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ORDERING CONSECUTIVE k-OUT-OF-n:F SYSTEMS

Published online by Cambridge University Press:  27 April 2012

Gaofeng Da ,
Ben Zheng  and
Taizhong Hu
Gaofeng Da
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026People's Republic of China E-mail: [email protected]; [email protected]; [email protected]
Ben Zheng
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026People's Republic of China E-mail: [email protected]; [email protected]; [email protected]
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026People's Republic of China E-mail: [email protected]; [email protected]; [email protected]
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Abstract

Stochastic comparisons of linear (circular) consecutive k-out-of-n:F systems with independent components are studied. A sufficient condition is given under which the lifetime of a circular consecutive k-out-of-n:F system with independent and nonidentically distributed components is stochastically decreasing in n for fixed k. Furthermore, the likelihood ratio orderings of the lifetimes of linear (circular) consecutive k-out-of-n:F systems with independent and identically distributed components are also established, and some counterexamples are given to show that these orderings are not true in general.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 2 , April 2012 , pp. 147 - 158
Copyright
Copyright © Cambridge University Press 2012

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References

REFERENCES

1.Aki, S. & Hirano, K. (1997). Lifetime distributions of consecutive k-out-of-n:F systems. Nonlinear Analysis, Theorey, Methods and Applications 30: 555–562.Google Scholar
2.Barlow, R.E. & Proschan, F. (1981). Statistical theorey of reliability and life testing: probability models. Silver Spring, MD: To Begin With.Google Scholar
3.Boland, P.J. & Samaniego, F.J. (2004). Stochastic ordering results for consecutive k-out-of-n systems. IEEE Transactions on Reliability 53: 7–10.CrossRefGoogle Scholar
4.Chao, M.T., Fu, J.C., & Koutras, M.V. (1995). Survey of reliability studies of consecutive k-out- of-n:F and related systems. IEEE Transactions on Reliability 44: 120–127.CrossRefGoogle Scholar
5.Chiang, D.T. & Niu, S.C. (1981). Reliability of consecutive k-out-of-n:F systems. IEEE Transactions on Reliability R30: 87–89.CrossRefGoogle Scholar
6.Eryilmaz, S. (2007). On the lifetime distribution of consecutive k-out-of-n:F system. IEEE Transactions on Reliability 56: 35–39.CrossRefGoogle Scholar
7.Eryilmaz, S. (2009). Reliability properties of consecutive k-out-of-n systems of arbitrily dependent components. Reliability Engineering and System Safety 94: 350–356.CrossRefGoogle Scholar
8.Eryilmaz, S. (2011). Circular consecutive k-out-of-n systems with exchangeable dependent components. Journal of Statistical Planning and Inference 141: 725–733.CrossRefGoogle Scholar
9.Eryilmaz, S. (2011). Review of recent advances in reliability of consecutive k-out-of-n and related systems. Journal of Risk and Reliability 224: 225–237.Google Scholar
10.Eryilmaz, S., Kan, C., & Akici, F. (2009). Consecutive k-within-m-out-of-n:F system with exchangeable components. Naval Research Logistics 56: 503–510.CrossRefGoogle Scholar
11.Fu, J.C. & Koutras, M. (1994). Distribution theory of runs: A Markov chain approach. Journal of American Statistical Association 89: 1050–1058.CrossRefGoogle Scholar
12.Kuo, W. & Zuo, M.J. (2003). Optimal Reliability Modeling, Principles and Applications. New York: Wiley.Google Scholar
13.Navarro, J. & Eryilmaz, S. (2007). Mean residual lifetimes of consecutive-k-out-of-n systems. Journal of Applied Probability 44: 82–98.CrossRefGoogle Scholar
14.Salehi, E.T., Asadi, M., & Eryilmaz, S. (2011). On the mean residual lifetime of consecutive k-out-of-n systems. Test 21: 93–115.CrossRefGoogle Scholar
15.Sfakianakis, M.E. & Papastavridis, S.G. (1993). Reliability of a general consecutive k-out-of-n:F system. IEEE Transactions Reliability 42: 491–496.CrossRefGoogle Scholar
16.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar