Weibull Distribution In The Case Of Random Right Censored Reliability Lower Confidence Limit

With the development of science and technology, a lot of large complex intelligent program control equipments or products are used in all social fields. Once these equipments or products go wrong, they will damage all social and economic aspects to some extent, and even endanger people's life-property safety. One of the import indexes of these products safety is the reliability. Therefore, it has been paid more and more attention.In the process of analyzing and studying the reliability, it is mainly, with the aid of statistic analysis method, to analysis test data of product life in order to confirm the reliability. Moreover, the usually used index of it is the lower confidence limits of the reliability. However, being affected by experiment equipment, observation method and cost of experiment, life test does not start at the same time; even so, it may not finish simultaneously. So at the end of the experiment, we get a group of randomly censored data on the right.Based on the right-censored data in the Weibull distribution, this paper discusses the lower confidence limits of the reliability. Above all, using maximum likelihood estimation theory, it makes a general exposition for estimating parameter of Weibull distribution. And then, on that basis using statistical estimation it analyses the calculation of the lower confidence limits of the reliability in the Weibull distribution. Because the calculation of the randomly right-censored data in the Weibull distribution is comparatively complicated, we can give certain limiting conditions to parameterβusing consistent property maximumlikelihood estimate and its own characteristic, and then relatively easily obtain the lower confidence limits of the reliability by the conversion formula of Weibull distribution and exponential distribution. This way simplifies the calculation, and can be applied actually. In the end, this paper gives the calculation formula of the lower confidence limits of the reliability by saddle point approximation algorithm, and simulative proves that this way is feasible based on data.