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Assessment of Shock Models for a Particular Class of Intershock Time Distributions

Author

Listed:
  • Coskun Kus

    (Selcuk University)

  • Altan Tuncel

    (Kirikkale University)

  • Serkan Eryilmaz

    (Atilim University)

Abstract

In this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems’ lifetimes are obtained in a matrix form. Survival functions of the systems are approximated based on the Laplace-Stieltjes transforms. The results are applied for the reliability evaluation of a certain repairable system consisting of two components.

Suggested Citation

  • Coskun Kus & Altan Tuncel & Serkan Eryilmaz, 2022. "Assessment of Shock Models for a Particular Class of Intershock Time Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 213-231, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09847-9
    DOI: 10.1007/s11009-021-09847-9
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    References listed on IDEAS

    as
    1. Markos V. Koutras & Serkan Eryilmaz, 2017. "Compound Geometric Distribution of Order k," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 377-393, June.
    2. Yi Jiang, 2020. "A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 138-150, February.
    3. Parvardeh, A. & Balakrishnan, N., 2015. "On mixed δ-shock models," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 51-60.
    4. Serkan Eryilmaz & Konul Bayramoglu, 2014. "Life behavior of $$\delta $$ δ -shock models for uniformly distributed interarrival times," Statistical Papers, Springer, vol. 55(3), pages 841-852, August.
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    Cited by:

    1. Xiaoyue Wang & Ru Ning & Xian Zhao, 2023. "Generalized mixed shock model for multi-component systems in the shock environment with a change point," Journal of Risk and Reliability, , vol. 237(4), pages 619-635, August.
    2. Lyu, Hao & Qu, Hongchen & Yang, Zaiyou & Ma, Li & Lu, Bing & Pecht, Michael, 2023. "Reliability analysis of dependent competing failure processes with time-varying δ shock model," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    3. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2023. "Reliability of a mixed δ-shock model with a random change point in shock magnitude distribution and an optimal replacement policy," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    4. Jewgeni H. Dshalalow & Hend Aljahani, 2023. "Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information," Mathematics, MDPI, vol. 11(16), pages 1-27, August.

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