On a Markov chain approach for the study of reliability structures

Journal of Applied Probability

Volumn 33, Issue 2, 1996, Pages 357-367

  Koutras, M V ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

Consecutive systems; Markov chain; Markov imbedding; Reliability generating function; Transition probability matrix

Indexed keywords

EID: 0030523225     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200099770     Document Type: Article

References (28)

1. AKI, S. AND HIRANO, K. (1989) Estimation of parameters in discrete distributions of order k. Ann. Inst. Statist. Math. 41, 47-61.
2. BARLOW, R. E. AND HEIDTMANN, K. D. (1984) Computing k-out-of-n system reliability. IEEE Trans. Reliab. R-33, 322-323.
3. BARLOW, R. E. AND PROSCHAN, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Reinhart and Winston, New York.
4. CHAO, M. T. AND FU, J. C. (1989) A limit theorem of certain repairable systems. Ann. Inst. Statist. Math. 41, 809-818.
5. CHAO, M. T. AND FU, J. C. (1991) The reliability of large series systems under Markov structure. Adv. Appl. Prob. 23, 894-908.
6. CHAO, M. T., FU, J. C. AND KOUTRAS, M. V. (1995) Survey of reliability studies of consecutive-k-out-of-n: F and related systems. IEEE Trans. Reliab. R-44, 120-127.
7. CHARALAMBIDES, CH. A. (1986) On discrete distributions of order k. Ann. Inst. Statist. Math. 38, 557-568.
8. FU, J. C. (1986) Reliability of consecutive-k-out-of-n: F systems with (k - 1)-step Markov dependence. IEEE Trans. Reliab. R-35, 602-606.
9. FU, J. C. (1992) Poisson convergence in reliability of a large linearly connected system as related to coin tossing. Statist. Sinica. 3, 261-275.
10. FU, J. C. AND KOUTRAS, M. V. (1994) Distribution theory of runs: a Markov chain approach. J. Amer. Statist. Assoc. 89, 1050-1058.
11. FU, J. C. AND LOU, W. Y. (1991) On reliabilities of certain large linearly connected engineering systems. Statist. Prob. Lett. 12, 291-296.
12. GODBOLE, A. P. (1990) Degenerate and Poisson convergence criteria for success runs. Statist. Prob. Lett. 10, 247-255.
13. GODBOLE, A. P. (1991) Poisson approximations for runs and patterns of rare events. Adv. Appl. Prob. 23, 851-865.
14. GODBOLE, A. P. (1993) Approximate reliabilities of m-consecutive-k-out-of-n: Failure systems. Statist. Sinica 3, 321-327.
15. GOULDEN, I. P. (1987) Generating functions and reliabilities for consecutive-k-out-of-n: F systems. Util. Math. 32, 141-147.
16. GREENBERG, I. (1970) The first occurrence of n successes in N trials. Technometrics 12, 627-634.
17. GRIFFITH, W. S. (1986) On consecutive-k-out-of-n: failure systems and their generalizations. Reliability and Quality Control, pp. 157-165. ed. A. P. Basu. Elsevier, Amsterdam.
18. IOSIFESCU, M. (1980) Finite Markov Processes and their Applications. Wiley, New York.
19. KONTOLEON, J. M. (1980) Reliability determination of a r-successive-out-of-n: F system. IEEE Trans. Reliab. R-29, 437.
20. KOUNIAS, S. AND SFAKIANAKIS, M. (1991) The reliability of a linear system and its connection with the generalized birthday problem. Statist. Applic. 3, 531-543.
21. PAPASTAVRIDIS, S. G. (1990) m-consecutive-k-out-of-n: F system. IEEE Trans. Reliab. R-39, 386-388.
22. PAPASTAVRIDIS, S. G. AND KOUTRAS, M. V. (1993) Consecutive-k-out-of-n systems. New Trends in System Reliability Evaluation. pp. 228-248. ed. K. B. Misra. Elsevier, Amsterdam.
23. PHILIPPOU, A. N. AND MAKRI, F. S. (1986) Success, runs and longest runs. Statist. Prob. Lett. 1, 171-175.
24. SAPERSTEIN, B. (1973) On the occurrences of n successes within N Bernoulli trials. Technometrics 15, 809-818.
25. SAPERSTEIN, B. (1975) Note on a clustering problem. J. Appl. Prob. 12, 629-632.
26. SENETA, E. (1981) Non-Negative Matrices and Markov Chains. 2nd edn. Springer, Berlin.
27. WU, J. S. AND CHEN, R. J. (1994a) An algorithm for computing the reliability of a weighted-k-out-of-n system. IEEE Trans. Reliab. R-43, 327-328.
28. WU, J. S. AND CHEN, R. J. (1994b) Reliability of consecutive-weighted-k-out-of-n: F systems. In Runs and Patterns in Probability: Selected Papers. pp. 205-211. ed. A. Godbole and S. Papastavridis. Kluwer, Amsterdam.