小样本加速寿命试验方法对比验证

Comparison and Verification of Small-Sample Accelerated Life Test Method

对小样本加速寿命试验方法(小样本法)与传统的基于极大似然估计的加速寿命试验方法(MLE法)和基于最佳线性无偏估计的加速寿命试验方法(BLUE法)进行了大量仿真对比验证。结果表明,在小样本情况下,MLE法求得的正常使用应力水平下的可靠寿命单侧置信下限,其仿真置信度低于设定置信度,不能满足置信度要求,工程应用偏于危险;BLUE法和小样本法求得的正常使用应力水平下可靠寿命单侧置信下限的仿真置信度,前者高于设定置信度,后者等于设定置信度,均满足置信度要求,工程上安全可用。正因为小样本法严格满足置信度要求,所以与BLUE法相比,在试样数相同的条件下,具有更高的评估精度;在精度相同的条件下,则可节省大量试样。文中在小样本法的基础上,还进一步给出了Weibull分布形状参数相同时的融合评估方法和正态分布完全数据且方差不相同时的小样本评估方法。

The small-sample accelerated life test method(small-sample method)is verified and compared with the traditional accelerated life test methods based on maximum likelihood estimation(MLE method)and best linear unbiased estimation(BLUE method)through extensive Monte Carlo simulations.The results indicate that,in the case of small samples,the coverage probability of the one-sided lower confidence limit of reliable life under normal use stress level obtained by the MLE method is lower than the set confidence degree,failing to meet the confidence requirements and posing a risk in engineering applications.In contrast,the coverage probabilities of the BLUE method and the small-sample method are higher than and equal to the set confidence degree,respectively,both satisfying the confidence requirements and being safe for engineering applications.Since the small-sample method strictly meets the confidence requirements,it offers higher evaluation accuracy compared to the BLUE method with the same number of samples and saves a considerable number of samples while maintaining the same accuracy.Furthermore,based on the small-sample method,this paper proposes a fusion assessment method for Weibull distribution with the same shape parameters and a small-sample assessment method for normal distribution with complete data but different variances.