定时截尾试验Weibull分布参数的近似置信区间

Approximate Confident Interval of Parameter for Weibull Distribution under Fix-time Censored Test

该文研究了Weibull分布大样本定时截尾试验 ,给出了总试验时间的极限分布。在给定任一参数的条件下 ,利用一种全新的途径得到了另一参数的近似置信区间。设产品寿命x服从Weibull分布W(λ,b) ,对受试产品xi 进行定时时间t0 的截尾试验 ,得到观察数据Si=min(xi,t0 )。由于总试验时间S=S1+S2 +…+Sn 近似服从正态分布 :S -E(S)(VarS) 1/2 =n( S-u)(2v -u2 ) 1/2 ∝N(0 ,1)。由此可以得到参数 (u ,v)的联合置信域D :v≥1+ β22 β2 (u- S1+ β2 ) 2 + S22 (1+ β2 ) 。由于Jacobi变换行列式｜J｜≠ 0 ,因此区域D的任意一点 (u ,v)都能找到唯一的点 (λ ,b)与之对应。对于任一给定的λ,参数曲线u =u(b) ,v=v(b)与区域D的边界曲线正好有 2个交点 ,解方程 :(1+ β2 )u2 (b) - 2 S·u(b) - 2 β2 v(b) + S2 =0 ,得到 2个根b1(λ)和b2 (λ) ,即为参数λ的置信水平 1-α的置信区间 :b1(λ) ≤b≤b2 (λ)。

In this paper,the fix time censored test of Weibull distribution is studied and the limit distribution of total test time is obtained.If a parameter is given,the approximate confident interval of the other by using a new method can be got.Suppose that the lifetime X of product is of W(λ,b) distribution,then the data x i with fix time t 0 is censored and S i= min (x i,t i) is available.As Jacobi's transformation determinant ｜J｜ is not equal to zero,any point (u,v) in the region D has only a corresponding point (λ,b). If λ is given,the parameter curves u=u(b),v=v(b) have two points of intersection with the margin curve of region D. Solving the following equation:(1+β 2)u 2(b)-2·u(b)-2β 2v(b)+ 2=0,two roots,i.e.,b 1(λ) and b 2(λ) can be got. When the confidence level is 1-α,the approximate confidence interval of is b 1(λ)≤b≤b 2(λ).