Numerical Solution And Reliability Of Stable Solution Of A Series-Parallel Repairable System With Three Unites

In the present paper, we study the numerical solution and reliability of a series-parallel repairable system with three unites. As we all known, reliability models have extensive applications in computer systems, telecommunication systems, and manufacturing systems, etc. With the improvement science and technology, the requirement of reliability of products is becoming higher and higher. Therefore, researching the reliability of system is very important.By using the supplementary variables method, probability analysis and ergodic theory, we obtain the integro-differential equations governing the behavior of the system. Since some of the system equations have two hazard functions involved, the numerical simulation methods are used to analyze the reliability of the system. Combining the boundary conditions and characteristic curve method, we transform the state equations into a set of integral equations. We use analogous to the Gauss-Seidel method for solving a system of linear equations, analogous to the SOR method for solving a system of linear equations and configuration method to study the numerical solutions of the integral equations. Then we obtain the numerical solutions of the steady-state reliability indices. At the same time, we can compare the difference of numerical solutions by different methods.In this paper, the non-Markov process transform into generalized Markov process by using appropriate variable. And we can get integro-differential equations governing the behavior of the system. In summary, we present the numerical solutions of the steady-state solution and reliability, and the methods may be useful for further research...