On stochastic ordering among extreme shock models
In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation 49 (1): 110–120] introduced two types of extreme shock models when the shocks arrive fr...
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| Vydané v: | Probability in the engineering and informational sciences Ročník 37; číslo 4; s. 961 - 972 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Cambridge
Cambridge University Press
01.10.2023
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| ISSN: | 0269-9648, 1469-8951 |
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| Abstract | In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications.
Communications in Statistics – Simulation and Computation
49
(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of
$m\geq 1$
possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of
$m$
sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2. |
|---|---|
| AbstractList | In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications.
Communications in Statistics – Simulation and Computation
49
(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of
$m\geq 1$
possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of
$m$
sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2. In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation 49(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of \(m\geq 1\) possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of \(m\) sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2. |
| Author | Khaledi, Baha-Eldin Manesh, Sirous Fathi Izadi, Muhyiddin |
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| Cites_doi | 10.2307/1427554 10.1142/S0218539399000231 10.1016/j.cie.2022.108426 10.1007/978-0-387-68276-1 10.1016/j.cie.2016.11.017 10.1239/jap/996986754 10.2307/3213896 10.1017/S0269964819000445 10.1016/j.ejor.2017.05.049 10.1016/j.spl.2015.04.006 10.1023/A:1009959004020 10.1109/TR.2007.895306 10.1007/978-0-387-34675-5 10.1080/00207720500032606 10.2307/3318501 10.1016/j.ress.2019.03.045 10.1016/j.cie.2018.03.005 10.1080/03610918.2018.1476699 10.2307/3213483 10.1016/j.cam.2018.12.011 |
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| References | S0269964822000328_ref21 S0269964822000328_ref10 S0269964822000328_ref20 S0269964822000328_ref12 S0269964822000328_ref23 Schmidt (S0269964822000328_ref18) 2014; 55 S0269964822000328_ref11 S0269964822000328_ref22 S0269964822000328_ref4 S0269964822000328_ref17 S0269964822000328_ref5 S0269964822000328_ref2 Nakagawa (S0269964822000328_ref16) 2007 S0269964822000328_ref19 S0269964822000328_ref3 S0269964822000328_ref14 S0269964822000328_ref24 S0269964822000328_ref15 Lorvand (S0269964822000328_ref13) 2022 Belzunce (S0269964822000328_ref1) 2016 S0269964822000328_ref8 S0269964822000328_ref9 S0269964822000328_ref6 S0269964822000328_ref7 |
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