Weibull分布定时截尾寿命试验参数的近似联合置信域

研究了Weibull分布大样本定时截尾寿命试验，利用一种新的途径给出了试验参数的近似联合置信域。设产品寿命X服从Weibull分布，对n个受试样本x1,x2，…，xn进行定时（时间为t0）截尾试验，得到观察数据Si=min(x1,x0)，i=1,2,…，n。利用似然方程，分别得到参数λ，b的极大似然估计λ和b。进一步考察联合分布（λ，b）可以用二元正态分布来近似。再利用多元正态分布与X^2分布的关系，可以推导出未知参数u=（λ，b）的置信度为1－a的联合置信区域（x-u)′I0（x-y)≤xa^2。

Simultaneous Confidence Region of Parameters for Weibull Distribution under Fix-Time Censored Test

The fix-time censored test of Weibull distribution is studied. By using a new method, the simultaneous confidence region of parameters is obtained. Suppose that the lifetime x of product is of W (λ,b) distribution, then we censor the data xi with fix-time t0, and Si=min(xi,t0) is available, (i= 1,2, … ,n). When the maximum likelihood eguation is solved, the maximum likelihood estimator ( , ) of the parameter (λ,b) can be obtained. The simultaneous distribution of ( , ) is asymptotically convergent to two-dimensional normal distribution . By using the relation between mutiple-dimension normal distribution and X2 distribution, the following conclusion is obtained,i. e. ,when the confidence level is 1－α,the simultaneous confidence region is the ellipse: ( －u)＇I0( －u)≤xα2, where u= (λ,b).