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

  • Dheeraj Goyal [2] ; Nil Kamal Hazra [2] ; Maxim Finkelstein [1]
    1. [1] University of the Free State

      University of the Free State

      Mangaung, Sudáfrica

    2. [2] Indian Institute of Technology Jodhpur, Karwar
  • Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 32, Nº. 3, 2023, págs. 1079-1105
  • Idioma: inglés
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • 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.


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