Method Of Mission Reliability Analysis Of Large PMS Based On Markov Model

into a series of continuous, disjoint and independent periods, according to the system structure, success criteria, and difference in subsystem behavior. Mission reliability of PMS, is the probability that PMS executes all sessions and task in all periods within the scheduled time. Normally, transition probability matrix in Markov model of the large PMS is large and sparse. The larger the dimension of the matrix tends, the lower the efficiency of matrix storage and computation is. As large PMS is often configured as the critical application in areas such as aerospace and military equipment, the mission reliability analysis of large PMS tends to be significant.In this paper, a combination method of the Fault Tree and Markov method is applied to model the large PMS according to its task characteristic. The Fault Tree is used to express the logic structure between system components, while the Markov model to descripe dynamic change of system state. A numerical analysis method based on compressed storage strategy, which consists of two stages, pre-processing and numerical solution, is proposed. In pre-processing stage, elements of the matrix are restored in a certain storage strategy, which made a vast compression in space, enhancing the computational efficiency of Matrix-Vector Multiplication in model solution stage.It is necessary to convert the solution of state probability vector in Markov model of the large PMS to the initial value problem of Kolmogorov differential equations Comparison and analysis of errors in a numerical example by Euler, improved Euler, Runge Kutta and Adams shows that Runge Kutta method has good accuracy. Therefore, the Runge Kutta method based on compressed row storage (CRS), block compressed row storage (BCRS) and fixed-size block storage (FSB) is proposed.The aerospace tracking, telemetering and command system (TT&C system) can be regard as a large dynamic system with multiple phase mission. In this paper, we analyze the task requirement of communication business in TT&C, define the mission reliability model, describe the model in XML, subdivide the arc, get a static logical structure of reliability in sub-stage and establish the Markov model accordingly. Then, we calculate the mission reliability with the proposed algorithm, analyze the space compression rate and running time of the algorithm, find that the Runge Kutta based on CRS makes best among four algorithms, which inventually verify that the algorithm can give an efficient solution to the mission reliability of large PMS.