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Study of a Stochastic Failure Model in a Random Environment

Part of: Special processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Ji Hwan Cha  and
Jie Mi
Ji Hwan Cha*
Affiliation:
Pukyong National University
Jie Mi*
Affiliation:
Florida International University
*
∗ Postal address: Division of Mathematical Sciences, Pukyong National University, Busan, 608-737, Korea. Email address: [email protected]
∗∗ Postal address: Department of Statistics, Florida International University, Miami, FL 33199, USA. Email address: [email protected]
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Abstract

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Most devices (systems) are operated under different environmental conditions. The failure process of a system not only depends on the intrinsic characteristics of the system itself but also on the external environmental conditions under which the system is being operated. In this paper we study a stochastic failure model in a random environment and investigate the effect of the environmental factors on the failure process of the system.

Keywords

Environmental conditionfailure processPoisson shock processbaseline failure rate functioncompound failure rate functionstochastic ordering

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 151 - 163
Copyright
Copyright © Applied Probability Trust 2007 

References

Abdel-Hameed, M. S. and Proschan, F. (1973). Nonstationary shock models. Stoch. Process. Appl. 1, 383–404.CrossRefGoogle Scholar
A-Hameed, M. S. and Proschan, F. (1975). Shock models with underlying birth process. J. Appl. Prob. 12, 18–28.Google Scholar
Arjas, E. (1981). The failure and hazard process in multivariate reliability systems. Math. Operat. Res. 6, 551–562.CrossRefGoogle Scholar
Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Çinlar, E. (1977). Shock and wear models and Markov additive processes. In The Theory and Applications of Reliability, Vol. 1, eds Shimi, I. N. and Tsokos, C. P., Academic Press, New York, pp. 193–214.Google Scholar
Çinlar, E. (1984). Markov and semi-Markov models of deterioration. In Reliability Theory and Models, eds A-Hameed, M. S., Çinlar, E. and Quinn, J., Academic Press, Orlando, FL, pp. 3–41.Google Scholar
Çinlar, E. and Özekici, S. (1987). Reliability of complex systems in random environments. Prob. Eng. Inf. Sci. 1, 97–115.Google Scholar
Çinlar, E., Shaked, M. and Shanthikumar, J. G. (1989). On lifetimes influenced by a common environment. Stoch. Process. Appl. 33, 347–359.Google Scholar
Esary, J. D. and Marshall, A. W. (1974). Families of components, and systems, exposed to a compound damage process. In Reliability and Biometry: Statistical Analysis of Lifelength (Proc. Conf., Florida State Univ., Tallahassee, FL, 1973), eds Proschan, F. and Serfling, R. J., SIAM, Philadelphia, PA, pp. 31–46.Google Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973). Shock models and wear processes. Ann. Prob. 1, 627–649.CrossRefGoogle Scholar
Feldman, R. M. (1976). Optimal replacement with semi-Markov shock models. J. Appl. Prob. 13, 108–117.Google Scholar
Feldman, R. M. (1977). Optimal replacement for systems governed by Markov additive shock processes. Ann. Prob. 5, 413–429.CrossRefGoogle Scholar
Gaver, D. P. (1963). Random hazard in reliability problems. Technometrics 5, 211–226.CrossRefGoogle Scholar
Kebir, Y. (1991). On hazard rate process. Naval Res. Logistics 38, 865–876.Google Scholar
Lemoine, A. J. and Wenocur, M. L. (1985). On failure modeling. Naval Res. Logistics 32, 497–508.Google Scholar
Lemoine, A. J. and Wenocur, M. L. (1986). A note on shot-noise and reliability modeling. Operat. Res. 34, 320–323.Google Scholar
Özekici, S. (1995). Optimal maintenance policies in random environments. Europ. J. Operat. Res. 82, 283–294.Google Scholar
Özekici, S. (1996). Complex systems in random environments. In Reliability and Maintenance of Complex Systems, ed. Özekici, S., Springer, Berlin, pp. 137–157.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1989). Some replacement policies in a random environment. Prob. Eng. Inf. Sci. 3, 117–134.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, New York.Google Scholar
Singpurwalla, N. D. (1995). Survival in dynamic environments. Statist. Sci. 10, 86–103.Google Scholar