A general class of shock models with dependent inter-arrival times

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

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 3, No 10, 1079-1105

Abstract: Abstract We introduce and study a general class of shock models with dependent inter-arrival times of shocks that occur according to the homogeneous Poisson generalized gamma process. A lifetime of a system affected by a shock process from this class is represented by the convolution of inter-arrival times of shocks. This class contains many popular shock models, namely the extreme shock model, the generalized extreme shock model, the run shock model, the generalized run shock model, specific mixed shock models, etc. For systems operating under shocks, we derive and discuss the main reliability characteristics (namely the survival function, the failure rate function, the mean residual lifetime function and the mean lifetime) and study relevant stochastic comparisons. Finally, we provide some numerical examples and illustrate our findings by the application that considers an optimal mission duration policy.

Keywords: Homogeneous Poisson generalized gamma process; Optimal mission duration; Shock models; Reliability; 60E15; 60K10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-023-00867-w

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