On Survival of Coherent Systems Subject to Random Shocks

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, 2024, vol. 26, issue 1, 1-29

Abstract: Abstract We consider coherent systems subject to random shocks that can damage a random number of components of a system. Based on the distribution of the number of failed components, we discuss three models, namely, (i) a shock can damage any number of components (including zero) with the same probability, (ii) each shock damages, at least, one component, and (iii) a shock can damage, at most, one component. Shocks arrival times are modeled using three important counting processes, namely, the Poisson generalized gamma process, the Poisson phase-type process and the renewal process with matrix Mittag-Leffler distributed inter-arrival times. For the defined shock models, we discuss relevant reliability properties of coherent systems. An optimal replacement policy for repairable systems is considered as an application of the proposed modeling.

Keywords: Coherent system; Shock models; Poisson generalized gamma process; Poisson phase-type process; Renewal process of the matrix Mittag-Leffler type; 60E15; 60K10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10077-y

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