park and J. S. Marron, Comparison of Data-Driven Bandwidth Selectors, Journal of the American Statistical Association, vol.9, issue.409, pp.66-72, 1990.
DOI : 10.1214/aoms/1177696810

P. Hall and J. S. Marron, Estimation of integrated squared density derivatives, Statistics & Probability Letters, vol.6, issue.2, pp.109-115, 1987.
DOI : 10.1016/0167-7152(87)90083-6

S. Sheather and M. Jones, A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society. Series B (Methodological), vol.53, issue.60, pp.683-690, 1991.

M. C. Jones and S. J. Sheather, Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives, Statistics & Probability Letters, vol.11, issue.6, pp.511-514, 1991.
DOI : 10.1016/0167-7152(91)90116-9

R. E. Barlow and L. Hunter, Optimum Preventive Maintenance Policies, Operations Research, vol.8, issue.1, pp.90-100, 1960.
DOI : 10.1287/opre.8.1.90

D. I. Cho and M. Parlar, A survey of maintenance models for multi-unit systems, European Journal of Operational Research, vol.51, issue.1, pp.1-23, 1991.
DOI : 10.1016/0377-2217(91)90141-H

R. Dekker, Applications of maintenance optimization models : a review and analysis. Reliability engineering & systems safety, pp.229-240

T. Nakagawa and S. Mizutani, A summary of maintenance policies for a finite interval, Reliability Engineering & System Safety, vol.94, issue.1, pp.89-96, 2009.
DOI : 10.1016/j.ress.2007.04.004

T. Nakagawa, Advanced reliability models and maintenance policies, p.80, 2008.

F. P. Coolen, P. Coolen-schrijner, and K. J. Yan, Nonparametric predictive inference in reliability, Reliability Engineering & System Safety, vol.78, issue.2, pp.185-193, 2002.
DOI : 10.1016/S0951-8320(02)00162-X

P. Coolen-schrijner and F. P. Coolen, Non-parametric predictive inference for age replacement with a renewal argument. quality and reliablity engineering, pp.203-215, 2004.

B. Bergman and B. Klefsjo, A Graphical Method Applicable to Age-Replacement Problems, IEEE Transactions on Reliability, vol.31, issue.5, pp.31-478, 1982.
DOI : 10.1109/TR.1982.5221439

B. Bergman and B. Klefsjo, The TTT-concept and replacement to extend system life, European Journal of Operational Research, vol.28, issue.3, pp.302-307, 1987.
DOI : 10.1016/S0377-2217(87)80173-X

R. E. Barlow and R. A. Campo, Total Time on Test Processes and Applications to Failure Data Analysis, Defense Technical Information Center, p.81, 1975.

T. Dohi, N. Matsushima, N. Kaio, and S. Osaki, Nonparametric repair-limit replacement policies with imperfect repair, European Journal of Operational Research, vol.96, issue.2, pp.260-273, 1987.
DOI : 10.1016/S0377-2217(96)00102-6

T. Dohi, N. Kaio, and S. Osaki, A new graphical method to estimate the optimal repair-time limit with incomplete repair and discounting, Computers & Mathematics with Applications, vol.46, issue.7, pp.999-1007, 2003.
DOI : 10.1016/S0898-1221(03)90114-3

T. Dohi, A. Ashioka, N. Kaio, and S. Osaki, Statistical estimation algorithms for repairs-time limit replacement scheduling under earning rate criteria, Computers & Mathematics with Applications, vol.51, issue.2, pp.345-356, 2006.
DOI : 10.1016/j.camwa.2005.11.004

K. Rinsaka and T. Dohi, Optimizing Software Rejuvenation Schedule Based on the Kernel Density Estimation, Quality Technology & Quantitative Management, vol.6, issue.1, pp.55-65, 2009.
DOI : 10.1109/FTCS.1995.466961

F. Jensen and N. E. Petersen, Burn-in : an engineering approach to the design and analysis of burn-in procedures, p.106, 1982.

J. Mi, Burn-in and Maintenance Policies, Advances in Applied Probability, vol.26, issue.01, pp.207-221, 1994.
DOI : 10.1109/PROC.1983.12763

J. H. Cha, On a better burn-in procedure, Journal of Applied Probability, vol.4, issue.04, pp.1099-1103, 2000.
DOI : 10.1214/ss/1029963258

J. H. Cha, On Optimal Burn-In Procedures ???A Generalized Model, IEEE Transactions on Reliability, vol.54, issue.2, pp.198-206, 2005.
DOI : 10.1109/TR.2005.845966

I. B. Sidibe, A. Khatab, and K. H. Adjallah, Kernel based estimation method for age replacement policy, 5th International Conference on Industrial Engineering and Systems Management, p.109, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01436719

I. B. Sidibe, A. Khatab, and K. H. Adjallah, Kernel estimation based method for the optimization of the system age preventive replacement policy, International Journal of Reliability, p.109
URL : https://hal.archives-ouvertes.fr/hal-01436719

T. Nakagawa and S. Osaki, Optimum replacement policies with delay, Journal of Applied Probability, vol.11, issue.01, pp.102-110, 1974.
DOI : 10.2307/3212587

C. Tilquin and R. Cléroux, The block replacement model with inactivity periods and general cost structure, Canadian Journal of Statistics, vol.13, issue.1-2, pp.197-213, 1974.
DOI : 10.2307/3314959

D. Ait-kadi and R. Cléroux, Optimal block replacement policies with multiple choice at failure, Naval Research Logistics, vol.5, issue.1, pp.99-110, 1988.
DOI : 10.1002/1520-6750(198802)35:1<99::AID-NAV3220350109>3.0.CO;2-3

D. Ait-kadi and R. Cléroux, Replacement strategies with mixed corrective actions at failure, Computers & Operations Research, vol.18, issue.2, pp.141-149, 1991.
DOI : 10.1016/0305-0548(91)90085-6

I. B. Sidibe, A. Khatab, and K. H. Adjallah, Reliability and preventive maintenance analysis of weibull distributed lifetime systems. 11th IFAC Workshop on Intelligent Manufacturing Systems, p.124, 2013.

G. Saporta, Probabilites, analyse des donnees et statistique, p.133, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01125195

P. Hall and M. P. Wand, On the minimization of absolute distance in kernel density estimation, Statistics & Probability Letters, vol.6, issue.5, pp.311-314, 1988.
DOI : 10.1016/0167-7152(88)90005-3

L. Devroye, The double kernel method in density estimation, Annal. Inst. Henri Poincare, vol.25, pp.533-580, 1989.

J. Beirlant and L. Devroye, On the impossibility of estimating densities in the extreme tail, Statistics & Probability Letters, vol.43, issue.1, pp.57-64, 1999.
DOI : 10.1016/S0167-7152(98)00246-6

P. Sarda, Smoothing parameter selection for smooth distribution functions, Journal of Statistical Planning and Inference, vol.35, issue.1, pp.65-75, 1993.
DOI : 10.1016/0378-3758(93)90068-H

N. Altman and C. Léger, Bandwidth selection for kernel distribution function estimation, Journal of Statistical Planning and Inference, vol.46, issue.2, pp.195-214, 1995.
DOI : 10.1016/0378-3758(94)00102-2

P. Hall and W. R. Schucany, A local cross-validation algorithm, Statistics & Probability Letters, vol.8, issue.2, pp.109-117, 1989.
DOI : 10.1016/0167-7152(89)90002-3