On the effect of redundancy for systems with dependent components

IIE Transactions (Institute of Industrial Engineers)

Volumn 35, Issue 12, 2003, Pages 1103-1110

  Kotz, Samuel ^a   Lai, Chin Diew ^b   Xie, Min ^c  

^a George Washington University   (United States)

^b MASSEY UNIVERSITY   (New Zealand)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; FAILURE (MECHANICAL); REDUNDANCY; RELIABILITY;

BIVARIATE DISTRIBUTIONS;

COMPONENTS;

EID: 0242708898     PISSN: 0740817X     EISSN: 15458830     Source Type: Journal    
DOI: 10.1080/714044440     Document Type: Article

References (29)

1. Abramowitz, M. and Stegun, I.A. (1964) Handbook of Mathematical Functions, Dover, New York, NY
2. Barlow, R.E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing: Probability Models, To Begin With, Silver Spring, MD.
3. Boland, P.J., El-Neweihi, E. and Proschan, F. (1988) Active redundancy allocation in coherent systems. Probability in the Engineering and Informational Sciences, 2, 343-353.
4. Boland, P.J., El-Neweihi, E. and Proschan, F. (1991) Redundancy importance and allocation of spares in coherent systems. Journal of Statistical Planning and Inference, 29, 55-66.
5. Coit, D.W and Smith, A.E. (1996) Reliability optimization of seriesparallel systems using a genetic algorithm. IEEE Transactions on Reliability, 45, 254-258.
6. Downton, F. (1970) Bivariate exponential distributions in reliability theory. Journal of the Royal Statistical Society-Series B, 32, 408-417.
7. Durling, F.C. (1975) The bivariate Burr distribution, in Statistical Distributions in Scientific Work, vol. 1 (G.P. Patil et al., eds.), Reidel, Dordrecht, Holland, pp. 329-335.
8. Esary, J.D., Proschan, F. and Walkup, D.W (1967) Association of random variables, with applications. Annuals of Mathematical Statistics, 38, 1466-1474.
9. Farlie, D.J.G. (1960) The performance of some correlation coefficient for a general bivariate distribution. Biometrika, 47, 307-323.
10. Gradshteyn, I.S. and Ryzhik, I.M. (1965) Tables of Integrals, Series and Products, 4th edn., Academic Press, New York, NY.
11. Gumbel, E.J. (1961) Bivariate exponential distributions. Journal of the American Statistical Association, 55, 698-707.
12. Huang, J.S. and Kotz, S. (1999) Modifications of the Farlie-Gumbel- Morgenstern distributions: a tough hill to climb. Metrika, 40, 135-143.
13. Hutchinson, T.P. and Lai, C.D. (1990) Continuous Bivariate Distributions, Emphasising Applications, Rumsby Scientific Publishing, Adelaide, Australia.
14. Kotz, S., Balakrishnan, N. and Johnson, N.L. (2000) Continuous Multivariate Distributions, Wiley, New York, NY.
15. Kuo, W and Prasad, V.R. (2000) An annotated overview of system- reliability optimization. IEEE Transactions on Reliability, 49, 176-187.
16. Lehmann, E.L. (1966) Some concepts of dependence. Annals ofMathe- maticalStatistics, 37, 1137-1153.
17. Levitin, G., Lisnianski, A., Ben-Haim, H. and Elmakis, D. (1998) Redundancy optimization for series-parallel multi-state systems. IEEE Transactions on Reliability, 47, 165-172.
18. Lindley, D.V. and Singpurwalla, N.D. (1986) Multivariate distribution for the life lengths of components of a system sharing a common environment. Journal of Applied Probability, 23, 418-431.
19. Ma, C. (1996) Multivariate survival functions characterized by the constant product of mean remaining lives and hazard rates. Metrika, 44, 71-83.
20. Marshall, A.W. and Olkin, I. (1967) A multivariate exponential distribution. Journal of the American Statistical Association, 62, 30-44.
21. Mi, J. (1998) Bolstering components for maximizing system lifetime. Naval Research Logistics, 45(5), 497-509.
22. Morgenstern, D. (1956) Einfache beispiele zweidimensionaler verteilungen. Mitteilungsblatt fur Mathematische Statistik, 8, 234-235.
23. Nelsen, R.B. (1992) On measures of association as measures of positive dependence. Statistics and Probability Letters, 14, 269-274.
24. Ng, K.YK. and Sancho, N.G.F. (2001) A hybrid “dynamic programming/depth-first search” algorithm, with an application to redundancy allocation. IIE Transactions, 33, 1047-1058.
25. Roy, D. (1989a) A characterization of Gumball’s bivariate exponential and Lindley and Singpurwalla’s bivariate Lomax distributions. Journal of Applied Probability, 27, 886-891.
26. Roy, D. (1989b) A correction to “A characterization of Gumball’s bivari- ate exponential and Lindley and Singpurwalla’s bivariate Lomax distributions.” Journal of Applied Probability, 28, 736.
27. Sankaran, P.G. and Nair, N.U. (1993) A bivariate Pareto model and its application to reliability. Naval Research Logistics, 40, 1013-1020.
28. Tchen, A.H. (1980) Inequalities for distributions with given marginals. Annals of Probability, 8, 814-827.
29. Xie, M. and Lai, C.D. (1996) On the increase of the expected lifetime by parallel redundancy. Asia-Pacific Journal of Operational Research, 13, 171-179.