On a New Point Process Approach to Reliability Improvement Modeling for Repairable Systems

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2024-11-24 DOI:10.1002/asmb.2906

Maxim Finkelstein, Ji Hwan Cha

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引用次数: 0

Abstract

In this paper, we are the first to consider the combination of the minimal repair with the defined better than minimal repair. With a given probability, each failure of a repairable system is minimally repaired and with complementary probability it is better than minimally repaired. The latter can be interpreted in terms of a reliability growth model when a defect of a system is eliminated on each failure. It turns out that the better than minimal repair can be even better than a perfect one if a perfect repair is understood as a replacement of the whole system or stochastically equivalent operation. We provide stochastic description of the failure/repair process by introducing and describing the corresponding bivariate point process via the concept of stochastic intensity. Distributions for the number of failures for the pooled and marginal processes are derived along with their expected values. The latter can describe the process of reliability growth in applications. Some meaningful special cases are discussed.

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可修系统可靠性改进建模的点过程新方法

在本文中，我们首次考虑了最小修复与定义的优于最小修复的结合。在给定的概率下，可修复系统的每次故障都得到最小修复，并且在互补概率下，它比最小修复要好。后者可以用可靠性增长模型来解释，当系统的缺陷在每次故障中被消除时。事实证明，如果完美的修复被理解为替换整个系统或随机等效操作，那么比最小修复更好的修复甚至可能比完美修复更好。我们通过随机强度的概念引入和描述相应的二元点过程，提供故障/修复过程的随机描述。汇集过程和边缘过程的失效数分布及其期望值都得到了推导。后者可以描述应用中可靠性增长的过程。讨论了一些有意义的特例。

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.