N. Beaucaire, E. Gayton, J. Duc, and . Dantan, Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods, Computer-Aided Design, vol.45, issue.12, pp.1547-1555, 2013.
DOI : 10.1016/j.cad.2013.06.011

D. Bertsimas and J. N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, 1997.

S. Bhide, G. Ameta, J. K. Davidson, and J. J. Shah, Tolerance-Maps Applied to the Straightness and Orientation of an Axis, CD ROM Proc., 9th CIRP International Seminar on Computer-Aided Tolerancing, 2005.
DOI : 10.1007/1-4020-5438-6_6

J. Barron, J. M. Bichon, . Mcfarland, and . Et-sankaran-mahadevan, Efficient surrogate models for reliability analysis of systems with multiple failure modes, Reliability Engineering & System Safety, issue.10, pp.961386-1395, 2011.

B. J. Bichon, M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. Mcfarland, Efficient global reliability analysis for non linear implicit performance functions, AIAA Journal, issue.10, pp.462459-68, 2008.

G. Blatman and . Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Probabilistic Engineering Mechanics, vol.25, issue.2, pp.183-197, 2010.
DOI : 10.1016/j.probengmech.2009.10.003

G. Blatman and B. Sudret, Efficient computation of global sensitivity indices using sparse polynomial chaos expansions, Reliability Engineering & System Safety, vol.95, issue.11, pp.1216-1229, 2010.
DOI : 10.1016/j.ress.2010.06.015

C. A. Sagastizábal, Numerical Optimization -Theoretical and Practical Aspects, 2006.

B. E. Boser, I. M. Guyon, and V. N. Vapnik, A training algorithm for optimal margin classifiers, Proceedings of the fifth annual workshop on Computational learning theory , COLT '92, 1992.
DOI : 10.1145/130385.130401

P. Bourdet and A. Clément, Controlling a complex surface with a 3 axis measuring machine, Annals of the CIRP, vol.25, pp.359-364, 1976.

J. Bourinet, F. Deheeger, and E. M. Lemaire, Assessing small failure probabilities by combined subset simulation and Support Vector Machines, Structural Safety, vol.33, issue.6, pp.343-353, 2011.
DOI : 10.1016/j.strusafe.2011.06.001

C. G. Bucher and U. Bourgund, A fast and efficient response surface approach for structural reliability problems, Structural Safety, vol.7, issue.1, pp.57-66, 1990.
DOI : 10.1016/0167-4730(90)90012-E

K. W. Chase, S. P. Magleby, and C. G. Glancy, Tolerance Analysis of 2-D and 3-D Mechanical Assemblies with Small Kinematic Adjustments Advanced Tolerancing Techniques, pp.1869-1873, 2004.

S. Choi and R. V. Grandhi, Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability, AIAA Journal, vol.42, issue.6, pp.1191-1198, 2004.
DOI : 10.2514/1.2220

J. Y. Dantan and A. Ballu, Assembly specification by Gauge with Internal Mobilities (GIM)???A specification semantics deduced from tolerance synthesis, Journal of Manufacturing Systems, vol.21, issue.3, pp.218-235, 2002.
DOI : 10.1016/S0278-6125(02)80163-7

J. Y. Dantan and J. Qureshi, Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation, Computer-Aided Design, vol.41, issue.1, pp.1-12, 2009.
DOI : 10.1016/j.cad.2008.11.003

J. K. Davidson and J. J. Shah, Modeling of geometric variations for line-profiles, Journal of Computing and Information Science in Engineering, vol.12, pp.1-10, 2012.

J. K. Davidson, A. Mujezinovic, and J. J. Shah, A New Mathematical Model for Geometric Tolerances as Applied to Round Faces, Journal of Mechanical Design, vol.124, issue.4, pp.609-622, 2002.
DOI : 10.1115/1.1497362

F. Deheeger and M. Lemaire, Reliability analysis using support vector machine classification, 2006.

A. Der-kiureghian and P. L. Liu, Structural Reliability under Incomplete Probability Information, Journal of Engineering Mechanics, vol.112, issue.1, pp.85-104, 1986.
DOI : 10.1061/(ASCE)0733-9399(1986)112:1(85)

A. Desrochers, Geometrical variations management in a multidisciplinary environment with the Jacobian-Torsor model, Models for Computer Aided Tolerancing in Design and Manufacturing, pp.75-84, 2007.

O. Ditlevsen and H. O. Madsen, Structural Reliability Methods, 1996.

P. J. Dossantos-uzarralde and A. Guittet, A polynomial chaos approach for nuclear data uncertainties evaluations. Nuclear Data Sheets, pp.2894-2899, 2008.

V. Dubourg, B. Sudret, and E. F. Deheeger, Metamodel-based importance sampling for structural reliability analysis, Probabilistic Engineering Mechanics, vol.33, pp.47-57, 2013.
DOI : 10.1016/j.probengmech.2013.02.002
URL : https://hal.archives-ouvertes.fr/hal-00590604

A. Dumas, B. Echard, N. Gayton, O. Rochat, J. Dantan et al., AK-ILS: An Active learning method based on Kriging for the Inspection of Large Surfaces, Precision Engineering, vol.37, issue.1, pp.1-9, 2013.
DOI : 10.1016/j.precisioneng.2012.07.007

A. Dumas, J. Dantan, and E. N. Gayton, Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms, Computer-Aided Design, vol.62, 2014.
DOI : 10.1016/j.cad.2014.11.002

A. Dumas, J. Dantan, N. Gayton, T. Bles, and E. R. Loebl, ????????????????????????????????????????????????, Journal of Zhejiang University-SCIENCE A, vol.16, issue.5, 2015.
DOI : 10.1631/jzus.A1400221

A. Dumas, N. Gayton, J. Dantan, and E. B. Sudret, A new system formulation for the tolerance analysis of overconstrained mechanisms, Probabilistic Engineering Mechanics, vol.40
DOI : 10.1016/j.probengmech.2014.12.005
URL : https://hal.archives-ouvertes.fr/hal-01432530

B. Echard, N. Gayton, and E. M. Lemaire, AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation, Structural Safety, vol.33, issue.2, pp.145-154, 2011.
DOI : 10.1016/j.strusafe.2011.01.002

B. Echard, N. Gayton, M. Lemaire, and E. N. Relun, A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models, Reliability Engineering & System Safety, vol.111, issue.0, pp.232-240, 2013.
DOI : 10.1016/j.ress.2012.10.008

W. Fauriat and N. Gayton, AK-SYS: An adaptation of the AK-MCS method for system reliability, Reliability Engineering & System Safety, vol.123, pp.137-144, 2014.
DOI : 10.1016/j.ress.2013.10.010

J. Gao, K. W. Chase, and S. P. Magleby, Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments, IIE Transactions, vol.2, issue.4, pp.367-377, 1998.
DOI : 10.1115/1.2919346

N. Gayton, J. M. Bourinet, and E. M. Lemaire, CQ2RS: a new statistical approach to the response surface method for reliability analysis, Structural Safety, vol.25, issue.1, pp.99-121, 2003.
DOI : 10.1016/S0167-4730(02)00045-0

A. Genz, Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, vol.1, issue.2, pp.141-149, 1992.
DOI : 10.1007/978-1-4613-9655-0

M. Giordano and D. Duret, Clearance space and deviation space : Application to three-dimensional chain of dimensions and positions, 1993.

M. Giordano, S. Samper, and J. P. Petit, Tolerance analysis and synthesis by means of deviation domains, axi-symmetric cases. 9th CIRP International Seminar on Computer- Aided Tolerancing, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00333030

A. Hasofer and N. Lind, Exact and invariant second-moment code format, Journal of Engineering Mechanics, vol.100, issue.1, pp.111-121, 1974.

Y. S. Hong and T. C. Chang, A comprehensive review of tolerancing research, International Journal of Production Research, vol.30, issue.11, pp.2425-59, 2002.
DOI : 10.1080/002075499189880

J. E. Hurtado, An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory, Structural Safety, vol.26, issue.3, pp.271-293, 2004.
DOI : 10.1016/j.strusafe.2003.05.002

J. E. Hurtado, Filtered importance sampling with support vector margin: A powerful method for structural reliability analysis, Structural Safety, vol.29, issue.1, pp.2-15, 2007.
DOI : 10.1016/j.strusafe.2005.12.002

J. E. Hurtado, An optimization method for learning statistical classifiers in structural reliability, Probabilistic Engineering Mechanics, vol.25, issue.1, pp.26-34, 2010.
DOI : 10.1016/j.probengmech.2009.05.006

D. R. Jones, M. Schonlau, and W. J. Welch, Efficient global optimization of expensive blackbox functions, Journal of Global Optimization, vol.13, issue.4, pp.455-492, 1998.
DOI : 10.1023/A:1008306431147

I. Kaymaz and C. A. Mcmahon, A response surface method based on weighted regression for structural reliability analysis, Probabilistic Engineering Mechanics, vol.20, issue.1, pp.11-17, 2005.
DOI : 10.1016/j.probengmech.2004.05.005

D. Kim, S. Ok, J. Son, and H. Koh, System reliability analysis using dominant failure modes identified by selective searching technique, Reliability Engineering & System Safety, vol.119, pp.316-331, 2013.
DOI : 10.1016/j.ress.2013.02.007

D. G. Krige, A statistical approach to some basic mine valuation problems on the witwatersrand, Journal of the Chemical, Metallurgical and Mining Society of South Africa, vol.52, issue.6, pp.119-139, 1951.

O. Legoff, S. Tichadou, and J. Y. Hascoet, Manufacturing errors modelling: Two three-dimensional approaches, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol.218, issue.12, pp.1869-1873, 2004.
DOI : 10.1177/095440540421801219

J. Qureshi, J. Y. Dantan, V. Sabri, P. Beaucaire, and E. N. Gayton, A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation, Computer-Aided Design, vol.44, issue.2, pp.132-142, 2012.
DOI : 10.1016/j.cad.2011.10.004

R. Rackwitz and B. Fiessler, Structural reliability under combined random load sequences, Computers & Structures, vol.9, issue.5, pp.489-494, 1979.
DOI : 10.1016/0045-7949(78)90046-9

M. Rosenblatt, Remarks on a Multivariate Transformation, The Annals of Mathematical Statistics, vol.23, issue.3, pp.470-472, 1952.
DOI : 10.1214/aoms/1177729394

O. Roustant, D. Ginsbourger, and Y. Deville, Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization, Journal of Statistical Software, vol.51, issue.1, p.52, 2010.
DOI : 10.18637/jss.v051.i01
URL : https://hal.archives-ouvertes.fr/hal-00495766

S. Samper, P. Adragna, H. Favreliere, and E. M. Pillet, Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces, Journal of Computing and Information Science in Engineering, vol.9, issue.4, pp.1-12, 2009.
DOI : 10.1115/1.3249575
URL : https://hal.archives-ouvertes.fr/hal-00451883

B. Schleich and S. Wartzack, A discrete geometry approach for tolerance analysis of mechanism . Mechanism and Machine Theory, pp.148-163, 2014.

A. J. Smola and B. Schölkopf, A tutorial on support vector regression, Statistics and Computing, vol.14, issue.3, pp.199-222, 2004.
DOI : 10.1023/B:STCO.0000035301.49549.88

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety, vol.93, issue.7, pp.964-979, 2008.
DOI : 10.1016/j.ress.2007.04.002
URL : https://hal.archives-ouvertes.fr/hal-01432217

D. Teissandier and V. Delos, Algorithm to calculate the Minkowski sums of 3-polytopes based on normal fans, Computer-Aided Design, vol.43, issue.12, pp.1567-1576, 2011.
DOI : 10.1016/j.cad.2011.06.016
URL : https://hal.archives-ouvertes.fr/hal-00635842

V. Vapnik, The Nature of Statistical Learning Theory, 1995.

V. Vapnik and A. Lerner, Pattern recognition using generalized portrait method. Automation and Remote Control, 1963.

J. Villemonteix, E. Vázquez, and E. E. Walter, An informational approach to the global optimization of expensive-to-evaluate functions, Journal of Global Optimization, vol.10, issue.5, p.31, 2006.
DOI : 10.1007/s10898-008-9354-2
URL : https://hal.archives-ouvertes.fr/hal-00354262

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

Y. Zhang and A. Kiureghian, Two improved algorithms for reliability analysis Reliability and Optimization of Structural Systems, The International Federation for Information Processing, pp.297-304, 1995.

Z. Zou and E. P. Morse, Applications of the GapSpace Model for Multidimensional Mechanical Assemblies, Journal of Computing and Information Science in Engineering, vol.3, issue.1, pp.22-30
DOI : 10.1115/1.1565072