Reliability modeling and evaluation of uncertain random cold standby k -out-of- m + n : G systems

Based on the uncertainty of the system working environment, this paper models and evaluates reliability for uncertain random cold standby k -out-of- m + n : G systems with uncertain parameters. Assume that the system is composed of m + n subsystems. The lifetime distributions of components in m subsystems obey probability distributions with uncertain parameters, and the lifetime distributions of components in n subsystems obey uncertainty distributions with uncertain parameters. The parameters of all the lifetime distributions are uncertain variables and obey the uncertainty distributions. Under the assumption that the switch is completely reliable, three types of reliability models for cold standby systems with uncertain parameters, including the random cold standby k -out-of- m : G system model, the uncertain cold standby k -out-of- n : G system model, and the uncertain random cold standby k -out-of- m + n : G system model are developed. The reliability functions and mean time to failure of these system models are evaluated by probability theory and uncertainty theory. Numerical examples are presented to illustrate the modeling and evaluation methods of the proposed models. The system reliability model with uncertain parameters is also compared with that with constant parameters in the examples provided. The comparison results show the usability and superiority of the reliability models developed in this paper.