Analysis Of A Multi-state Warm Standby Repairable System With Delay In Repair

In the study of the reliability of the repairable system, most of the literature considers the system which is assumed that the components of fault can be repaired immediately, but the actual situation is not usually the case, products always need to wait for a long or short random time before the repair (commonly known as the repair delay time), such as the repairman is just in the fault site or needing to please the other repairman to repair. So, considering the repair delay repairable system will be necessary.In the theoretical study of the reliability of the system, a considerable part of the article discusses only by two state (normal state and failure state) system components. But in many applications, components often have more than one failure state. For example, relays and diodes have two failure states (open circuit failure and closed circuit failure). Therefore, the multi state components of repairable system reliability composition are an important subject.In this paper, the steady state reliability indexes of a class of warm-standby repairable system with delay repair are studied.In the first part of this article the reliability of repairable system quantitative index is briefly introduced, then the Markov process and some related theories to solving Markov-repairable system steady reliability are roughly introduced, and the theory of renewal process is also simply introduced.The second part is the main part of this paper:Firstly, under the condition that the working time^the repair delay time and the repair time are all exponential distributions, a two different units warm standby repairable system with delay repair is studied, and by using the Markov repairable system knowledge, the steady reliability index of the system is obtained.Secondly, the single parts with repair delay of repairable system with three states is studied, the system reliability, availability and steady-state failure frequency is obtained by using the theory of renewal process.Thirdly, under the condition that this system is Markov repairable system and each part of the system has two kinds of failure state, a two identity unit’s warm standby repairable system with delay repair is studied, and the steady reliability index of the system is obtained.Lastly, the two different units with three states warm standby repairable system with delay repair is studied, the approaches and concrete steps to obtain the steady reliability index of the system are been found.