Standby Redundancy Optimization Of Uncertain Parallel-Series System

Reliability optimization design is an important issue that needs to be solved during the system design phase.In the traditional reliability modeling,the element lifetime is assumed to be random variables or fuzzy variables.The objective function is designed as some index function related to probability measure or credibility measure.In this paper,we will intro-duce uncertainty theory,regard the element lifetime as an uncertain variable,and further study the system reliability modeling and optimization.Firstly,the optimization problem of a class of uncertain parallel-series systems with el-ements redundant in cold standby mode is studied.With the objective of maximizing system reliability,maximizing the system lifetime optimistic value and minimizing the expected cost of the system,the Cold Standby Uncertain Measure Programming Model(CUMPM),the Cold Standby Uncertain Optimistic Value Programming Model(CUOVPM)and the Cold Standby Uncertain Cost Programming Model(CUCPM)are constructed respectively.Un-der the framework of uncertainty theory,the equivalent models of three models are given.According to the degree of preference of decision makers,a corresponding priority model is constructed and the model is solved to verify the rationality of the model.Secondly,the optimization problem of a class of uncertain parallel-series systems with elements redundant in warm standby mode is studied.Under the framework of uncertain-ty theory,using measure criterion,optimistic value criterion and expected value criterion to compare the system reliability,system lifetime and system cost,the Warm Standby Un-certain Measure Programming Model(WUMPM),the Warm Standby Uncertain Optimistic Value Programming Model(WUOVPM)and the Warm Standby Uncertain Cost Program-ming Model(WUCPM)are constructed respectively.In response to the complexity of the model,an uncertain simulation algorithm is proposed,and the model is solved to verify the rationality of the model and the effectiveness of the algorithm.Finally,the optimization problem of a class of uncertain parallel-series systems with elements redundant in mixed standby mode is studied.Under the framework of uncertainty theory,the objective functions related to the measure criterion,the optimistic value criterion and the expected value criterion are created,and the Mixed Standby Uncertain Measure Pro-gramming Model(MUMPM),the Mixed Standby Uncertain Optimistic Value ProgrammingModel(MUOVOM)and the Mixed Standby Uncertain Cost Programming Model(MUCPM)are constructed respectively.According to the complexity of the model,a genetic algorithm based on uncertain simulation is proposed.In the process of solving the model,the algorith-m is further improved,the BP neural network is used to fit the target function,and then the genetic algorithm is used to verify the rationality of the model and the effectiveness of the algorithm.