1. Bai, J.M. and Xiao, H.M. (2008). A class of new cumulative shock models and its application in insurance risk. Journal-Lanzhou University Natural Sciences, 44, 132-136. 2. Eryilmaz, S. (2012). Life behavior of a system under discrete shock model. Discrete Dynamics in Nature and Society. [ DOI:10.1155/2012/238641] 3. Eryilmaz, S. (2013). On the lifetime behaviour of discrete time shock model. Journal of Computational and Applied Mathematics, 237, 384-388. [ DOI:10.1016/j.cam.2012.06.008] 4. Eryilmaz, S. (2015a). Assessment of a multi-state system under a shock model. Journal of Computational and Applied Mathematics, 269, 1-8. [ DOI:10.1016/j.amc.2015.06.129] 5. Eryilmaz, S. (2015b). Discrete time shock models involving runs. Statistics and Probability Letters, 107, 93-100. [ DOI:10.1016/j.spl.2015.08.007] 6. Eryilmaz, S. (2016). Discrete time shocks models in a Markovian environment, IEEE Translation Reliability, 65, 141-146. [ DOI:10.1109/TR.2015.2427800] 7. Eryilmaz, S. (2017). $delta$-shock model based on Polya process and its optimal replacement policy. European Journal of Operational Research, 263, 690-697. [ DOI:10.1016/j.ejor.2017.05.049] 8. Eryilmaz, S. and Bayramoglu, K. (2014). Life behaviour of $delta$-shock models for uniformly distributed interarrival times. Statistical Papers, 55, 841-852. [ DOI:10.1007/s00362-013-0530-1] 9. Eryilmaz, S. and Kan, C. (2021). Reliability assessment for discrete time shock models via phase-type distributions. Applied Stochastic Models in Business and Industry, 37, 513-524. [ DOI:10.1002/asmb.2580] 10. Eryilmaz, S. and Tekin, M. (2019). Reliability evaluation of a system under a mixed shock model. Journal of Computational and Applied Mathematics, 352, 255-261. [ DOI:10.1016/j.cam.2018.12.011] 11. Gut, A. (1990). Cumulative shock models. Advances in Applied Probability, 22, 504-507. [ DOI:10.2307/1427554] 12. Gut, A. and Husler, J. (1999). Extreme shock models. Extremes, 2, 293-305. 13. Li, Z.H., Chan, L.Y. and Yuan, Z.X. (1999). 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, 237-247. [ DOI:10.1142/S0218539399000231] 14. Li, Z.H. and Zhao, P. (2007). Reliability analysis on the $delta$-shock model of complex systems. IEEE Transactions on Reliability, 56, 340-348. [ DOI:10.1109/TR.2007.895306] 15. Lorvand, H.; Nematollahi, A.R. and Poursaeed, M.H. (2019). Life distribution properties of a new $delta$-shock model. Communications in Statistics-Theory and Methods, 49, 3010-3025. [ DOI:10.1080/03610926.2019.1584316] 16. Lorvand, H., Nematollahi, A.R. and Poursaeed, M.H. (2020). Assessment of a generalized discrete time mixed $delta$-shock model for the multi-state systems. Journal of Computational and Applied Mathematics, 366, 112415. [ DOI:10.1016/j.cam.2019.112415] 17. Makri, F.S., Philippou, A.N. and Psillakis, Z.M. (2007). Success run statistics defined on an urn model, Advances in Applied Probability, 39, 991-1019. [ DOI:10.1239/aap/1198177236] 18. Mallor, F. and Omey, E. (2001). Shocks, runs and random sums. Journal of Applied Probability, 38, 438-448. [ DOI:10.1239/jap/996986754] 19. Nair, N.U., Sankaran, P.G. and Balakrishnan, N. (2018). Reliability Modeling and Analysis in Discrete Time. Academic Press. [ DOI:10.1016/B978-0-12-801913-9.00001-4] 20. Parvardeh, A. and Balakrishnan, N. (2015). On mixed $delta$-shock models. Statistics and Probability Letters, 102, 51-60. [ DOI:10.1016/j.spl.2015.04.006] 21. Roozegar, R. and Entezari, M. (2022). A new mixed $delta$-shock model and associated reliability properties. Submitted. [ DOI:10.1080/15326349.2023.2166962] 22. Shanthikumar, J.G. and Sumita, U. (1983). General shock-models associated with correlated renewal sequences. Journal of Applied Probability, 20, 600-614. [ DOI:10.2307/3213896] 23. Tuncel, A. and Eryilmaz, S. (2018). System reliability under $delta$-shock model. Communications in Statistics-Theory and Methods, 47, 487-4880. [ DOI:10.1080/03610926.2018.1459708] 24. Wang, G.J. and Zhang, Y.L. (2001). $delta$-shock model and its optimal replacement policy. Journal Southeast University, 31, 121-124.
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