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Instantaneous Reliability Index of a Typical repairable system

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Journal of Donghua University(English Edition) 2015年第6期32卷 1038-1041页

作者：范若楠徐厚宝田佳艳 College of Mathematics and Statistics Beijing Institute of Technology

A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of *** paper first described the system as an abstract Cauchy problem by choosing suitable operators and state ***,with the TrotterKato theorem and strong continuous semi-group theorem,the method of solving the instantaneous reliability index of the repairable system was *** convergence of the method was also proved in theory in this *** show the effectiveness of this method,some numerical examples were given at the end of the paper.

关键词： repairable system instantaneous reliability index TrotterKato theorem

Reliability Analysis of a Cold Standby repairable system with Repairman Extra Work

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Journal of systems Engineering and Electronics 2015年第5期26卷 1015-1032页

作者： ZHANG Xin Department of Basic Courses Beijing Union University Academy of Mathematics and systems Science Chinese Academy of Sciences

This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.

关键词： C0-semigroup exponential stability repairable system resolvent positive operator.

A Two-Unit Cold Standby repairable system with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

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Journal of Electronic Science and Technology of China 2004年第4期2卷 68-71页

作者：魏瑛源唐应辉 School of Mathmatics Hexi University of China Gansu Zhangye 734000 China School of Applied Mathematics UESTC Chengdu 610054 China

This paper considers a two–unit same cold standby repairable system with a replaceable repair facility and delay repair .The failure time of unit is assumed to follow exponential distribution , and the repair time and delay time of failed unit are assumed to follow arbitrary distributions , whereas the failure and replacement time distributions of the repair facility are exponential and arbitrary . By using the Markov renewal process theory, some primary reliability quantities of the system are obtained.

关键词： repairable system delay repair availability failure number

Well-posedness and Stability of the repairable system with Three Units and Vacation

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Journal of systems Science and Information 2014年第1期2卷 54-76页

作者： Xiaoshuang HAN Mingyan TENG Ming FANG Science College Yanbian University College of Science & Technology Department of Mathematics Bohai University

The stability of the repairable system with three units and vacation was investigated by two different methods in this note. The repairable system is described by a set of ordinary differential equation coupled with partial differential equations with initial values and integral boundaries. To apply the theory of positive operator semigroups to discuss the repairable system, the system equations were transformed into an abstract Cauchy problem on some Banach lattice. The system equations have a unique non-negative dynamic solution and positive steady-state solution and dynamic solution strongly converges to steady-state solution were shown on the basis of the detailed spectral analysis of the system operator. Furthermore, the Cesaro mean ergodicity of the semigroup T(t) generated by the system operator was also shown through the irreducibility of the semigroup.

关键词： repairable system positive operator semigroups spectral analysis stability

Study of Optimal Frequency to the repairable system Due to Failure Finding Interval to Maximize Availability system

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Journal of Applied Mathematics and Physics 2023年第6期11卷 1795-1805页

作者： Emmanuel Hagenimana Charline Uwilingiyimana Umuraza Clarisse Department of Civil Engineering Institut d’Enseignement Supérieur de Ruhengeri Musanze Rwanda Department of Statistics Applied to Economy Institut d’Enseignement Supérieur de Ruhengeri Musanze Rwanda School of Economics Shandong University Qingdao China

This research article is based on a study of optimal frequency to the repairable system due to the failure finding interval to maximize as well as minimize the availability of some components devices. We studied together maintenance and corrective actions that carried out item of failure and periodic failure finding designed to check whether a system is still working. The model is proved as well as useful application in detecting the problem related to finding failure tasks of different scheme devices by maximization. The model formulated and the numerical application to the relevant mathematical model have been discussed to demonstrate the article quality. Therefore based on probability analytic development, the optimal maintenance policy is then obtained as solution of an optimization problem in which the maintenance cost rate is the objective function and the risk of corrective maintenance is the constraint function. Finally, the solution to the optimal device in the considered development model has been well adjusted due to derivation to the experimental observation rather than theory which will be taken into consideration in the next applied practical design research related and the system device provided that, the proactive device agreed with using the exponential distribution to the survive distribution function which can not be considered as valid.

关键词： Maximization Failure Interval repairable system Inspection Interval Availability system Optimal Inspection

Model for Failure Point Process of a repairable system and Application

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International Journal of Plant Engineering and Management 2018年第2期23卷 89-96页

作者： JIANG Renyan CHEN Hao Faculty of Automotive and Mechanical Engineering Changsha University of Science and Technology

A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process. This paper introduces the concept and model for the failure process of repairable system. The method of parameter estimation is developed, and failure observations are fitted into a power-law model by using the least square method. Two applications of the pressent model are discussed according to the practical failure data of the central cooling system of a nuclear power plant. One application is determining the optimal overhaul time, and the other is evaluating the quality of maintenance. This paper provides references for the overhaul decision making and maintenance quality evaluation in reality.

关键词： repairable system failure point process overhaul decision maintenance quality

The Linear Stability of a Solution of a Parallel Redundant repairable system

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Chinese Quarterly Journal of Mathematics 2009年第3期24卷 458-463页

作者：王鸿燕赵占锋亓正申 Department of Information and Engineering Xuchang Vocational Technical College

In this paper,the solution of a parallel redundant repairable system is *** using the method of functional ***,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant e... 详细信息

关键词： redundant repairable system strictly dominant eigenvalue linear stability

Exponential Asymptotic Stability of repairable system with Randomly Selected Repairman

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Exponential Asymptotic Stability of Repairable System with R...

A Multi-indentured repairable Inventory system with Limited and Different Diagnostic Repair Resources

2009中国控制与决策会议

作者： Xing QIAO~(1,2),Dan MA~1,Zhaoxing LI~1 1.Dept.of Math.,Daqing Normal University,Daqing 163712,China 2.Beijing Institute of Information and Control,Beijing 100037,China

＜正＞In this paper,the repairable system solution’s exponential asymptotic stability was *** we prove that the positive contraction strongly continuous semigroup which is generated by the operator corresponding to these equations describing a system with randomly selected repairman is a quasi-compact *** the result that 0 is an eigenvalue of the operator with algebraic index one and the strongly continuous semigroup is contraction,we deduce that the spectral bound of the operator is *** the above results we obtain easily the exponential asymptotic stability of the solution of the repairable system.

关键词： Exponential asymptotic stability Quasi-compact operator Positive contraction strongly continuous semigroup repairable system

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Journal of systems Science and Information 2006年第3期4卷 455-466页

作者： Fang Liu Jianyin Zhao Bo Guo system Engineering Institute National University of Defense Technology Changsha 410073 China

This paper describes the characteristics of a single-base repairable inventory system and multi-indenture structure with communality and redundancy. At the base, there are a working field that has a maximum of z equipment on line and its repair channels, which mainly consist of two centers： line replaceable units （LRUs） diagnostic center and shop replaceable units （SRUs） repair center. In these two centers, the resources are finite and different. We introduce routing probabilities to express the repair relationships between resources and failed replaced units. The diagnostic time follows exponential distribution and SRU repair time follows general distribution with known average. We analyze the general model of this system, and present an approximate solution that uses two-step negative binomial approximation to obtain the expected backorders of all LRUs. The first step is fitting negative binomial distributions to the distributions of the number for all SitUs at the repair center, and the second is fitting negative binomial distributions to the convolutions of the distributions of the number for all LRUs in diagnostic and assemblydelayed. Thus, we give the approximate value of operational awilability of equipment based on this method. Finally, the results under two policies of routing probabilities are compared by the optimal curves.

关键词： inventory multi-indenture operational availability repairable system routing probability