Reliability Analysis Of Two Kinds Of Repairable Systems

The structure which several or many components are combined with in a certain order to achieve a specific function is called a system.Due to factors such as nature,environment,maintenance,and human operation,the performance degradation or failure of the components can cause the performance of the entire system to decline.In order to improve the security and reliability of the system,fault-tolerance,redundancy,or automatic recovery mechanisms are often designed to prevent the system from losing its full functionality due to the failure of certain components.Hybrid system and cold standby system are two types of systems that are often used in engineering technology.Extensive applications,reasonable testing and maintenance,for improving the system's safety and reliability,reducing operating costs,Improving economic efficiency,have important theoretical and practical significance.This article takes the hybrid and the cold standby system as the research objects,is divided into continue and discrete two conditions,and analyzes and studies the reliability of the system under the assumption that the components are mutually independent.The main research contents and research results are as follows:(1)Take the most basic hybrid repairable system which two components areconnected in parallel and then in series with another component as an example,under the assumption that the working time and maintenance time of the component are subject to the exponential distribution,the transfer rules among the ten states that may occur in the system are analyzed,the reliability differential equation model of the repairable system of the hybrid system is established,by solving differential equations,the calculation formulas for reliability parameters such as instantaneous availability.steady-state fault frequency,steady state availability,average downtime,average start-up time,average period and so on all are derived,which verify,analyze and promote the relevant conclusions.(2)Take the most basic cold standby system which is consisted of a transfer switch and two different components as an example,Assuming that there is only one repairman,taking multiple vacations,the vacation time and the repair time of components are subject to different parameters of the general continuous distribution,the working life of the components are subject to different parameters of the exponents distribution,etc.The nine possible states of the system are analyzed.By using the supplemental variables method,a partial differential equation model with some initial and boundary conditions,which reflects the reliability of the cold standby system is established.Through the Laplace transformation,the system probability at any moment in each state is deduced,some steady-state reliability index also is obtained.At last,the correctness of the conclusion in the special circumstances such as the same two parts is verified.(3)Take a cold standby system which is consisted of a transfer switch andtwo different components as an example,under the assumption that the switch is completely reliable,the repairman taking multiple vacation,and the working life of the components is subject to different geometric distribution,the repair time and the vacation time are subject to general discrete distribution and so on,a discrete reliability model about the cold standby system is established.By using Z-transformation and other methods,some main reliability calculation formulas such as steady state availability,fault frequency,repair probability and so on are deduced in the discrete time.