Reliability analysis of nonrepairable cold-standby system based on the Wiener process

This paper considers a two-unit nonrepairable cold-standby reliability model for an air cooling system in a nuclear power plant, where one unit is the operating unit and the other is a cold-standby spare. When the operating unit breaks, it is replaced by the cold-standby spare. We consider two different cases: where unit replacement time is either negligible (zero) or non-negligible (stochastic time). The degradation of the system is influenced by whether the unit works well or not, which is described with temperature by the Wiener process. When the unit is in the operating state, the temperature will rise slowly (a small drift parameter) over time. When the unit is broken, the temperature will rise sharply over time (a relatively big drift parameter), and when the temperature exceeds the threshold, the system will fail. We calculate the distribution of the two units and their related parameters, and use this to obtain the reliability function over time. A numerical example is then given, to confirm the validity of our proposed model.