摘要
设产品寿命服从Ｗｅｉｂｕｌ分布，尺度参数为η＞０，形状参数为ｍ＞０，在双应力Ｓ１ｉ和Ｓ２ｊ下，加速方程为模型Ⅰ：ｌｎηｉｊ＝β０＋β１φ１（Ｓ１ｉ）＋β２φ２（Ｓ２ｊ）（ｉ＝１，２，…，ｋ，ｊ＝１，２，…，ｌ）或模型Ⅱ：ｌｎηｉｊ＝β０＋β１φ１（Ｓ１ｉ）＋β２φ２（Ｓ２ｊ）＋β３φ１（Ｓ１ｉ）φ２（Ｓ２ｊ）（ｉ＝１，２，…，ｋ，ｊ＝１，２，…，ｌ）本文给出了定时截尾Ｗｅｉｂｕｌ分布各组应力下形状参数ｍｉｊ的极大似然估计的一种改进迭代算法，利用〔１〕类似的方法对各组应力下所得估计进行修正，后对各组应力下ｍｉｊ的估计值进行加权平均得ｍ的近似无偏估计；利用定时截尾Ｗｅｉｂｕｌ分布尺度参数ηｉｊ的极大似然估计，通过Ｗｅｉｂｕｌ分布与指数分布之间的关系以及指数分布的性质，求得各组应力下尺度参数的自然对数ｌｎηｉｊ的近似无偏估计，利用ｌｎηｉｊ的估计值与加速方程，建立线性模型，利用Ｇａｕｓ－Ｍａｒｋｏｖ定理得参数βｉ（ｉ＝０，１，２，３）的近似最佳线性无偏估计且对所得参数βｉ（ｉ＝０，１，２，３）进行检验。通过模型由此可求出正常应力（Ｓ１０，Ｓ２０）下各种可靠性特征量的估计。模拟结果表明本方法得出参数的估计值与其真实?
Suppose that the distribution of the lifetime of the products follows Weibull Law,the scale parameter is η>0,and the shape parameter is m>0 .Under the stress (S 1i ,S 2j ) the accelerated model is \ \ Model Ⅰ:lnη ij =β 0+β 1φ 1(S 1i )+β 2φ 2(S 2j ),\ \ (i=1,2,…,k,\ j=1,2,…,l) \ \ or Model Ⅱ:lnη ij =β 0+β 1φ 1(S 1i )+β 2φ 2(S 2j )+β 3φ 1(S 1i )φ 2(S 2j ),\ \ (i=1,2,…,k,\ j=1,2,…,l) where φ 1(S 1),φ 2(S 2) are the known functions of stresses S 1 and S 2, respectively.In this paper we use the type Ⅰ censoring data of alternate constant-stress accelerated life testing to estimate the testing coefficients in above two models.The approximate unibased estimator of the shape parameter,and the approximate best linear unibased esimator of the coefficients of the accelerated model are obtained.Using the model and shape parameter,the estimators of the various reliability characteristics under the usual stress (S 10 ,S 20 ) can be obtained.The results of random simulation show the methods given above have high precision.
出处
《南昌大学学报（理科版）》
CAS
1997年第3期251-258,共8页
Journal of Nanchang University(Natural Science)
关键词
定时截尾试验
威布尔分布
寿命试验
统计
weibull distribution,linear model,random simulation,type Ⅰ censoring test,alternate constant-stress accelerated life test,weighted average
