双参数指数分布下两应力交叉步加试验的统计分析

Statistical Analysis of Accelerated Life Test Using Two Alternate Step Stress Under Two Parameter Exponential Distribution

设产品寿命服从双参数指数分布，失效率和保证寿命的加速模型分别为ｌｎθｉｊ＝β０＋β１φ１（Ｓ１ｉ）＋β２φ２（Ｓ２ｊ）＋β３φ１（Ｓ１ｉ）φ２（Ｓ２ｊ）ｕｉｊ＝α０－α１ｆ１（Ｓ１ｉ）－α２ｆ２（Ｓ２ｊ）ｉ＝１，２，…，ｌ；ｊ＝１，２，…，ｋ本文研究了用两应力交叉步加试验的数据对参数βｉ（ｉ＝０，１，２，３）和αｊ（ｊ＝０，１，２）进行估计和检验，然后由模型可以求得正常工作应力（Ｓ１０，Ｓ２０）下各种可靠性特征的估计值。最后给出的随机模拟例子表明，本文给出的统计方法具有较高的精度。

Suppose that the distribution of the lifetime of products follows the two parameter exponential law, under the stress (S 1i , S 2j ), the failure rate accelerated model and the life guarantee accelerated model are  ln θ ij =β 0+β 1φ 1(S 1i )+β 2φ 2(S 2j )+β 3φ 1(S 1i )φ 2(S 2j ) andu ij =α 0-α 1f 1(S 1i )-α 2f 2(S 2j ) i=1,2,…,l; j=1,2,…,k In this paper, we have given the method of estimating and testing the coefficients β 0, β 1, β 2, β 3, α 0, α 1 and α 2 with the datas of accelerated life test using two alternate step stress. Using the two models, we can obtain the estimators of the various reliability characteristics under the usual stress (S 10 , S 20 ), the results of random simulation show that the method given above is of more high precision.