On history-dependent mixed shock models. Issue 4 (October 2022)

• Record Type: Journal Article
• Authors: Goyal, Dheeraj; Finkelstein, Maxim; Hazra, Nil Kamal
• Is Part Of: Probability in the engineering and informational sciences. Volume 36:Issue 4(2022)
• Page Start: 1080
• Page End: 1097
• Publication Date: 2022-10
• Subjects: δ-shock model -- Extreme shock model -- Optimal mission duration -- Optimal replacement policy -- Reliability; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964821000255
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract : In this paper, we consider a history-dependent mixed shock model which is a combination of the history-dependent extreme shock model and the history-dependent $\delta$ -shock model. We assume that shocks occur according to the generalized Pólya process that contains the homogeneous Poisson process, the non-homogeneous Poisson process and the Pólya process as the particular cases. For the defined survival model, we derive the corresponding survival function, the mean lifetime and the failure rate. Further, we study the asymptotic and monotonicity properties of the failure rate. Finally, some applications of the proposed model have also been included with relevant numerical examples.