A note on a generalization of the δ-shock model

Document Type : Original Scientific Paper

Authors

Department of Statistics‎, ‎Razi University‎, ‎Kermanshah‎, ‎Iran

Abstract

According to the δ-shock model‎, ‎a shock-exposed system fails when an intershock time falls below a critical threshold δ. ‎Recently‎, ‎a generalization of the δ-shock model was introduced by Poursaeed (2019)‎ ‎under which the system fails when the intershock time falls below a threshold δ1‎>0 ‎and also the system probably fails with probability θ if the intershock time falls in the interval (δ1‎,δ2‎] for ‎δ1‎<δ2. ‎In this paper‎, ‎we look at this generalized model with new assumptions for intershock times‎. ‎More precisely‎, ‎we assume that the intershock times have a discrete distribution‎, ‎and the chance of their occurrence at a critical time point is significantly high‎. ‎We investigate some statistical properties of the system's lifetime‎, ‎and by providing an illustrative example‎, ‎we examine theoretical results numerically‎. ‎Numerical results show that when the chance of intershock times occurring at a critical time point increases‎, ‎the system reliability decreases significantly‎. ‎Finally‎, ‎the paper ends with a conclusion‎.
 

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References


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Journal of Statistical Modelling: Theory and Applications
Volume 5, Issue 2
July 2024
Pages 65-76

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History

  • Receive Date: 07 December 2024
  • Revise Date: 13 February 2025
  • Accept Date: 11 March 2025

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