Approximation method for reliability of one-unit repairable system with time redundancy

For some engineering repairable systems like the spaceflight Telemetry, Tracking and Control (TTC) system, mission can be executed within a given time interval and been regarded as successful so long as the system remains in operational state for a minimum length of time. Thus, such system has time redundancy in mission execution and higher mission reliability. This paper presents a discrete approximation method to numerically calculate the mission reliability of such kind of system with one repairable unit and binary states. The time window is divided into a number of time slices and then the mission reliability of the system is derived by solving two groups of recursive discrete time equations. All these equations are established by decomposing the corresponding random event into a number of disjoint events at discrete time points with reduced time lengths. A numerical example is provided for a one unit system. The results of the example are compared with those previously obtained by other solution methods. It was shown that the proposed methods are computationally efficient, and the approximated missionreliability converges to the analytical results when the width of the divided time slices decreases.