Journal of Applied Probability

Study of a stochastic failure model in a random environment

Ji Hwan Cha and Jie Mi

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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.

Article information

J. Appl. Probab. Volume 44, Number 1 (2007), 151-163.

First available in Project Euclid: 30 March 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E99: None of the above, but in this section
Secondary: 60K10: Applications (reliability, demand theory, etc.)

Environmental condition failure process Poisson shock process baseline failure rate function compound failure rate function stochastic ordering


Cha, Ji Hwan; Mi, Jie. Study of a stochastic failure model in a random environment. J. Appl. Probab. 44 (2007), no. 1, 151--163. doi:10.1239/jap/1175267169.

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