Analyzing the multi-state system under a run shock model

IF 0.7 3区工程技术 Q4 ENGINEERING, INDUSTRIAL Probability in the Engineering and Informational Sciences Pub Date : 2024-02-16 DOI:10.1017/s0269964824000019

Murat Ozkut, Cihangir Kan, Ceki Franko

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Abstract

A system experiences random shocks over time, with two critical levels, d1 and d2, where

$d_{1} \lt d_{2}$

. k consecutive shocks with magnitudes between d1 and d2 partially damaging the system, causing it to transition to a lower, partially working state. Shocks with magnitudes above d2 have a catastrophic effect, resulting in complete failure. This theoretical framework gives rise to a multi-state system characterized by an indeterminate quantity of states. When the time between successive shocks follows a phase-type distribution, a detailed analysis of the system’s dynamic reliability properties such as the lifetime of the system, the time it spends in perfect functioning, as well as the total time it spends in partially working states are discussed.

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分析运行冲击模型下的多态系统

一个系统在一段时间内经历随机冲击，有两个临界水平，即 d1 和 d2，其中 $d_{1}\连续 k 次冲击，冲击强度介于 d1 和 d2 之间，会对系统造成部分破坏，使其过渡到较低的、部分工作的状态。震级高于 d2 的冲击会产生灾难性影响，导致系统完全失效。这一理论框架产生了一个多状态系统，其特点是状态数量不确定。当连续冲击之间的时间遵循阶段型分布时，就可以对系统的动态可靠性特性进行详细分析，如系统的寿命、系统完全正常运行的时间以及系统处于部分工作状态的总时间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.