Statistical Inference For Type Ⅱ Censored Lifetime Data Of Coherent System

Several components can constitute a system in a certain way while each component in the system of life distribution parameters directly affects the reliability of the system.The research can be divided into two types by different sources of life data: component life data is known;component life is unknown.Most of the existing research is the first case,namely,using a method for different types of distribution in the life of existing data to estimate the distribution parameter.The second case is less.Especially due to the experimental conditions,component life can not be obtained while life data of the entire system can be obtained,namely using the system lifetime data to estimate component distribution parameters.This type of study is rare.Thus,the dissertation targets on the life of the system,introduces the concept of system minimum signature,combines the knowledge of order statistics and further studies coherent systems based on type II censored data location-scale distribution family parameter estimation problem.In this dissertation,the probability density function of order statistics,combined with system minimum signature,is to obtain the probability density function and the reliability function of the system.The author uses the maximum likelihood estimation(MLE)method,the best linear unbiased estimation(BLUE)to estimate the distribution parameters of the components subject to the locationscale distribution family,taking the most commonly used Weibull distribution in industry as an example.The idea of Tayor expansion is introduced.The above mentioned two methods are transformed into approximation of best linear unbiased estimation(ABLUE)and approximation of maximum likelihood estimate(AMLE),re-estimating component distribution parameters.Finally,a system parameters are estimated in the different censoring numbers by the above mentioned four methods,and explored by Monte Carlo simulation method in different systems(namely,structurally different systems,different number of system components),different ways at different censoring numbers parameters be estimated.Studies have shown that when the censoring number of different systems increases,the estimated value of each method are closer to the true value,and the main effect of the estimated results is the system minimum signature under same censoring number.However,there is no evidence that the number of system components and the system minimum signature have a significant positive / inverse relationship with the final estimation error or other contact.There is no absolute best option of the four methods.Specific analysis is needed in specific systems.Nevertheless,the research process and results show that the ABLUE method in the actual operation is the most convenient one which should be considered first.In general,the number of system components has no obvious influence on the estimation result while the system minimum signature has important influence on the parameter estimation.When the number of censored is greater,differences of the four methods are smaller and estimates are closer to the real value.