Parameter Estimation For Weibull Distribution Based On Incomplete Samples

Reliability theory mainly consider the life characteristics of products in a wide range of practice areas.The progress of modern technology promote the rapid development of reliability theory. Weibull distribution is one of the most widely applied distribution in reliability theory.This paper focuses on parameter estimation of which the sample is incomplete observational data.First of all,the relevant background information is introduced,including the Weibull distribution model, the basic types of censored data.Chapter 2 expound a variety of censored data estimation methods for both two-parameter Weibull distribution and three-parameter Weibull distribution.These include: least squares estimation,maximum likelihood estimation(MLE),Bayesian estimation,inverse moment estimation,etc.In discussing the three-parameter Weibull estimation,the method of modified weibull moment estimation(MME) is mainly introduced,and it's applied in censored data.In type-â…¡censored data circumstance,Mean residual lifetime is used to construct sample moment. Samples from three-parameter Weibull distribution are transformed into Uniform distribution samples.Meanwhile,the three-order-moment functions is replaced by the first order statistic function,the modiefied moment equation is derived.Under typeâ… and typeâ…¡censored samples,the MME's bias and mean square error are obtained by Monte-Carlo method.Compared with the MLE,MME has better statistical property.The last chapter introduces a special situation in typeâ… censored samples test:all samples without failure,and the previous methods could not be used.Based on this analysis of the reliability of data without failure, there are many issues that must be resolved.This paper introduces the zero-failure data as well as the current progress of the study and improvement of the methods.