Linear multi-state sliding-window systems

IEEE Transactions on Reliability

Volumn 52, Issue 2, 2003, Pages 263-269

  Levitin, Gregory ^a  

^a ISRAEL ELECTRIC CORPORATION   (Israel)

Author keywords

Consecutive k out of r from n:F system; Multi state element; Sliding window system; Universal moment generating function

Indexed keywords

ALGORITHMS; FAILURE (MECHANICAL); MATHEMATICAL MODELS; PERFORMANCE; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; Z TRANSFORMS;

LINEAR MULTI-STATE SLIDING-WINDOW SYSTEMS; MULTI-STATE ELEMENT; UNIVERSAL MOMENT GENERATING FUNCTION;

RELIABILITY;

EID: 0041672461     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2003.814136     Document Type: Article

References (27)

1. W. Griffith, "On consecutive k-out-of-n failure systems and their generalizations," in Reliability and Quality Control, A. P. Basu, Ed: Elsevier (North-Holland), 1986, pp. 157-165.
2. Y. Tong, "A rearrangement inequality for the longest run with an application in network reliability," J. Applied Probability, vol. 22, pp. 386-393, 1985.
3. B. Saperstain, "The generalized birthday problem," J. Amer. Statistical Assoc., vol. 67, pp. 425-428, 1972.
4. ____, "On the occurrence of n successes within N Bernoulli trails," Technometrics, vol. 15, pp. 809-818, 1973.
5. J. Naus, "Probabilities for a generalized birthday problem," J. Amer. Statistical Assoc., vol. 69, pp. 810-815, 1974.
6. J. Nelson, "Minimal-order models for false-alarm calculations on sliding windows," IEEE Trans. Aerospace Electronic Systems, vol. AES-14, pp. 351-363, 1978.
7. S. Papastavridis and M. Sfakianakis, "Optimal-arrangement and importance of the components in a consecutive-k-out-of-r-from-n : F system," IEEE Trans. Reliability, vol. 40, pp. 277-279, 1991.
8. M. Sfakianakis, S. Kounias, and A. Hillaris, "Reliability of consecutive-k-out-of-r-from-n : F systems," IEEE Trans. Reliability, vol. 41, pp. 442-447, 1992.
9. J. Cai, "Reliability of a large consecutive-k-out-of-r-from-n : F system with unequal component-reliability," IEEE Trans. Reliability, vol. 43, pp. 107-111, 1994.
10. Z. Psillakis, "A simulation algorithm for computing failure probability of a consecutive-k-out-of-r-from-n : F system," IEEE Trans. Reliability, vol. 44, pp. 523-531, 1995.
11. D. Chiang and S. Niu, "Reliability of consecutive-k-out-of-n : F systems," IEEE Trans. Reliability, vol. R-30, pp. 87-89, 1981.
12. R. Bollinger, "Direct computations for consecutive-k-out-of-n : F systems," IEEE Trans. Reliability, vol. R-31, pp. 444-446, 1982.
13. R. Bollinger and A. Salvia, "Consecutive-k-out-of-n : F networks," IEEE Trans. Reliability, vol. R-31, pp. 53-56, 1987.
14. J. Wu and R. Chen, "An algorithm for computing the reliability of weighted-k-out-of-n systems," IEEE Trans. Reliability, vol. 43, pp. 327-328, 1994.
15. G. Levitin and A. Lisnianski, "A new approach to solving problems of multi-state system reliability optimization," Quality and Reliability Eng'g. Int'l., vol. 47, pp. 93-104, 2001.
16. F. Hwang and Y. Yao, "Multistate consecutively-connected systems," IEEE Trans. Reliability, vol. 38, pp. 472-474, 1989.
17. J. Shanthikumar, "A recursive algorithm to evaluate the reliability of a consecutive-k-out-of-n : F system," IEEE Trans. Reliability, vol. R-31, pp. 442-443, 1982.
18. ____, "Reliability of systems with consecutive minimal cutsets," IEEE Trans. Reliability, vol. R-36, pp. 546-550, 1987.
19. A. Kossow and W. Preuss, "Reliability of linear consecutively-connected systems with multistate components," IEEE Trans. Reliability, vol. 44, pp. 518-522, 1995.
20. M. Zuo and M. Liang, "Reliability of multistate consecutively-connected systems," Reliability Eng'g. and System Safety, vol. 44, pp. 173-176, 1994.
21. G. Levitin, "Reliability evaluation for linear consecutively-connected systems with multistate elements and retransmission delays," Quality and Reliability Eng'g. Int'l., vol. 17, 2001.
22. I. Ushakov, "Universal generating function," Sov. J. Computing System Science, vol. 24, no. 5, pp. 118-129, 1986.
23. G. Levitin, "Evaluating correct classification probability for weighted voting classifiers with plurality voting," European J. Operational Research, vol. 141, pp. 596-607, 2002.
24. ____, "Reliability evaluation for acyclic consecutively-connected networks with multistate elements," Reliability Eng'g. and System Safety, vol. 73, pp. 137-143, 2001.
25. G. Levitin and A. Lisnianski, "Optimal separation of elements in vulnerable multi-state systems," Reliability Eng'g. and System Safety, vol. 73, pp. 55-66, 2001.
26. G. Levitin, "Redundancy optimization for multi-state system with fixed resource requirements and unreliable sources," IEEE Trans. Reliability, vol. 50, pp. 52-58, 2000.
27. ____, "Incorporating common-cause failures into nonrepairable multi-state series-parallel system analysis," IEEE Trans. Reliability, vol. 51, pp. 380-388, 2001.