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

Author

Listed:
  • Dheeraj Goyal

    (Indian Institute of Technology Jodhpur)

  • Nil Kamal Hazra

    (Indian Institute of Technology Jodhpur
    Indian Institute of Technology Jodhpur)

  • Maxim Finkelstein

    (University of the Free State
    University of Strathclyde)

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.

Suggested Citation

  • Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2023. "A general class of shock models with dependent inter-arrival times," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 1079-1105, September.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:3:d:10.1007_s11749-023-00867-w
    DOI: 10.1007/s11749-023-00867-w
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