基于广义逆理论的步进应力加速寿命试验的最优设计

Optimal Design of Step-Stress Accelerated Life Test on the Theory of Generalized Inverse Theory

步进应力加速寿命试验的最优设计问题早在20世纪60年代就已提出.本文在应力个数和未知参数个数不相等的情况下,以MLE渐近方差最小为准则,运用广义加号逆的理论,解决指数分布时定数截尾寿命试验和定时截尾寿命试验的最优设计问题.通过理论推导,得出定数截尾寿命试验时的不同应力下失效产品数的安排,以及定时截尾寿命试验时的最优应力变换点.并且,对每一种情况进行了数据模拟,结果显示,这些理论和方法在实际运用中是可行的和有效的.

The problem of optimal design for step-stress accelerated life test has been proposed since the 60s of the twentieth century. By using the method of generalized inverse matrix of positive sign and based on the minimum of asymptotic variance of MLE, this paper solved the optimum design of censored life test and type-I life test under exponential distribution when the number of stress and parameter is not equal. We obtained the arrangement of failure product for censored life test and the optimal transfer time for type-I life test. And, we conducted the data simulation for each condition. It shows that the re- suits and methods are feasible and effective in practice .