Reliability Analysis Of Discrete-time Systems With Uncertain Parameters

In practical engineering,professional technicians often periodically test,repair or re-place system units.Therefore,it is more practical reference value to establish a discrete time system reliability model that the lifetimes of system units are considered as discrete random variables.In traditional reliability analysis,the study of system reliability based on prob-ability theory has been made certain progress.However,in the case of scarce data or no samples,there are some shortcomings in using traditional reliability theory to evaluate the lifetime parameters of system units and analyze the reliability indexes of the system.In this paper,the reliability models of discrete time systems are studied based on both uncertainty theory and probability theory when the lifetimes of system units are assumed to be random uncertain variables.Firstly,the reliability models of the discrete time unrepairable systems with uncertain parameters are researched.Based on the proposed system reliability indexes with uncertain parameters,four system models of the series,parallel,series-parallel and parallel-series sys-tems are established respectively.The reliability functions and mean time to failures of these systems are obtained,and compared with the traditional reliability systems by numerical ex-amples.Secondly,the reliability models of discrete time redundant standby series-parallel sys-tems with uncertain parameters are studied.Based on uncertainty theory and probability the-ory,the redundant standby series-parallel system models of hot,cold and warm with uncer-tain parameters are constructed respectively.According to the random uncertain geometric distribution and discrete random uncertain Weibull distribution,the reliability functions and the mean time to failures of the redundant standby systems are calculated,and the rationality of system models are verified by numerical examples.Finally,the reliability models of discrete time redundant standby systems with uncertain parameters and imperfect switches are considered.Under the framework of uncertainty the-ory,probability theory and reliability theory,the random uncertain 0-1 switch and random uncertain geometric switch are proposed.The cold standby and warm standby series-parallel system models with uncertain parameters and imperfect switches are constructed respective-ly.Some numerical examples are given to compare the system reliability indexes under different switches and different standby conditions.