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On history-dependent mixed shock models

Published online by Cambridge University Press:  06 August 2021

Dheeraj Goyal ,
Maxim Finkelstein Open the ORCID record for Maxim Finkelstein [Opens in a new window]  and
Nil Kamal Hazra
Dheeraj Goyal
Affiliation:
Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, Rajasthan, India.
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics and Actuarial Science, University of the Free State, 339, Bloemfontein, South Africa. Department of Management Science, University of Strathclyde, Glasgow, UK. E-mail: [email protected]
Nil Kamal Hazra
Affiliation:
Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, Rajasthan, India. School of AI & DS, Indian Institute of Technology Jodhpur, Karwar, Rajasthan, India
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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.

Keywords

δ-shock modelExtreme shock modelOptimal mission durationOptimal replacement policyReliability
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 4 , October 2022 , pp. 1080 - 1097
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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