On survival function of the generalized δ-shock model based on Polya process

Document Type : Original Scientific Paper

Author

Department of Statistics, Yazd University, Yazd, Iran

Abstract

The shock models have attracted a great deal of attention because of their important role in engineering systems. If the time between two successive shocks is less than the pre-defined threshold δ, the system fails, which is called the δ-shock model. In this article, we studied the generalized δ-shock model with two types of arrival shocks under a Polya process which has dependent interarrival times. The survival function and the mean lifetime of this system are obtained. Finally, some illustrative examples are presented.

Keywords


Cha, J.H. and Finkelstein, M. (2016). New shock models based on the generalized Polya process. European Journal of Operational Research, 251(1), 135–141.
Eryilmaz, S. (2012). Generalized $\delta$-shock model via runs. Statistics and Probability Letters, 82(2), 326–331.
Eryilmaz, S. (2017). $\delta$-shock model based on Polya process and its optimal replacement policy. European Journal of Operational Research, 263(2), 690–697.
Li, Z.H., Chan, L.Y. and Yuan, Z.X. (1999a). Failure time distribution under a $\delta$-shock model and its application to economic design of system. International Journal of Reliability, Quality and Safety Engineering, 6(3), 237–247.
Li, Z.H., Huang, B.S. and Wang, G.J. (1999b). Life distribution and its properties of shock models under random shocks. Journal of Lanzhou University, 35(4), 1–7.
Li, Z.H. and Kong, X.B. (2007). Life behavior of $\delta$-shock model. Statistics and Probability Letters, 77(6), 577–587.
Li, Z.H. and Zhao, P. (2007). Reliability analysis on the $\delta$-shock model of complex systems. IEEE Transactions on Reliability, 56(2), 340–348.
Lorvand, H., Nematollahi, A. and Poursaeed, M.H. (2019). Life distribution properties of a new $\delta$-shock model. Communications in Statistics: Theory and Methods. https://doi.org/10.1080/03610926.2019.1584316.
Tuncel, A. and Eryilmaz, S. (2018). System reliability under $\delta$-shock model. Communications in Statistics: Theory and Methods, 47(19), 4872–4880.
Wang, G.J. and Zhang, Y.L. (2007). A shock model with two-type failures and optimal replacement policy. International Journal of Systems Science, 36(4), 209–214.
Wang, G.J. and Peng, R. (2016). A generalized $\delta$-shock model with two types of shocks. International Journal of System Science: Operations and Logistics, 4(4), 372–383.