威布尔分布下平均寿命置信限的评估方法研究

On the Confidence Limits for the Mean of Weibull Distributions

设备的平均寿命是可靠性研究中的的一个重要指标.对威布尔分布来说,由于平均寿命没有明显的枢轴量,因此给出平均寿命的精确的置信限较为困难.本文分别利用广义枢轴量、WCF展开以及三阶法三种方法,得到了设备寿命服从威布尔分布时的平均寿命的(近似)置信下限.最后对上述三种方法分别进行了模拟比较,结果显示文中给出的方法对于中小样本情形下得到的平均寿命的置信限是比较精确的.

The mean of products is an important performance index in reliability analysis. It is difficult to gain the exact confidence limits for the mean of Weibull distribution with two parameters, because there is no evident pivotal quantity for the mean. In this paper, we get the approximate confidence limits for the mean of Weibull distribution with two parameters by generalized pivotal quantity, WCF approximation and third-order procedure. Numerical examples axe presented to show the accuracy of the methods when the sample is moderate and small.