A new stochastic model for systems under general repairs

IEEE Transactions on Reliability

Volumn 56, Issue 1, 2007, Pages 40-49

  Guo, Huairui R ^a   Liao, Haitao ^b   Zhao, Wenbiao ^c   Mettas, Adamantios ^a  

^a RELIASOFT CORPORATION   (United States)

^b WICHITA STATE UNIVERSITY   (United States)

^c American Express ^*  (United States)

Author keywords

Closed form solution; Confidence bounds; General repair; Maximum likelihood estimation; Proportional failure intensity; Repairable system; Virtual age

Indexed keywords

CLOSED-FORM SOLUTION; CONFIDENCE BOUNDS; REPAIRABLE SYSTEM; VIRTUAL AGE;

DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; REPAIR; SET THEORY;

RELIABILITY THEORY;

EID: 34047143720     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2006.890895     Document Type: Article

References (22)

1. M. Brown and F. Proschan, "Imperfect repair," Journal of Applied Probability, vol. 20, pp. 851-859, 1983.
2. C. R. Cassady, I. M. Iyoob, K. Schneider, and E. A. Pohl, "A generic model of equipment availability under imperfect maintenance," IEEE Trans. on Reliability, vol. 54, no. 4, pp. 564-571, 2005.
3. D. R. Cox and P. A. W. Lewis, The Statistical Analysis of Series of Events. London, U.K.: Methuen, 1966.
4. D. R. Cox, "The statistical analysis of dependencies in point processes," in Stochastic Point Processes, P. A. W. Lewis, Ed. New York: John Wiley, 1972, pp. 55-66.
5. L. H. Crow, "Reliability analysis for complex, repairable systems," in Reliability and Biometry, F. Proschan and R. J. Serfling, Eds. Philadelphia, PA: SIAM, 1974, pp. 379-410.
6. L. R. Cui, W. Kuo, H. T. Loh, and M. Xie, "Optimal allocation of minimal & perfect repairs under resource constraints," IEEE Trans. on Reliability, vol. 53, no. 2, pp. 193-199, 2004.
7. L. Doyen and O. Gaudoin, "Classes of imperfect repair models based on reduction of failure intensity or virtual age," Reliability Engineering and System Safety, vol. 84, no. 1, pp. 45-56, 2004.
8. S. Gasmi, C. E. Love, and W. Kahle, "A general repair, proportional-hazards, framework to model complex repairable systems," IEEE Trans. on Reliability, vol. 52, no. 1, pp. 26-32, 2003.
9. R. Guo, H. Ascher, and C. E. Love, "Generalized models of repairable systems - A survey via stochastic processes formalism," ORION, vol. 16, no. 2, pp. 87-128, 2000.
10. M. Kaminskiy and V. Krivtsov, "A Monte Carlo approach to repairable system reliability analysis," in Probabilistic Safety Assessment and Management. New York: Springer, 1998, pp. 1063-1068.
11. M. Kijima and N. Sumita, "A useful generalization of renewal theory: Counting process governed by non-negative Markovian increments," Journal of Applied Probability, vol. 23, pp. 71-88, 1986.
12. M. Kijima, "Some results for repairable systems with general repair," Journal of Applied Probability, vol. 26, pp. 89-102, 1989.
13. J. F. Lawless and K. Thiagarajah, "A point-process model incorporating renewals and time trends, with application to repairable systems," Technometics, vol. 38, pp. 131-138, 1996.
14. W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data. New York: John Wiley & Sons, 1998.
15. A. Mettas and W. Zhao, "Modeling and analysis of complex repairable systems with general repair," in Proceedings of RAMS, Jan. 2005.
16. W. Nelson, Accelerated Testing: Statistical Methods, Test Plans, and Data Analysis. New York: John Wiley & Sons, 1990.
17. H. Pham, Software Reliability. Singapore: Springer-Verlag, 2000.
18. F. Proschan, "Theoretical explanation of observed decreasing failure rate," Technometrics, vol. 5, pp. 375-383, 1963.
19. G. Pulcini, "A bounded intensity process for the reliability of repairable equipment," Journal of Quality Technology, vol. 33, no. 4, pp. 480-492, 2001.
20. H. Wang and H. Pham, "Optimal age-dependent preventive maintenance policies with imperfect maintenance," International Journal of Reliability, Quality and Safety Engineering, vol. 3, pp. 119-135, 1996.
21. H. Wang and H. Pham, "Some maintenance models and availability with imperfect maintenance in production systems," Annals of Operations Research, vol. 91, pp. 305-318, 1999.
22. M. Yanez, F. Joglar, and M. Modarres, "Generalized renewal process for analysis of repairable systems with limited failure experience," Reliability Engineering and System Safety, vol. 77, pp. 167-180, 2002.