Reliability Analysis Of Several Kinds Of Repairable Cold Standby Systems

Cold standby repairable system is one kind of important system in reliability research,and a lot of achievements have been made on the reliability of the cold standby system of two components.With the deepening of research,many scholars began to study the cold standby system of three components.Taking into consideration the actual needs,some scholars have introduced "priority" into the repairable standby system.However,in the study of three parts,the standby part is usually assumed to be the same part as the working part,which will not only cause costly waste.And it is impossible to reflect the actual meaning of "priority".Therefore,based on the existing results,this paper studies the reliability of three types of priority cold repairable spare parts system,and establishes the mathematical model to obtain the reliability index of each system.Firstly,under the condition that the system has a maintenance equipment and the transfer switch is reliable,the reliability of the repairable cold standby system composed of three different components with priority is discussed.The working part 1 and the working part 2 work in series at the initial time,and the part 3 is a cold stock part of the part 1.Assuming that component 2 has priority for maintenance than component 1,component 1 has priority use rights and priority maintenance rights over component 3,and the working time and maintenance time of the three components are obey the exponential distributions with different parameters.The mathematical model of the system is established and analyzed,and all possible states of the system are obtained.Based on the Markov model,Laplace transform is used to obtain the expression of the system reliability index.Then use Matlab software to give a numerical example and explain the stability of the system.Secondly,under the condition that the system has two maintenance devices a and b and the transfer switch is not reliable,the reliability of the repairable cold standby system composed of three different components with priority is discussed.The working part 1 and the working part 2 work in series at the initial time,part 3 is a cold standby part of two working parts.It is assumed that the parts 1 and 2 have priority over the cold stock part 3,the repair apparatus a repairs the work parts 1,2 and the standby part 3,the repair equipment b repairs the transfer switch,and the working time and maintenance time of each part and transfer switch obey parameters different exponential distributions.Establish and analyze the system model to obtain the state transition probability matrix of the system.Using the relevant theory of Markov process,we derive the steady state index and average index of the system.Then use Matlab to make a function image of the different switch life parameters affecting the system reliability.Finally,under the condition of one repair equipment and the transfer switch is reliable,the exponential distribution of the working time of each component obeys different parameters,and the reliability of the repairable cold standby system composed of three different components generally distributed is considered.The working member 1 is operated at the initial time,and the component 2 and the component 3 serve as the cold standby component of the working component 1.Assuming that component 1 has priority over component 2,component 2 has priority over component 3.The system model was established and analyzed.Using the Markov updating process theory and the Laplace-Stieltjes transform,the average time before the system's first failure and the availability of the system were obtained.