Comparisons of series and parallel systems with components sharing the same copula

Applied Stochastic Models in Business and Industry

Volumn 26, Issue 6, 2010, Pages 775-791

  Navarro, Jorge ^a   Spizzichino, Fabio ^b  

^a UNIVERSITY OF MURCIA   (Spain)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

coherent systems; mean functions; Schur concave copulas; series systems; stochastic comparisons

Indexed keywords

COHERENT SYSTEM; MEAN FUNCTIONS; SCHUR-CONCAVE COPULAS; SERIES SYSTEM; STOCHASTIC COMPARISONS;

STOCHASTIC SYSTEMS;

EID: 78650468550     PISSN: 15241904     EISSN: 15264025     Source Type: Journal    
DOI: 10.1002/asmb.819     Document Type: Article

References (31)

1. Navarro J, Balakrishnan N,. Study of some measures of dependence between order statistics and systems. Journal of Multivariate Analysis 2010; 101 (1): 52-67.
2. Barlow RE, Proschan F,. Statistical Theory of Reliability and Life Testing. Reliability Models. International Series in Decision Processes. Series in Quantitative Methods for Decision Making. Holt, Rinehart and Winston, Inc.: New York, Montreal, Que., London, 1975.
3. Kochar S, Mukerjee H, Samaniego FJ,. The 'signature' of a coherent system and its application to comparison among systems. Naval Research Logistics 1999; 46: 507-523.
4. Navarro J, Shaked M,. Hazard rate ordering of order statistics and systems. Journal of Applied Probability 2006; 43: 391-408.
5. Dugas MR, Samaniego FJ,. On optimal system designs in reliability-economics frameworks. Naval Research Logistics 2007; 54: 568-582.
6. Bairamov I, Arnold BC,. On the residual lifelengths of the remaining components in an n-k+ 1 out of n system. Statistics and Probability Letters 2008; 78: 945-952.
7. Bhattacharya D, Samaniego FJ,. On the optimal allocation of components within coherent systems. Statistics and Probability Letters 2008; 78: 938-943.
8. Li X, Zhang Z,. Some stochastic comparisons of conditional coherent systems. Applied Stochastic Models in Business and Industry 2008; 24: 541-549.
9. Navarro J,. Likelihood ratio ordering of order statistics, mixtures and systems. Journal of Statistical Planning and Inference 2008; 138: 1242-1257.
10. Navarro J, Balakrishnan N, Samaniego FJ,. Mixture representations of residual lifetimes of used systems. Journal of Applied Probability 2008; 45: 1097-1112.
11. Navarro J, Hernandez PJ,. Mean residual life functions of finite mixtures and systems. Metrika 2008; 67: 277-298.
12. Navarro J, Samaniego FJ, Balakrishnan N, Bhattacharya D,. On the application and extension of system signatures to problems in engineering reliability. Naval Research Logistics 2008; 55: 313-327.
13. Spizzichino F,. The role of signature and symmetrization for systems with non-exchangeable components. In Advances in Mathematical Modeling for Reliability, Bedford T, Quigley J, Walls L, Alkali B, Daneshkhah A, Hardman G, (eds). IOS Press: Amsterdam, 2008; 138-148.
14. Hu T, Wang Y,. Optimal allocation of active redundancies in r-out-of-n systems. Journal of Statistical Planning and Inference 2009; 139: 3733-3737.
15. Navarro J, Guillamon A, Ruiz MC,. Generalized mixtures in reliability modelling: applications to the construction of bathtub shaped hazard models and the study of systems. Applied Stochastic Models in Business and Industry 2009; 25: 323-337.
16. Navarro J, Shaked M,. Some properties of the minimum and the maximum of random variables with joint logconcave distributions. Metrika; DOI: 10.1007/s00184-009-0232-9. Published online first.
17. Di Crescenzo A,. A Parrondo paradox in reliability theory. The Mathematical Scientist 2007; 32: 17-22.
18. Nelsen RB,. An Introduction to Copulas. Springer: New York, 2006.
19. Marshall AW, Olkin I,. Inequalities: theory of majorization and its applications. Mathematics in Science and Engineering, vol. 143. Academic Press Inc.: New York, London, 1979.
20. Boland P, Proschan F,. The impact of reliability theory on some branches of mathematics and statistics. In Handbook of Statistics, vol. 7, Krishnaiah PR, Rao CR, (eds). Elsevier Science Pub.: Amsterdam, 1988; 157-174.
21. Spizzichino F,. Subjective probability models for lifetimes. Monographs on Statistics and Applied Probability, vol. 91. Chapman and Hall, CRC: Boca Raton, FL, 2001.
22. Durante F, Sempi C,. Copulae and Schur-concavity. International Mathematical Journal 2003; 3: 893-905.
23. Durante F, Papini PL,. A weakening of Schur-concavity for copulas. Fuzzy Sets and Systems 2007; 158: 1378-1383.
24. de Finetti B,. Sul concetto di media. Giornale dell'Istituto Italiano degli Attuari 1931; 2: 369-396.
25. Hardy GH, Littlewood JE, Polya G,. Inequalities. Cambridge University Press: Cambridge, 1934.
26. Joe H,. Multivariate models and dependence concepts. Monographs on Statistics and Applied Probability, vol. 73. Chapman and Hall: London, 1997.
27. Jaworski P,. On copulas and their diagonals. Information Sciences 2009; 179: 2863-2871.
28. Nelsen RB, Quesada-Molina JJ, Rodriguez-Lallena JA, Ubeda-Flores M,. On the construction of copulas and quasi-copulas with given diagonal section. Insurance: Mathematics and Economics 2008; 42: 473-483.
29. Shaked M, Shanthikumar JG,. Stochastic Orders. Springer: New York, 2007.
30. Navarro J, Ruiz JM, Sandoval CJ,. Properties of coherent systems with dependent components. Communications in Statistics-Theory Methods 2007; 36: 1-17.
31. Esary JD, Proschan F,. Relationship between system failure rate and component failure rates. Technometrics 1963; 5: 183-189.