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Comparison of combined stochastic risk processes and its applications

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  • Cha, Ji Hwan

Abstract

In this article we compare combined stochastic risk processes and consider its applications to various fields of relevance. Initially, the problem is formulated in terms of optimal transportation under fatal risks which may cause the failure of the transportation. Various transportation policies are considered and the problem of determining optimal policy maximizing the probability of success of transportation is suggested. Then the suggested problem is reformulated in the context of reliability modelling under more general settings and the main results are derived. Applications of the results to many different areas are discussed.

Suggested Citation

  • Cha, Ji Hwan, 2011. "Comparison of combined stochastic risk processes and its applications," European Journal of Operational Research, Elsevier, vol. 215(2), pages 404-410, December.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:2:p:404-410
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    References listed on IDEAS

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    1. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    2. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, March.
    3. Cha, Ji Hwan & Finkelstein, Maxim, 2010. "Burn-in by environmental shocks for two ordered subpopulations," European Journal of Operational Research, Elsevier, vol. 206(1), pages 111-117, October.
    4. Sheu, Shey-Huei, 1998. "A generalized age and block replacement of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 108(2), pages 345-362, July.
    5. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    6. Chien, Yu-Hung & Sheu, Shey-Huei, 2006. "Extended optimal age-replacement policy with minimal repair of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 174(1), pages 169-181, October.
    7. A-Hameed, M. S. & Proschan, F., 1973. "Nonstationary shock models," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 383-404, October.
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    Cited by:

    1. Cha, Ji Hwan, 2019. "Poisson Lindley process and its main properties," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 74-81.
    2. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    3. Hazra, Nil Kamal & Finkelstein, Maxim & Cha, Ji Hwan, 2017. "On optimal grouping and stochastic comparisons for heterogeneous items," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 146-156.
    4. Omid Shojaee & Majid Asadi & Maxim Finkelstein, 2021. "On Some Properties of $$\alpha $$ α -Mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1213-1240, November.

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