Parameter Estimation Of Lifetime Data In Weibull Distribution

To people who are engineers or work in biomedical field,various data with lifetime,survive time or failure time have been concerned.And many statistical analysis methods have widely used in the reliability of product as well as in diseases research.In this paper,we concerned the parameter estimation in the reliability-test when the products life distribution is Weibull distribution.In chapter one,the problem's background is introduced,including the characteristics of lifetime data and analysis methods.In chapter two,we discussed the parameter estimation of Weibull distribution under complete sample.Including moment estimation,maximum likelihood estimation(MLE),Bayesian estimation,graph method.Numerical method has been used to solve the moment estimation for a long time.In this paper,taking advantage of some properties of Gamma function,we get the explicit solution. Some simulation results are also given in this paper。In chapter three, we discuss the problem under censored data in three circumstances. To the Type-Ⅱcensored data we take it concerned from the Extreme distribution. Because the parameters in Extreme distribution are location & scale parameters, while in Weibull distribution are shape & scale parameters. Therefore, from the first we can discuss the problem easier. From this point, making use of some properties of the extreme value distribution and the fixed-point theorem, we also get the explicit solution. And a new algorithm is given, through some simulation results, we see that this algorithm converges fast and does not depend on any conditions.In chapter four, we introduce the zero-failure data. Because many traditional methods can not be used directly in this case, so some improvements have made. We get the quasi-moment estimation, modified MLE. We pay more attention to the application of partition distribution curve method and least square estimation. In this problem the most important work is how to give the failure probability reasonably. We discuss the Bayesian estimators and hierarchical Bayesian estimators. At last, some unsolved problems have been listed.