A generalization of δ- shock model

Document Type : Original Paper

Author

Department of Statistics, Lorestan university, Khoramabad, Iran

Abstract

Suppose that a system is exposed to a sequence of shocks that occur randomly over time, and δ_1 and δ_2 are two critical levels such that 0 < δ_1

Keywords

Main Subjects


[1] Li, Z.H. (1984). Some distributions related to Poisson processes and their application in solving the problem of traffic jam. J. Lanzhou Univ. Nat. Sci., 20, 127–136.
[2] Sumita, U. and Shanthikumar, J.G. (1985). A class of correlated cumulative shock models. Ann. Appl. Probab., 17, 347–366.
[3] Aven, T. and Gaarder, S. (1987). Optimal replacement in a shock model: Discrete-time, J. Appl. Probab., 24, 281–287.
[4] Gut, A. (1990). Cumulative shock models. Ann. Appl. Probab., 22, 504–507.
[5] Mallor, F. and Omey, E. (2001). Shocks, runs and random sums. J. Appl. Probab., 38, 438–448.
[6] Wang, G.J. and Zhang, Y.L. (2001). -shock model and its optimal replacement policy. J. Southeast Univ., 31, 121–124.
[7] Li, Z.H. and Kong, X.B. (2007). Life behavior of -shock model. Statist. Probab. Lett., 77, 577–587.
[8] Li, Z.H. and Zhao, P. (2007). Reliability analysis on the -shock model of complex systems. IEEE Trans. Reliab., 56, 340–348.
[9] Finkelstein, M. and Cha, J. H. (2013). Stochastic Modeling for Reliability, Shocks, Burn-in and Heterogeneous Populations. London, U.K.: Springer-Verlag.
[10] Eryilmaz,S. and Bayromoglu, K. (2014). Life behavior of -shock models for uniformly distributed inter-arrival times, Stat. Papers, 55, 841-852.
[11] Parvardeh, A. and Balakrishnan, N. (2015). On mixed -shock models, Statist. Probab. Lett., 102, 51-60.