由反伽马混合泊松过程控制的冲击模型

IF 0.7 3区工程技术 Q4 ENGINEERING, INDUSTRIAL

Probability in the Engineering and Informational Sciences Pub Date : 2023-12-15 DOI:10.1017/s0269964823000232

Antonella Iuliano, Barbara Martinucci, Verdiana Mustaro

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引用次数: 0

摘要

我们研究了由反伽马混合泊松过程（IGMP）（即具有反伽马混合分布的混合泊松过程）控制的三类冲击模型。我们特别分析了（1）极端冲击模型、（2）δ冲击模型和（3）累积冲击模型。对于后者，我们假设了一个常数和一个指数分布的随机阈值，并考虑了单次冲击造成的破坏量分布的不同选择。对于所有处理过的情况，我们都得到了生存函数，以及失效时间的期望值和方差。我们还揭示了反伽马混合泊松过程的一些特性。

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Shock models governed by an inverse gamma mixed Poisson process

We study three classes of shock models governed by an inverse gamma mixed Poisson process (IGMP), namely a mixed Poisson process with an inverse gamma mixing distribution. In particular, we analyze (1) the extreme shock model, (2) the δ-shock model, and the (3) cumulative shock model. For the latter, we assume a constant and an exponentially distributed random threshold and consider different choices for the distribution of the amount of damage caused by a single shock. For all the treated cases, we obtain the survival function, together with the expected value and the variance of the failure time. Some properties of the inverse gamma mixed Poisson process are also disclosed.

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来源期刊

Probability in the Engineering and Informational Sciences 数学-工程：工业

CiteScore

2.20

自引率

18.20%

发文量

审稿时长

>12 weeks

期刊介绍： The primary focus of the journal is on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, mathematical finance and probabilistic networks and graphs. Papers on analytic properties and related disciplines are also considered, as well as more general papers on applied and computational probability, if appropriate. Readers include academics working in statistics, operations research, computer science, engineering, management science and physical sciences as well as industrial practitioners engaged in telecommunications, computer science, financial engineering, operations research and management science.