Cautious reliability analysis of multi-state and continuum-state systems based on the imprecise Dirichlet model

International Journal of Reliability, Quality and Safety Engineering

Volumn 13, Issue 5, 2006, Pages 433-453

  Utkin, Lev V ^a  

^a SAINT PETERSBURG STATE FOREST TECHNICAL UNIVERSITY   (Russian Federation)

Author keywords

Bayesian updating; Continuum state system; Dirichlet distribution; Multi state system; Random set theory; Robust model; Series and parallel systems

Indexed keywords

MATHEMATICAL MODELS; RELIABILITY THEORY; STATISTICAL METHODS; SYSTEMS ENGINEERING;

BAYESIAN UPDATING; CONTINUUM STATE SYSTEMS; DIRICHLET DISTRIBUTION; MULTI STATE SYSTEMS; PARALLEL SYSTEMS; RANDOM SET THEORY; ROBUST MODELS;

CONTINUUM MECHANICS;

EID: 33751062173     PISSN: 02185393     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218539306002367     Document Type: Article

References (26)

1. A. M. Abouammoh and M. A. Al-Kadi, Multistate coherent systems of order k, Microelectronics and Reliability 35 (1995) 1415-1421.
2. R. E. Barlow and A. S. Wu, Coherent systems with multistate components, Math. Ops. Res. 3 (1978) 275-281.
3. W. S. Griffith, Multistate reliability models, J. Appl. Prob. 17 (1980) 735-744.
4. J. Montero, J. Tejada and J. Yanez, General structure functions, Kybernetes 23 (1994) 10-19.
5. G. Levitin and A. Lisnianski, Multi-State System Reliability. Assessment, Optimization and Applications (World Scientific, Singapore, New Jersey, 2003).
6. P. Walley, Statistical Reasoning with Imprecise Probabilities (Chapman and Hall, London, 1991).
7. V. P. Kuznetsov, Interval Statistical Models (Radio and Communication, Moscow, 1991, in Russian).
8. K. Weichselberger, Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung, vol. I Intervallwahrscheinlichkeit als umfassendes Konzept (Physika, Heidelberg, 2001).
9. L. V. Utkin and S. V. Gurov, imprecise reliability of general structures, Knowledge and Information Systems 1 (1999) 459-480.
10. L. V. Utkin and I. O. Kozine, A reliability model of multi-state units under partial information, eds. H. Langseth and B. Lindqvist, in Proc. of the Third Int. Conf. on Mathematical Methods in Reliability (Methodology and Practice), pp. 643-646 (Trondheim, Norway, June 2002, NTNU).
11. I. O. Kozine and L. V. Utkin, Variety of judgements admitted in imprecise statistical reasoning, Risk, Decision and Policy 8 (2003) 111-120.
12. L. V. Utkin and S. V. Gurov, New reliability models based on imprecise probabilities, ed. C. Hsu, in Advanced Signal Processing Technology, Chap. 6 (World Scientific, 2001), pp. 110-139.
13. B. Lindqvist and H. Langseth, Uncertainty bounds for a monotone multistate system, Probability in the Engineering and Informational Sciences 12 (1998) 239-260.
14. A. P. Dempster, Upper and lower probabilities induced by a multi-valued mapping, Ann, Math. Stat. 38 (1967) 325-339.
15. G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, 1976).
16. R. G. Almond, Models for incomplete failure data. Statistical Science Research Report 9, Statistical Sciences, Inc., Seattle, May 1992.
17. P. Limbourg and D. Germann, Reliability assessment and optimization under uncertainty in the Dempster-Shafer framework, in Proc. of the 27th European Safety, Reliability and Data Association Seminar on Assembling Evidence of Reliability. The Reliability Case as a Decision Support Tool (Glasgow, UK, November 2004), pp. 77-89.
18. P. Walley, Inferences from multinomial data L earning about a bag of marbles, Journal of the Royal Statistical Society, Series B 58 (1996) 3-57.
19. M. DeGroot, Optimal Statistical Decisions. (McGraw-Hill, New York, 1970).
20. F. P. A. Coolen, An imprecise Dirichlet model for Bayesian analysis of failure data including right-censored observations, Reliability Engineering and System Safety 56 (1997) 61-68.
21. M. Smithson, T. Bartos and K. Takemura, Human judgment under sample space ignorance, eds. G. de Cooman, F. G. Cozman, S. Moral and P. Walley, in Proc. of the First International Symposium on Imprecise Probabilities and Their Applications (Zwijnaarde, Belgium, June 1999), pp. 324-332.
22. L. V. Utkin, Belief functions and the imprecise Dirichlet model, eds. I. Batyrshin, J. Kacprzyk and L. Sheremetov, in Proc. of the Int. Conf. on Fuzzy Sets and Soft Computing in Economics and Finance, Vol. 1 (St.Petersburg, Russia, June 2004, Mexican Petroleum Institute), pp. 178-185.
23. L. V. Utkin, Probabilities of judgments provided by unknown experts by using the imprecise Dirichlet model, Risk, Decision and Policy 9(4) (2004) 391-400.
24. J. Y. Halpern and R. Fagin, Two views of belief Belief as generalized probability and belief as evidence, Artificial Intelligence 54 (1992) 275-317.
25. P. J. Huber, Robust Statistics (Wiley, New York, 1981).
26. B. Natvig, S. Soermo, A. T. Holen and G. Hogasen, Multistate reliability theory -a case study, Adv. Appl. Prob. 18 (1986) 577-579.