Α new mixed δ-shock model with a change in shock distribution

• Stathis Chadjiconstantinidis ^[1] ; Altan Tuncel ^[2] ; Serkan Eryilmaz ^[3]
  1. [1] University of Piraeus

     University of Piraeus

     Grecia

     
  2. [2] Kırıkkale University

     Kırıkkale University

     Turquía

     
  3. [3] Atilim University

     Atilim University

     Turquía

     

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• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 31, Nº. 3, 2023, págs. 491-509
• Idioma: inglés
• DOI: 10.1007/s11750-022-00649-x
• Enlaces
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• Resumen

  • In this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.

• Referencias bibliográficas
  • Asmussen S, Bladt M (1997) Renewal theory and queueing algorithms for matrix-exponen-tial distributions. In: Alfa A, Chakravarthy SR (eds)...
  • Bladt M, Nielsen BF (2017) Matrix-exponential Distributions in Applied Probability. Springer, New York
  • Chadjiconstantinidis S, Eryilmaz S (2022) Reliability assessment for censored δ-shock Models. Methodol Comput Appl Probab. https:// doi. org/...
  • Eryilmaz S (2012) Generalized δ-shock model via runs. Stat Probab Lett 82:326–331
  • Eryilmaz S (2017) δ-shock model based on Polya process and its optimal replacement policy. Eur J Oper Res 263:690–697 Eryilmaz S, Kan C...
  • Goyal D, Hazra NK, Finkelstein M (2022a) On the general δ-shock model. TEST. https://doi.org/10.1007/s11749-022-00810-5
  • Goyal D, Hazra NK, Finkelstein M (2022b) On the time-dependent delta-shock model governed by the generalized Polya process. Methodol Comput...
  • Jiang Y (2020) A new δ-shock model for systems subject to multiple failure types and its optimal orderreplacement policy. Proce Instit Mechan...
  • Kus C, Tuncel A, Eryilmaz S (2022) Assessment of shock models for a particular class of intershock time distributions. Methodol Comput Appl...
  • Li ZH (1984) Some distributions related to Poisson processes and their application in solving the problem of traffic jam. J Lanzhou Univ Nat...
  • Li ZH, Kong XB (2007) Life behavior of δ-shock model. Statist Probab Lett 77:577–587
  • Li ZH, Zhao P (2007) Analysis on the δ-shock model of complex systems. IEEE Trans Reliab 56:340–348
  • Lorvand H, Nematollahi AR, Poursaeed MH (2019) Life distribution properties of a new delta-shock model. Commun Statist Theory Methods 49:3010–3025
  • Lorvard H, Nematollahi AR (2022) Generalized mixed delta-shock models with random interarrival times and magnitude of shocks. J Comput Appl...
  • Mallor F, Santos J (2003) Reliability of systems subject to shocks with a stochastic dependence for the damages. TEST 12:427–444
  • Parvardeh A, Balakrishnan N (2015) On mixed δ-shock models. Statist Probab Lett 102:51–60
  • Poursaeed MH (2021) Reliability analysis of an extended shock model. Proce Instit Mech Eng Part O J Risk Reliab 235:845–852
  • Tuncel A, Eryilmaz S (2018) System reliability under shock model. Commun Statist Theory Methods 47:4872–4880
  • Wang GJ, Zhang YL (2005) A shock model with two-type failures and optimal replacement policy. Int J Syst Sci 36:209–214
  • Willis HL, Scott WG (2000) Distributed power generation Planning and Evaluation. CRC Press, Taylor & Francis Group