The censored delta shock model with non-identical intershock times distribution and an optimal replacement policy

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2024-03-10 DOI:10.1002/asmb.2852

Stathis Chadjiconstantinidis

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引用次数: 0

Abstract

In this article, we consider the censored $δ - shock$ model in which the distribution of intershock times do not have the same distribution, but it is assumed that a change occurs in the distribution of the intershock times due to an environmental effect and hence this distribution changes after a random number of shocks. For this shock model, several reliability characteristics are evaluated by assuming that the random change point has a discrete phase-type distribution. Analytical results for evaluating the reliability function of the system for several continuous as well discrete distributions of the interarrival times, are also given. Also, the optimal replacement policy that is based on a control limit is proposed for a mixed censored $δ$ -shock model in which both the distributions of the magnitudes of shocks and the distributions of the interarrival times of shocks change after a random number of shocks. Finally, several numerical examples are given to illustrate our results.

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具有非同冲击间时间分布的删减三角冲击模型和最优替换策略

在本文中，我们考虑了有删减的 δ-shock$$ \delta -\mathrm{shock}$$ 模型，在该模型中，冲击间隔时间的分布不具有相同的分布，但假设由于环境影响，冲击间隔时间的分布发生了变化，因此该分布在经过随机次数的冲击后发生了变化。对于这种冲击模型，通过假设随机变化点具有离散相型分布，对若干可靠性特征进行了评估。此外，还给出了针对到达时间的几种连续和离散分布评估系统可靠性函数的分析结果。此外，还针对一个混合删减 δ$$ \delta $$ 冲击模型提出了基于控制极限的最优替换策略，在该模型中，冲击大小的分布和冲击到达时间的分布都会在随机冲击次数后发生变化。最后，我们给出了几个数值示例来说明我们的结果。

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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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.