Lower Confidence Limits For Complex System Reliability Described By The Minimal Path

Complex systems are widely exist in the agricultural,industrial,medical equipment,military equipment,and other fields.The estimation of the degree of reliability is an important work,the estimation of the degree of reliability reflect the reliability of system.But we can't only rely on the evaluation of the reliability to estimate the reliability of the system,lower confidence limit for reliability is also important o estimate the reliability of the system.At present,there are a lot of methods to solve the lower confidence limit for system reliability.the asymptotically normal method is commonly used by researchers,the process of calculation is simple and easy to understand,but there are some deficiencies that we need to choose the estimate to express the variance of normal distribution,the estimate is gradual biased will bring errors.Especially when the sample size of the subsystem is small,the estimation of lower confidence limit of reliability is not accuracy.However,the precision has been improved by WCF method to solve the lower confidence limit,and the method is commonly used by many researchers.So in this paper,we give the lower confidence limit of reliability for complex system by WCF method.In daily life,there are important work elements in a working system,so people usually add a spare part to improve the reliability of system,this kind of system has been described as the complex system containing spare component.However,the exponential distribution is common.Therefore,in this paper,we study the complex system containing spare component and described by the minimal path.Under the condition of the subsystem life obeys exponential distribution,for the sample of type-? and type-?? censoring,we give the lower confidence limit of reliability for the system by WCF method.Besides exponential distribution,the logarithmic normal distribution is also common.Therefore,in this paper,we study the complex system described by the minimal path matrix,under the condition of the subsystem life obeys logarithmic normal distribution,we give the lower confidence limit of reliability for the system.Then we simulate reliability lower confidence limit for bridge system,for the convenience of using,a simplified analytical expression is be given.The results of this paper have great significance in theory research and wide applicability.The study is not only suitable for complex systems,but also be applied to many common simple systems,such as serial system,parallel system,series-parallel system and so on.