Reliability Analysis Of A Repairable System With Warning Device And Different Maintenance Policies

With the rapid development of modern science and technology, the requirement of the higher performance and reliability of high-tech products is more and more im-portant. But the reliability theory is widely applied in aviation, aerospace, defense, finance, network, transportation, communications and other fields, the reliability study and its related problems are receiving more and more attention.Repairable system is an important kind of system discussed in reliability theory and also a main object in reliability mathematics. Using Stochastic process theory to establish system model, Using the method of functional analysis to study the well-posedness of the system solution, Using Laplace transform to discuss the reliability index of the system, and then discussing the optimal replacement and maintenance strategy, etc, are basic research methods and focus of the reliability theory. And reliability theory has the fruitful results.In reliability theory study, the dynamic solution of the system is difficult to be obtained, it is ordinary to substitute the steady-state solution (steady-state indices) for the instantaneous solution (instantaneous indices). But the substitute is based on two points. The time-dependent solution of the system is existed and unique. The time-dependent solution converges to the steady-state solution. And in practice, it will hold at least on the guarantee of a safety coefficient or a reliable interval. So the instantaneous solution and the stability are problems to be solved in reliability theory.We discuss a kind of repairable system with warning device, different maintenance policies and a repairman who can have delayed-multiple vacations as a research ob-ject. Firstly, by using stochastic process theory and probability analysis method, the repairable system model can be expressed by a group of integro-differential equations. Then by using Co semigroup theory and spectral theory, we discuss the well-posedness of the system solution. On the basis of this, some main reliability indices of the sys-tem are analyzed from the point of view of the system operator characteristic function. Then the performance of the system with warning device and without warning sys-tem(including only send true warning signal and may send false warning signal), with different maintenance policies system and only a single maintenance policy (including availability, failure frequency and total profit of the system) are compared. Finally, when ε, λ1, λ2 and λ3 are all related to the running time of the system, we discussed the existence and uniqueness of the classical solution of the system and the continuous dependence of the solution on the initial value.The main contents and innovations in this dissertation can be summarized as follows:In chapter 1, the development background and the research statu of repairable system, methods, significance and main contents of the research, in this dissertation are briefly introduced.In chapter 2, the system model of interest is established and the corresponding parameters and conditions are given. By using the probability analysis method, the system is firstly transformed into a group of integro-differential equations.In chapter 3, the preliminary knowledge related to this article are given.In chapter 4, the existence and uniqueness as well as the regularity of the system classical solution are given with the functional analysis method.In chapter 5, by analyzing semigroup theory and spectral theory, the unique exis-tence of the time-dependent solution and the asymptotic stability of the solution of the system are discussed.In chapter 6, Some main reliability indexes of the system are considered from the point of view of the system operator characteristic function. And by using the theoret- ical analysis method, we considered the system with different maintenance policies and single maintenance policy and the system with warning device and without warning device in terms of availability, failure frequency and the profit.In chapter 7, in a special case(i.e. ε, λ1, λ2 and λ3 are all related to the running time of the system), the existence and uniqueness and the continuous dependent condition of the classical solution of the system are discussed by using the semigroup theory.