定时截尾试验Weibull分布参数的近似置信区间

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一另一参数的近似置信敬意 ，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)/(2u-u^2)^1/2∞N(0,1)，由此可以得到参数（u,v)的联合置信域D：u≥1 β^2/2β^2(u-S/1 β^2)^2 S^2/2(1 β^2) 。由于Jacobi变换地列式|J|≠,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 β^2)u^2(b)-2S.u(b)-2β^2v(b) S^2=0,得到了2个根b1(λ),即为参数λ的置信水平1-α的置信区间:b1(λ)≤b≤b2(λ).

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

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 t０ is censored and Si＝min(xi,ti) 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＋β２）u２（b)-2*u(b)-2β２v(b)＋２＝0,two roots,i.e.,b1(λ） and b２（λ) can be got. When the confidence level is 1-α,the approximate confidence interval of λ is b1（λ）≤b≤b２（λ).