W. Kuo and M. J. Zuo, Optimal Reliability Modeling: Principles and Applications, 2003.

A. Lisnianski and G. Levitin, Multi-state System Reliability: Assessment, Optimization and Applications, 2003.
DOI : 10.1142/5221

W. J. Li and H. Pham, Reliability Modeling of Multi-State Degraded Systems With Multi-Competing Failures and Random Shocks, IEEE Transactions on Reliability, vol.54, issue.2, pp.297-303, 2005.
DOI : 10.1109/TR.2005.847278

. Levitin, Optimal Structure of Multi-State Systems With Uncovered Failures, IEEE Transactions on Reliability, vol.57, issue.1, pp.140-148, 2008.
DOI : 10.1109/TR.2007.909767

C. Park and W. J. Padgett, Stochastic Degradation Models With Several Accelerating Variables, IEEE Transactions on Reliability, vol.55, issue.2, pp.379-390, 2006.
DOI : 10.1109/TR.2006.874937

N. Gebraeel, A. Elwany, and J. And-pan, Residual Life Predictions in the Absence of Prior Degradation Knowledge, IEEE Transactions on Reliability, vol.58, issue.1, pp.106-117, 2009.
DOI : 10.1109/TR.2008.2011659

R. Billinton and R. Allan, Reliability Evaluation of Engineering Systems, 1992.

E. Zio, Computational Methods For Reliability And Risk Analysis, Series on Quality, Reliability & Engineering Statistics, vol.14, 2009.
DOI : 10.1142/7190

Y. Li and E. Zio, A Multi-state Physics Model of Component Degradation based on Stochastic Petri Nets and Simulation, IEEE Transactions on Reliability, vol.61, pp.921-931, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00737618

S. D. Unwin, P. P. Lowry, R. F. Layton, P. G. Heasler, and M. B. Toloczko, Multistate physics models of aging passive components in probabilistic risk assessment, Proceedings of ANS PSA 2011 International Topical Meeting on Probabilistic Safety Assessment and Analysis, pp.1-12, 2011.

W. G. Schneeweiss, Tutorial: Petri nets as a graphical description medium for many reliability scenarios, IEEE Transactions on Reliability, vol.50, issue.2, pp.39-48, 2002.
DOI : 10.1109/24.963123

B. Havekort and A. Meewissen, Sensitivity and uncertainty analysis of Markov-reward models, IEEE Transactions on Reliability, vol.44, issue.1, pp.147-153, 1995.
DOI : 10.1109/24.376541

F. Campolongo, A. Saltelli, and J. Cariboni, From screening to quantitative sensitivity analysis. A unified approach, Computer Physics Communications, vol.182, issue.4, pp.978-988, 2011.
DOI : 10.1016/j.cpc.2010.12.039

A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis, Probability and Statistics series, pp.355-365, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00386559

S. Tarantola, V. Kopustinskas, R. Bolado-lavin, A. Kaliatka, E. U?puras et al., Sensitivity analysis using contribution to sample variance plot: Application to a water hammer model, Reliability Engineering and System Safety, pp.62-73, 2012.

M. Xu, T. Chen, and X. Yang, The effect of parameter uncertainty on achieved safety, integrity of safety system, Reliability Engineering and System Safety, 2012.

C. M. Rocco and E. Zio, Global Sensitivity Analysis of Power Systems Components???Markov Reliability Models, Vulnerability, Uncertainty, and Risk, 2014.
DOI : 10.1061/9780784413609.152

E. Haro, F. Anstett-collin, and M. Basset, Sensitivity study of dynamic systems using polynomial Chaos, Reliability Engineering and System Safety, pp.15-26, 2012.

R. Ghanem and P. D. Spanos, Polynomial Chaos in Stochastic Finite Elements, Journal of Applied Mechanics, vol.57, issue.1, pp.197-202, 1990.
DOI : 10.1115/1.2888303

D. Xiu and G. E. Karniadakis, Modeling uncertainty in flow simulations via generalized polynomial chaos, Journal of Computational Physics, vol.187, issue.1, pp.137-167, 2003.
DOI : 10.1016/S0021-9991(03)00092-5

D. Lucor, C. Enaux, H. Jourdren, and P. Sagaut, Stochastic design optimization: Application to reacting flows, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.49-52, pp.49-52, 2007.
DOI : 10.1016/j.cma.2007.07.003

N. Agarwal and N. R. Aluru, Stochastic modeling of coupled electromechanical interaction for uncertainty quantification in electrostatically actuated MEMS, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.43-44, pp.43-44, 2008.
DOI : 10.1016/j.cma.2008.01.005

R. G. Ghanem, A. Doostan, and J. Red-horse, A probabilistic construction of model validation, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.29-32, pp.29-32, 2008.
DOI : 10.1016/j.cma.2007.08.029

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering and System Safety, pp.964-979, 2008.

T. Crestaux, O. L. Maitre, and J. Martinez, Polynomial chaos expansion for sensitivity analysis, Reliability Engineering and System Safety, pp.1161-1172, 2009.

G. Blatman and B. Sudret, Efficient computation of global sensitivity indices using sparse polynomial chaos expansions, Reliability Engineering and System Safety 95, pp.1216-1229, 2010.

C. Soize, Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.33-36, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00684324

F. Simon, P. Guillen, P. Sagaut, and D. Lucor, A gPC-based approach to uncertain transonic aerodynamics, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.17-20, pp.17-20, 1091.
DOI : 10.1016/j.cma.2009.11.021

G. Poëtte, B. Després, and D. Lucor, Treatment of uncertain material interfaces in compressible flows, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.1-4, pp.1-4, 2011.
DOI : 10.1016/j.cma.2010.08.011

S. Oladyshkin, H. Class, R. Helmig, and W. Nowak, A concept for data-driven uncertainty quantification and its application to carbon dioxide storage in geological formations, Advances in Water Resources, vol.34, issue.11, pp.1508-1518, 2011.
DOI : 10.1016/j.advwatres.2011.08.005

G. T. Buzzard, Global sensitivity analysis using sparse grid interpolation and polynomial chaos, Reliability Engineering & System Safety, vol.107, pp.82-89, 2012.
DOI : 10.1016/j.ress.2011.07.011

S. Rahman, Global sensitivity analysis by polynomial dimensional decomposition, Reliability Engineering and System Safety 96, pp.825-837, 2011.

P. G. Constantine, M. S. Eldred, and E. T. Phipps, Sparse pseudo-spectral approximation method, Computer Methods in Applied Mechanics and Engineering, pp.229-232, 2012.

M. Tootkaboni, A. Asadpoure, and J. K. Guest, Topology optimization of continuum structures under uncertainty ??? A Polynomial Chaos approach, Computer Methods in Applied Mechanics and Engineering, vol.201, issue.204, pp.201-204, 2012.
DOI : 10.1016/j.cma.2011.09.009

B. Tombuyses and J. Devooght, Solving Markovian systems of O.D.E. for availability and reliability calculations, Reliability Engineering & System Safety, vol.48, issue.1, pp.47-55, 1995.
DOI : 10.1016/0951-8320(94)00065-V

M. E. Hosea and L. F. Shampine, Analysis and implementation of TR-BDF2, Applied Numerical Mathematics, vol.20, issue.1-2, pp.21-37, 1996.
DOI : 10.1016/0168-9274(95)00115-8

A. P. Van-moorsely and K. Wolterz, Numerical Solution of Non-Homogeneous Markov Processes through Uniformization, Proceedings of the 12th European Simulation Multiconference on Simulation -Past, Present and Future, pp.710-717, 1998.

A. Saltelli, S. Tarantola, F. Campolongo, and M. Ratto, Sensitivity Analysis in Practice. A Guide to Assessing Scientific Models, Probability and Statistics series, 2004.

A. Saltelli, S. Tarantola, and K. Chan, A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output, Technometrics, vol.60, issue.1, pp.39-56, 1999.
DOI : 10.1007/BF01166355

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

D. Xiu and G. Karniadakis, The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.24, issue.2, pp.619-644, 2002.
DOI : 10.1137/S1064827501387826

B. Liang, S. P. Huang, and K. K. Phoon, An EXCEL add-in implementation for collocation-based stochastic response surface method, ISGSR2007 First International Symposium on Geotechnical Safety & Risk, 2007.

H. M. Panayirci and . I. Schuëller·g, On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis???An Overview, Archives of Computational Methods in Engineering, vol.187, issue.1, pp.43-55, 2011.
DOI : 10.1007/s11831-011-9058-5

K. Petras, Smolyak cubature of given polynomial degree with few nodes for increasing dimension, Numerische Mathematik, vol.93, issue.4, pp.729-753, 2002.
DOI : 10.1007/s002110200401

M. Baudin and J. Martinez, Polynômes de chaos sous Scilab via librairie NISP, emes Journees de Statistique, p.42, 2010.

F. Heiss and V. Winschel, Likelihood approximation by numerical integration on sparse grids, Journal of Econometrics, vol.144, issue.1, pp.62-80, 2008.
DOI : 10.1016/j.jeconom.2007.12.004

URL : https://hal.archives-ouvertes.fr/hal-00501810

C. M. Rocco, ) and Ph.D. degree from The Robert Gordon University He is a Full Professor at Universidad Central de Venezuela, currently at Operation Research post-graduate courses. His main areas of research interest are Statistics, Reliability, Evolutionary Multi-objective Optimization and Machine Learning techniques. He has published more than 170 refereed manuscripts related to these areas in technical journals, conference proceedings and industry reports, 1980.