On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process

Dheeraj Goyal, Nil Kamal Hazra and Maxim Finkelstein ()
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Dheeraj Goyal: Indian Institute of Technology Jodhpur
Nil Kamal Hazra: Indian Institute of Technology Jodhpur
Maxim Finkelstein: University of the Free State

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1627-1650

Abstract: Abstract One of the widely discussed in the literature and relevant in practice shock models is the delta-shock model that is described by the constant time of a system’s recovery after a shock. However, in practice, as time progresses and due to deterioration of a system, this recovery time is gradually increasing. This important phenomenon was not discussed in the literature so far. Therefore, in this paper, we are considering a time-dependent delta-shock model, i.e., the recovery time becomes an increasing function of time. Moreover, 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 particular cases. For the defined survival model, we derive the corresponding survival function and the mean lifetime and study the related optimal replacement policy along with some relevant stochastic properties.

Keywords: Reliability; Delta-shock model; Generalized Pólya process; Failure rate function; Replacement policy; 60E15; 60K10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s11009-021-09880-8

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