随机右截尾情形下威布尔分布可靠度的置信下限

【作者】 李庆华；

【导师】 郭鹏江；

【作者基本信息】 西北大学 ， 应用数学， 2009， 硕士

【摘要】 随着科学技术的发展,许多大型复杂的智能化程控设备或产品广泛应用于社会各个领域,这些设备或产品一旦发生故障,将会对社会、经济等方面造成不同程度的损害,这些损害有时甚至会危及到人民生命财产的安全。而描述这些设备或产品安全性的一个重要指标就是可靠性。因此,可靠性越来越受到人们的重视。在产品可靠性分析、研究过程中,主要是借助统计分析方法,对产品寿命试验数据进行分析以确定其可靠性,而可靠性指标中较常用的是可靠度的置信下限。但因实验设备、观测手段、实验成本等方面的影响,造成寿命实验有时并不是同时开始,既使同时开始,也可能不同时结束。因此在实验结束时,我们就得到一组“随机右截尾数据”。本文基于威布尔分布下的右截尾数据,对可靠度的置信下限进行讨论。首先利用极大似然估计理论对威布尔分布的参数估计进行了一般论述。然后,在此基础上采用统计量方法对威布尔分布下可靠度的置信下限的计算进行了分析。由于威布尔分布在随机右截尾下的计算比较复杂,因此利用极大似然估计的相合性和参数β的特点对参数β给出一定的限制条件,再通过威布尔分布与指数分布的转换公式,就可以比较容易的求出可靠度的近似置信下限,大大简化了计算,使其在实际中的应用成为可能。本文最后用鞍点逼近计算方法给出了可靠度的置信下限的计算公式,并通过数据模拟证明了本方法是可行的。更多还原

【Abstract】 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.更多还原