Abstract
In this paper we study multi-state systems consisting of two components when the number of system states and the number of states of each component are the same, i.e. the systems under consideration are homogeneous multi-state systems. In particular we evaluate multi-state series and cold standby systems assuming that the degradation in their components follow a Markov process. The behaviour of systems with respect to degradation rates is also investigated in terms of stochastic ordering.
Keywords
Failure rate Mean residual life Reliability Standby system Stochastic order 2000 AMS Classification: 62 N 05
References
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- Navarro, J. Tail hazard rate ordering properties of order statistics and coherent systems, Naval Research Logistics 54, 820–828, 2007.
- Navarro, J. and Hernandez, P. J. Mean residual life functions of finite mixtures, order sta- tistics and coherent systems, Metrika 67, 277–298, 2008.
- Navarro, J. Guillamon, A. and Ruiz, M. Generalized mixtures in reliability modelling: Ap- plications to the construction of bathtub shaped hazard models and the study of systems, Applied Stochastic Models in Business and Industry 25, 323–337, 2009.
- Shaked, M. and Shanthikumar, J. G. Stochastic orders (Springer, New York, 2007).
- Zuo, M. J. and Tian, Z. Performance evaluation for generalized multi-state k-out-of-n sys- tems, IEEE Transactions on Reliability 55, 319–327, 2006.
Abstract
References
- Brunelle, R. D. and Kapur, K. C. Review and classification of reliability measures for mul- tistate and continuum models, IIE Transactions 31, 1171–1180, 1999.
- Cha, J. H., Mi, J. and Yun, W. Y. Modelling a general standby system and evaluation of its performance, Applied Stochastic Models in Business and Industry 24, 159–169, 2008.
- Eryilmaz, S. and Iscioglu F. Reliability evaluation for a multi-state system under stress- strength setup, Communications in Statistics: Theory and Methods 40, 547–558, 2011.
- Kuo, W. and Zuo, M. J. Optimal Reliability Modeling, Principles and Applications (John Wiley & Sons, New Jersey, 2003).
- Li, W. and Zuo, M.J. Reliability evaluation of multi-state weighted k-out-of-n systems. Reliability Engineering & System Safety 93, 160–167, 2008.
- Li, X., Yan, R. and Zuo, M. J. Evaluating a warm standby system with components having proportional hazard rates, Operations Research Letters 37, 56–60, 2009.
- Lisnianski, A. and Levitin, G. Multi-state System Reliability: Assessment, Optimization and Applications(World Scientific Pub. Co., Inc., Singapore, 2003).
- Lisnianski, A. and Ding, Y. Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique,Relia- bility Engineering & System Safety 94, 1788–1795, 2009.
- Lisnianski, A. and Frenkel, I. Non-homogeneous Markov reward model for aging multi-state system under minimal repair, International Journal of Performability Engineering 5, 303– 312, 2009.
- Navarro, J. and Hernandez, P. J. Negative mixtures, order statistics and systems. In: Ad- vances in Mathematical and Statistical Modelling. Series: Statistics for Industry and Tech- nology Arnold, B.C.; Balakrishnan, N.; Sarabia, J.M.; Minguez, R. (Eds.) (Birkhauser, Boston, 2008), 89–100.
- Navarro, J. Tail hazard rate ordering properties of order statistics and coherent systems, Naval Research Logistics 54, 820–828, 2007.
- Navarro, J. and Hernandez, P. J. Mean residual life functions of finite mixtures, order sta- tistics and coherent systems, Metrika 67, 277–298, 2008.
- Navarro, J. Guillamon, A. and Ruiz, M. Generalized mixtures in reliability modelling: Ap- plications to the construction of bathtub shaped hazard models and the study of systems, Applied Stochastic Models in Business and Industry 25, 323–337, 2009.
- Shaked, M. and Shanthikumar, J. G. Stochastic orders (Springer, New York, 2007).
- Zuo, M. J. and Tian, Z. Performance evaluation for generalized multi-state k-out-of-n sys- tems, IEEE Transactions on Reliability 55, 319–327, 2006.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | January 1, 2011 |
| Published in Issue | Year 2011 Volume: 40 Issue: 1 |