Stochastic ordering results for consecutive k-out-of-n: F systems

IEEE Transactions on Reliability

Volumn 53, Issue 1, 2004, Pages 7-10

  Boland, Philip J ^a   Samaniego, Francisco J ^b  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Linear and circular consecutive k out of n systems; Stochastic order; System reliability

Indexed keywords

LINEAR SYSTEMS; POLYNOMIALS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; THEOREM PROVING; VECTORS;

CIRCULAR SYSTEMS; CONSECUTIVE-K-OUT-OF-N: F SYSTEMS; STOCHASTIC ORDERING; SYSTEM RELIABILITY;

RELIABILITY;

EID: 1942468205     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2004.824830     Document Type: Article

References (18)

1. S. Aki and K. Hirano, "Lifetime distributions of consecutive-k-out-of-n: F systems," Nonlinear Anal.-Theor., vol. 30, no. 1, pp. 555-562, 1997.
2. R. E. Barlow and F. Proschan, Statistical Theory of Reliability and Life Testing: Probability Models Silver Spring, MD, USA, 1981.
3. P. J. Boland, F. Proschan, and Y. L. Tong, Linear Dependence in Consecutive k-out-of-n Systems, 1990, vol. 4, Prob. Eng. Inf. Sc., pp. 391-397.
4. P. J. Boland and F. Samaniego, "The signature of a coherent system and its applications in reliability," in Mathematical Reliability: An Expository Perspective, R. Soyer, T. Mazzuchi, and N. Singpurwalla, Eds: Kluwer, 2003, vol. 67, International Series in Operations Research and Management Science, pp. 1-29.
5. P. J. Boland, M. Shaked, and J. G. Shanthikumar, Stochastic Ordering of Order Statistics. San Diego, CA: Academic Press, 1998, vol. 16, Handbook of Statistics, ch. 5, pp. 89-103.
6. D. Chiang and S. C. Niu, "Reliability of consecutive k-out-of-n," IEEE Trans. Reliabil., vol. R-30, pp. 87-89, 1981.
7. C. J. Chang, L. R. Cui, and F. K. Hwang, "New comparisons in birnbaum importance for the consecutive-k-out-of-n systems," Probab. Eng. Inform. Sc., vol. 13, no. 2, pp. 187-192, 1999.
8. ____, Reliabilities of Consecutive k-out-of-n Systems. Dorrecht: Kluwer Academic Publishers, 2000.
9. M. T. Chao, J. C. Fu, and M. V. Koutras, "Survey of reliability studies of consecutive k-out-of-n: F and related systems," IEEE Trans. Reliability, vol. R-44, no. 1, pp. 120-127, 1995.
10. C. Derman, G. J. Lieberman, and S. Ross, "On the consecutive k-out-of-n: F system," IEEE Trans. Reliability, vol. R-31, pp. 57-63, 1982.
11. D. Z. Du, F. K. Hwang, and Y. Jung, "Optimal consecutive-k-out-of-(2k + 1): G cycle," J. Global Optim., vol. 19, no. 1, pp. 51-60, 2001.
12. D. Z. Du and F. K. Hwang, "A direct algorithm for computing reliabilities of consecutive k-out-of-n cycles," IEEE Trans. Reliability, vol. R-37, no. 2, pp. 70-72, 1988.
13. A. E. Gera, "A consecutive k-out-of-n: G system with dependent elements - A matrix formulation and solution," Reliab. Eng. Syst. Safe., vol. 68, no. 1, pp. 61-67, 2000.
14. M. Koutras and S. G. Papastavridis, "Consecutive k-out-of-n: F systems and their generalizations," in New Trends in System Reliability Evaluation, K. B. Misra, Ed. Amsterdam: Elsevier, 1993, pp. 228-248.
15. A. Satyanarayana and M. K. Chang, "Network reliability and the factoring theorem," Networks, vol. 13, pp. 107-120, 1983.
16. M. Shaked and J. G. Shanthikumar, Stochastic Orders and their Applications. San Diego, CA: Academic Press, 1994.
17. Y. L. Tong, "A rearrangement inequality for the longest run, with an application to network reliability," Journal of Applied Probability, vol. 22, pp. 386-393, 1985.
18. M. J. Zuo, "Reliability and component importance of a consecutive-k-out-n system," Microelectronics Reliab., vol. 33, no. 2, pp. 243-258, 1993.