The Estimation For Mean Life Of Complex Systems With Stand-by Components

Complex systems are widespread in industrial, agricultural, military, and medical and health fields. The mean life of the system which is described by the minimum path or minimal cut sets is an indicator that people are very concerned. The complex systems with stand-by components which described by the minimum path matrix are relatively common in practical problems as well, while the study to assess the reliability of complex system are relatively less. Therefore the study contains the estimation of the mean life for the complex system of stand-by components, derives an estimation form and develops the asymptotic distribution. Naturally it is an issue both has theoretical significance and application value.The main contents and conclusions are as follows:First, describe the complex systems containing stand-by component, introduce the relevant knowledge of complex systems described by the minimum path, and defines a number of special operations.Next, based on the complex systems described by minimum path, this paper gets the expression of the mean life for the complex system with a stand-by component under exponential distribution. Furthermore, we give the estimator for the mean life of it by using this expression. We also prove the asymptotic normality of this estimator.Finally, based on the complex systems described by the minimum path, when the subsystem contains two stand-by components under the exponential distribution, the mean life expectancy of the system will also be given. Furthermore, the estimator of the mean life for the system is obtained. The asymptotic normality of this estimator is proved.