From differential to difference importance measures for Markov reliability models

European Journal of Operational Research

Volumn 204, Issue 3, 2010, Pages 513-521

  Do Van, Phuc ^a   Barros, Anne ^a   Bérenguer, Christophe ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE TROYES   (France)

Author keywords

Differential importance measures; Markov process; Reliability; Sensitivity analysis

Indexed keywords

DIFFERENTIAL IMPORTANCE MEASURES; DIRECTIONAL DERIVATIVE; DYNAMIC SYSTEMS; EVALUATION APPROACH; IMPORTANCE MEASURE; INFORMED DECISION; NUMERICAL EXAMPLE; RELATIVE CONTRIBUTION; RELIABILITY MODEL; SINGLE SAMPLE; STEADY STATE; TOTAL VARIATION;

DYNAMICAL SYSTEMS; MARKOV PROCESSES; RELIABILITY ANALYSIS; SENSITIVITY ANALYSIS;

QUALITY ASSURANCE;

EID: 75149140500     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2009.11.025     Document Type: Article

References (25)

1. Borgonovo E., Apostolakis G., Tarantola S., and Saltelli A. Comparison of global sensitivity analysis techniques and importance measures in PSA. Reliability Engineering and System Safety 79 (2003) 175-185
2. Borgonovo E., and Apostolakis G.-E. A new importance measure for risk-informed decision making. Reliability Engineering and System Safety 72 2 (2001) 193-212
3. Borgonovo E. The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions. European Journal of Operational Research 204 (2010) 485-495
4. Breiman L. Probability (1968), Addison-Wesley, Reading, MA
5. Cao X.-R. The MacLaurin series for performance functions of Markov chains. Advances in Applied Probability 30 (1998) 676-692
6. Cao X.-R., and Chen H.-F. Perturbation realization, potentials, and sensitivity analysis of Markov processes. IEEE Transactions on Automatic Control 42 10 (1997) 1382-1393
7. Cao X.-R., and Wan Y.-W. Algorithms for sensitivity analysis of Markov systems through potential and perturbation realization. IEEE Transactions on Automatic Control 6 4 (1998) 482-494
8. Dai L. Rate of convergence for derivative estimation of discrete-time Markov chains via finite-difference approximation with common random numbers. SIAM Journal on Applied Mathematics 57 3 (1997) 731-751
9. Do Van P., Barros A., and Bérenguer C. Importance measure on finite time horizon and application to Markovian multi-state production systems. Journal of Risk and Reliability 222 (2008) 449-461
10. P. Do Van, A. Barros, C. Bérenguer, A new result on the differential importance measures of Markov systems, in: Proceedings of the Ninth International Probabilistic Safety Assessment and Management Conference (PSAM9), 18-23 May 2008, Hong Kong, China.
11. Do Van P., Barros A., and Bérenguer C. Reliability importance analysis of Markovian systems at steady state using perturbation analysis. Reliability Engineering and System Safety 93 11 (2008) 1605-1615
12. P. Do Van, Contribution to the development and to the study of reliability importance measures for Markovian systems, Ph.D. Thesis, Troyes University of Technology (UTT), France, October 2008.
13. Dwyer P.S., and Waugh F.V. On errors in matrix inversion. Journal of the American Statistical Association 48 262 (1953) 289-319
14. George Yin G., and Zhang Q. Continuous-Time Markov Chains and Applications. Application of Mathematics (1998), Springer
15. Jacobsen M. Statistical Analysis of Counting Process. Lecture Notes in Statistics vol. 12 (1982), Springer-Verlag, New York
16. Kuchler U., and Sorensen M. Exponential Families of Stochastic Processes. Springer Series in Statistics (1997), Spinger
17. Marseguerra M., and Zio E. Monte Carlo estimation of the differential importance measure: application to the protection system of a nuclear reactor. Reliability Engineering and System Safety 86 1 (2004) 11-24
18. Marseguerra M., Zio E., and Podofillini L. First-order differential sensitivity analysis of a nuclear safety system by Monte Carlo simulation. Reliability Engineering and System Safety 90 2 (2005) 162-168
19. Meyer Jr. C.D. The role of the group generalized inverse in the theory of finite Markov chains. SIAM Review 17 (1975) 443-464
20. Meyer Jr. C.D. The condition of a finite Markov chain and perturbation bounds for the limiting probabilities. SIAM Journal of Algebraic and Discrete Mathematics 1 (1980) 273-283
21. Meyer Jr. C.D. Sensitivity of the stationary distribution of Markov chain. SIAM Journal of Matrix Analysis and Application 15 3 (1994) 715-728
22. Ou Y., and Bechta-Dugan J. Approximate sensitivity analysis for acyclic Markov reliability models. IEEE Transactions on Reliability 52 2 (2003) 220-231
23. Ross S. Stochastic Processes. Wiley Series in Probability and Statistics (1996), John Wiley & Sons Inc.
24. Vinod G., Kushwaha H., Verma A., and Srividya A. Importance measures in ranking piping components for risk informed in-service inspection. Reliability Engineering and System Safety 80 2 (2003) 107-113
25. Zio E., and Podofillini L. Accounting for components interactions in the differential importance measure. Reliability Engineering and System Safety 91 (2006) 1163-1174