基于Bootstrap理论的小子样寿命评估模型

针对航天产品小子样、长寿命的特点，提出了基于Bootstrap理论的小子样寿命评估模型。采用B-样条函数构造Bootstrap样本经验分布函数，进行放回抽样。在此基础上，分别采用非参数Bootstrap方法和参数Bootstrap方法建立了寿命评估模型。采用提出的模型对空心阴极循环点火寿命试验数据进行评估，得到多个寿命特征结果，与传统的参数极大似然估计方法的计算结果进行了对比分析，其评估精度满足工程的应用需求，验证了该模型的工程实用性和有效性。 

Lifetime evaluation model of small sample based on Bootstrap theory

This paper proposes a small sample lifetime evaluation model based on Bootstrap method for aerospace products which have the characteristics of small sample and long service life. Using B-spline function as the Bootstrap sample empirical distribution function, a random case sample with replacement is obtained. And on this basis, the lifetime evaluation model is established by using non-parametric Bootstrap method and parametric Bootstrap method respectively. Hollow cathode ignition test data are evaluated based on the proposed method, and multiple lifetime characteristic results are acquired. The results are contrastively analyzed with those concluded by conventional maximum likelihood estimation method of parameters, and it meets the need of the engineering precision, which demonstrates the engineering practicability and effectiveness of the method.