Reliability Equivalence Design And Optimization Of Random Uncertain Systems

Traditional reliability research mainly uses the method of random reliability analysis based on probability and statistical model.This method needs a large number of sample data to construct system lifetime distribution with precise parameters.However,due to uncertainties in the working environment or other uncertainties,there are no samples to ascertain the distribution parameter value of system lifetime.This paper combines probability theory and uncertainty theory to analyze system reliability.Random uncertain variables and uncertain variables are employed to model the lifetimes and the lifetime distribution parameters of the system components,respectively.Firstly,the reliability index of random uncertain unrepairable system is defined based on chance theory which is a generalization of both probability theory and uncertainty theory.Some reliability models of random uncertain unrepairable systems are established,including random uncertain series system,parallel system,series-parallel system and cold standby system.Then the expressions of system reliability and MTTF of each random uncertain system are given.Secondly,the reliability equivalence factors of a random uncertain series-parallel system are studied based on different system improvement designs.The expressions of reliability and MTTF of the random uncertain series-parallel system are derived when the lifetimes of system components are assumed to have random uncertain exponential distributions.Then reduction and duplication methods are applied to improve the reliability of the system.The reliability function and mean time to failure are used as characteristics to compare different system designs.The reliability equivalence factor of random uncertain unrepairable system is defined according to the distance between uncertain variables.In addition,two types of reliability equivalence factors are calculated.Finally,the optimal reliability equivalence factor of the random uncertain series-parallel system is studied based on system optimization design.The redundancy optimization model for maximizing reliability subject to three linear constraints on uncertain cost,weight and volume is established.An algorithm for solving the redundancy optimization model is given.Then all passible reliability equivalence factors can be obtained by equating the reliability function based on reduction method with maximum reliability function according to the redundancy optimization.A detection model is constructed to select optimal reliability equivalence factor.