Component Reliability Estimation Based On System Under Progressive Type-? Interval Censored Data

For the components in the system,their lifetime can not be directly observed.However,the lifetime of the system is determined by the components.If the internal series parallel structure of the system is known,the lifetime of the components can be estimated by the lifetime of the system.In the past,most researches estimated lifetime of the component in the system based on complete data,and the failure time of each system should be recorded.In reality,complete data is difficult to collect and costly.In this paper,the progressive type-I interval censored data is introduced,in which only the number of failed systems is observed at the specific point in time,and some systems that are still working are removed.This can not only reduce the loss of the system and thus reduce the cost of testing.It can also alleviate the confusion that the experimenter has to stay at every step of the process,and at the same time greatly reduce the data that needs to be recorded.Based on the relationship between the system and the components,this paper discusses the lifetime of the components under progressive type-I interval censored data.In this paper,based on maximum likelihood estimation,moment estimation and least square estimation,the parameter of components with exponential life distribution in the known systems is estimated.Meanwhile,?-method is used twice to get weight which used in weighted least square estimation.And the calculation formula of confidence interval is given.For some intractable situdation,bootstrap is introduced to get the confidence interval.Then,the numerical simulation of the internal components in a 3-component system is given under different sample size and different censored proportions by Newton-Rhapson method in R.The results show that the maximum likelihood estimation is the best among these methods,and the second is the moment estimation.The results of the least squares method and the weighted least squares method are dissatisfied.For the same method,the larger sample size gets the better simulation effect.In the case of same estimation method and sample size,the result of censored proportion increasing with time is better thanof censored proportion decreasing with time.Then,in the case of specific sample size,censored proportion and system construction,nonparametric maximum likelihood method is used to estimate the reliability of components,which does not need to know the specific probability density function of the component's lifetime,just according to the inverse function.Kolmogorov-Smirnov test is used to test the rationality of nonparametric estimation.Then ?-method is used again to obtain asymptotic properties of component's reliability and confidence interval.Finally,the advantages and disadvantages of several methods are compared.