基于马尔可夫到达过程的 δ 冲击模型的可靠性分析

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2024-04-02 DOI:10.1002/asmb.2858

Dheeraj Goyal, Ramjan Ali, Nil Kamal Hazra

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引用次数: 0

摘要

马尔可夫到达过程（MAP）是一种多变的计数过程，其到达时间之间具有相位型分布的依赖性和非同分布性。本文通过假设冲击的 MAP，研究了经典冲击模型和混合冲击模型。我们得出了系统可靠性和平均寿命的明确表达式。此外，我们还研究了基于 MAP 的最优替换策略。我们通过几个数值示例来说明所得出的结果。

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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Reliability analysis of δ-shock models based on the Markovian arrival process

The Markovian arrival process (MAP) is a versatile counting process with dependent and non-identically distributed inter-arrival times following the phase-type distribution. In this article, we study the classical $δ$ -shock model and a mixed $δ$ -shock model by assuming the MAP of shocks. We derive explicit expressions for the reliability and the mean lifetime of the system. Further, we study an optimal replacement policy based on the MAP. We illustrate the developed results through several numerical examples.

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来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.