. Par-conséquent, 36) peut s'écrire : JIM(i, j) = ?A(1 i , 1 j ) + ?A(0 i , 0 j ) ? ?A(1 i , 0 j ) ? ?A

. De-façon-similaire, on a : ?A(0 µ i , 0 µ j ) = ?(µ i Q µ i + µ j

M. Abuelma-'atti and I. S. And-qambar, SPICE application in the study of the behaviour of multi-state systems described by Markov models, Microelectronics Reliability, vol.37, issue.4, pp.609-613, 1997.
DOI : 10.1016/S0026-2714(96)00077-7

A. , H. And-davis, and P. , Du grafcet aux réseaux de petri, Traité des nouvelles Technologies , éd. Hermès, 1998.

A. , G. And-moieni, and P. , The foundations of models of dependence in probabilistic safety assessment, Reliability Engineering, vol.18, issue.3, pp.177-195, 1987.

R. Barlow and F. And-proschan, Statistical Theory of Reliability and Life Testing. International Serie in Decision Processes, 1975.

B. , C. Dieulle, L. Grall, A. And-vasseur, and D. , Etudes de sensibilité, facteurs d'importance et défaillances de cause commune, Journal européen des systèmes automatisés, vol.40, issue.7, pp.763-785, 2006.

B. , M. And, and M. Sorensen, Statistical inference discretely observed markov jum processes, Royal Statistical Society, vol.67, issue.3, pp.395-410, 2005.

B. , J. Reibman, A. And-trivedi, and K. , Sensitivity analysis of reliability and performability measures for multiprocessor systems, Performance Evaluation Review, vol.16, issue.1, pp.177-186, 1988.

A. Bobbio, A. Premoli, and O. And-saracco, Multi-state homogeneous Markov models in reliability analysis, Microelectronics Reliability, vol.20, issue.6, pp.875-880, 1980.
DOI : 10.1016/0026-2714(80)90011-6

B. , M. Dutuit, Y. Rauzy, A. , A. et al., The altarica data-flow language in use : modeling of production availability of a multi-state system, Reliability Engineering and System Safety, vol.91, pp.747-755, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00182500

E. Borgonovo, Differential, criticality and Birnbaum importance measures: An application to basic event, groups and SSCs in event trees and binary decision diagrams, Reliability Engineering & System Safety, vol.92, issue.10, pp.1458-1467, 2007.
DOI : 10.1016/j.ress.2006.09.023

E. Borgonovo, G. Apostolakis, S. Tarantola, and A. And-saltelli, Comparison of global sensitivity analysis techniques and importance measures in PSA, Reliability Engineering & System Safety, vol.79, issue.2, pp.175-185, 2003.
DOI : 10.1016/S0951-8320(02)00228-4

E. Borgonovo and G. And-apostolakis, A new importance measure for risk-informed decision making, Reliability Engineering & System Safety, vol.72, issue.2, pp.193-212, 2001.
DOI : 10.1016/S0951-8320(00)00108-3

B. , I. N. Semendiaev, K. And, H. , and K. , Handbook of mathematics, 1997.

C. , X. And, C. , and H. , Pertubation realization, potentials, and sensitivity analysis of markov processes, IEEE Transactions on Automatic Control, vol.42, issue.10, pp.1382-1393, 1997.

C. , X. And-wan, and Y. , Algorithms for sensitivity analysis of markov systems through potential and perturbation realization, IEEE Transactions on Automatic Control, vol.6, issue.4, pp.482-494, 1998.

C. , X. Yuan, X. And-qiu, and L. , A single sample path-based performance sensitivity formula for Markov chains, IEEE Transactions on Automatic Control, vol.41, issue.12, pp.1814-1817, 1996.

C. , Y. Amari, S. And-kuo, and S. , Computing system failure frequencies and reliability importance measures using obdd, IEEE Transactions on Computers, vol.53, issue.1, pp.54-68, 2004.

C. , M. Parry, G. And-sherry, and R. , Use of importance measures in risk informed regulatory applications, Reliability Engineering and System Safety, vol.60, pp.213-226, 1998.

C. , G. And-meyer, and C. , Comparison of perturbation bounds for the stationary distribution of a markov chain, Linear Algebra and its Applications, vol.335, pp.137-150, 2001.

D. , L. And, and C. Ho, Structural infinitesimal perturbation analysis (SIPA) for derivative estimation of discrete-event dynamic systems, IEEE Transactions on Automatic Control, vol.40, issue.7, pp.1154-1166, 1995.

D. Van and P. , Facteurs d'importance fiabilistes et leurs extensions pour les systèmes dynamiques Rapport de dea toric -optimisation et sûreté des systèmes, 2004.

D. Van, P. Barros, A. And-berenguer, and C. , Etude de sensibilité par analyse de perturbation pour un système markovien : application à la fiabilité, 2ème journées doctorales, pp.9-11, 2007.

D. Van, P. Barros, A. And-berenguer, and C. T. , Importance measure on finite time horizon and application to markovian multi-state production systems, Risk, Reliability and Societal Safety -Proc.ESREL 2007, pp.25-27, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00705221

D. Van, P. Barros, A. And-berenguer, and C. , Importance measure on finite time horizon and application to markovian multi-state production systems, Journal of Risk and Reliability, special issue paper, vol.222, pp.449-461, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00705221

D. Van, P. Barros, A. And-berenguer, and C. , A new result on the differential importance measures of markov systems, Ninth International Probabilistic Safety

D. Van, P. Barros, A. And-berenguer, and C. , Reliability importance analysis of Markovian systems at steady state using perturbation analysis, Reliability Engineering & System Safety, vol.93, issue.11, pp.1605-1615, 2008.
DOI : 10.1016/j.ress.2008.02.020
URL : https://hal.archives-ouvertes.fr/hal-00705179

D. Van, P. Berenguer, C. And-dieulle, and L. , Comparaison et evaluation des méthodes de calcul des facteurs d'importance fiabilistes pour les systèmes dynamique, 6ème congrès international pluridisciplinaire qualité et sûreté de fonctionnement -Proc. of QUALITA 2005, pp.16-18, 2005.

D. Van, P. Khalouli, S. Barros, A. And-berenguer, and C. , Sensitivity & importance analysis of markov models using perturbation analysis : Applications in reliability, Safety and Reliability for Managing Risk -Proc. of ESREL 2006, pp.1769-1775, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00705234

D. , Y. And-rauzy, and A. , New algorithms to compute importance factors cpr,mif, cif, dif,rawand rrw, Safety and Reliability -Proc.ESREL'99, -10th European Conference on Safety and Reliability, A.A. Balkema, 1999.

D. , Y. And-rauzy, and A. , Efficient algorithms to assess component and gate importance in fault tree analysis, Reliability Engineering and System Safety, vol.72, pp.213-222, 2001.

D. , Y. Rauzy, A. Signoret, J. P. And-thomas, and P. , Modélisation d'un système dynamique simple et évaluation de sa fiabilité par réseaux de petri stochastiques, pp.648-659, 1996.

D. Des-arbres-d-'événements and S. , André cabarbaye -centre national d'etudes spatiales (cnes) et lamine ngom -institut national des sciences appliquées (insa toulouse)

E. , N. And-sagarb, and B. , Importance measures for nuclear waste repositories, Reliability Engineering and System Safety, vol.70, issue.3, pp.217-239, 2003.

E. , R. And-mercie, and S. , Comparison of numerical methods for the assessment of production availability of a hybrid system, Reliability Engineering and System Safety, vol.93, pp.168-177, 2007.

P. Frank, Introduction to system sensitivity, 1978.

M. Fu and J. And-hu, Smoothed perturbation analysis derivative estimation for Markov chains, Operations Research Letters, vol.15, issue.5, pp.241-251, 1994.
DOI : 10.1016/0167-6377(94)90084-1

G. , X. Cui, L. And-li, and J. , Analysis for joint importance of components in a coherent system, European Journal of Operational Research

G. Yin, G. And-zhang, and Q. , Continuous-Time Markov Chains and Applications, Application of Mathematics, 1998.

G. , P. Tayur, and S. , Sensitivity analysis for base-stock levels in multiechelon production-inventory systems, Management Science, vol.41, issue.2, 1995.

G. , L. And-mumtaz, and S. Z. , A homogeneous markov model for phased-mission reliability characteristics, Microelectronics and Reliability, vol.33, issue.8, pp.1107-1111, 1993.

H. , P. And-goyal, and A. , Sensitivity of continuous time markov chains using uniformization, Computer Performance and Reliability, 1987.

H. , B. And-hordijk, and A. , Taylor series expansions of stationary markov chains, Avances in Applied Probability, vol.35, pp.1046-1070, 2003.

H. , Y. And-cao, and X. , Perturbation Analysis of Discrete-Event Dynamic Systems, 1991.

H. , J. Koo, H. And-lie, and C. , Joint reliability importance of two edges in an undirected network, IEEE Transactions on Reliability, vol.42, issue.1, pp.17-23, 1995.

H. , J. H. And, and B. West, Differential Equations : A Dynamical Systems Approach, Texts in Applied Mathematics, vol.18, 1990.

I. , F. And-dutuit, and Y. , Evaluation de la performance d'un système de production et des contributions individuelles de ses unités constitutives, 6ème Conférence Francophone de Modélisation et Simulation -MOSIM'06, pp.3-5, 2006.

K. , Y. And-rausand, and M. , A new approach to production regularity assessment in the oil and chemical industries, Reliability Engineering and System Safety, vol.75, pp.379-388, 2002.

L. , H. Lie, C. And-hong, and J. , A computation method for evaluating importancemeasure of gate in a fault tree, IEEE Transactions on reliability, vol.46, issue.3, 1997.

L. , G. And-lisnianski, and A. , Importance and sensitivity analysis of multi-state systems using the universal generating function method, Reliability Engineering and System Safety, vol.65, pp.271-281, 1999.

L. , G. Podofillini, L. And-zio, and E. , Generalised importance measure for multi-state elements based on performance level restrictions, Reliability Engineering and System Safety, vol.82, pp.287-298, 2003.

L. , A. And-levitin, and G. , Multi-state system reliability, Wiley Series in Quality, Reliability & Engineering Statistics. World Scientific, 2003.

L. , Z. And-tu, and F. , Single sample path-based sensitivity analysis of markov processes using uniformization, IEEE Transactions on Automatic Control, vol.44, issue.4, pp.872-875, 1999.

M. , J. K. And-trivedi, and K. S. , System dependencies in markov dependability modelling, Fault-Tolerant Systems and Software,Proceedings of FTS-95, pp.38-47, 1995.

O. , Y. And-bechta-dugan, and J. , Approximate sensitivity analysis for acyclic markov reliability models, IEEE Transactions on Reliability, vol.52, issue.2, pp.220-231, 2003.

P. , M. Wynn, H. And-bates, and R. , Principal components analysis in sensitivity studies of dynamic systems, Probabilistic Engineering Mechanics, vol.4, 2006.

R. , A. And-trivedi, and K. , On the sensitivity of transient solutions of Markov models, ACM Sigmetrics, vol.5, pp.122-134, 1993.

R. , J. E. And-coit, and D. W. , Composite importance measures for multi-state systems with multi-state components, IEEE Transactions on Reliability, vol.54, issue.3, pp.517-529, 2005.

R. , M. And-hoyland, and H. , System Reliability Theory -Models, Statistical methods and Application, 2004.

R. , S. Stochastic, and . Processes, Wiley Series in Probability and Statistics, 1996.

S. , M. And-zemoudeh, and K. , A non-homogeneous markov model for phased-mission reliability analysis, Microelectronics and Reliability, vol.38, issue.5, 1989.

M. Van-der-borst and H. And-schoonakker, An overview of PSA importance measures, Reliability Engineering & System Safety, vol.72, issue.3, pp.241-245, 2001.
DOI : 10.1016/S0951-8320(01)00007-2

V. , G. Kushwaha, H. S. Verma, A. K. And-srividya, and A. , Importance measures in ranking piping components for risk informed in-service inspection, Reliability Engineering and System Safety, vol.80, issue.2, pp.107-113, 2003.

X. , L. And-amari, and S. , Effective component importance analysis for the maintenance of systems with common-cause failures, International Journal of Reliability, Quality and Safety Engineering, vol.14, issue.5, pp.459-478, 2007.

Z. , E. And-podofillini, and L. , Importance measures of multi-state components in multi-state systems, International Journal of Reliability, Quality and Safety Engineering, vol.10, issue.3, pp.289-310, 2003.

Z. , E. And-podofillini, and L. , Monte carlo simulation analysis of the effects of different system performance levels on the importance of multi-state components, Reliability Engineering and System Safety, vol.82, pp.63-73, 2003.

Z. , E. And-podofillini, and L. , Accounting for components interactions in the differential importance measure, Reliability Engineering and System Safety, vol.91, pp.1163-1174, 2006.