小子样条件下幂律退化模型的加速因子分析

结合长寿命、高可靠性产品加速寿命试验的特点,在失效机理不变的条件下,提出了幂律退化模型加速因子的概念。推导了加速寿命试验条件下幂律退化模型参数的极大似然估计。并利用Bayes方法,结合额定应力环境下的小子样数据和加速因子的先验分布,推导出加速因子后验分布。在此基础上,给出了小子样条件下可靠性的一、二阶矩的估计公式,进而运用矩等效方法得到可靠性的验后分布,结合实例说明了方法的有效性。

Accelerate factor analysis for power law degradation model under the condition of small sampling test

Foundation on the characteristics of long life and high reliability products,on the condition of const failure mechanism,the accelerate factor definition of power law degradation model is proposed firstly.Then the parameter's MLE of power law model was carried out under accelerated environment.Combined with product's field small sampling test and the accelerate factor's prior distribution,the factor's posterior distribution is presented based on Bayesian method.With the above result,the reliability's first and second order moment estimation under small sampling field test was presented.Furthermore,the reliability posterior distribution was presented by moment equivalent method.At last,an example is given to illustrate the validity of this method.