Weibull分布产品恒加应力缺失数据下的Bayes可靠性评估

在加速寿命试验过程中,由于试验设备、观测手段或其他方面的困难可能会造成某些试验数据丢失或未观测到.为解决Weibull分布产品在恒加应力试验中出现的小子样缺失数据情形下的可靠性评估问题,提出了可以综合利用多源信息的Bayes可靠性评估方法.首先通过概率元方法得到缺失数据的似然函数,同时根据似然函数中各未知参数的物理含义确定其验前分布类型,再利用第二类极大似然估计原理得到验前分布中超参数的估计.最后通过仿真实例说明了该评估方法在小子样缺失数据情形下的有效性.

Bayesian reliability assessment based on constant-stress accelerated life testing for long-life products with Weibull Distribution when missing data

In accelerated life test,some test data may be missed or not observed because of the test equipment or observation difficulty.A Bayesian method,which can appropriately utilize information coming from multiple sources,is proposed to solve the problem of reliability assessment for Weibull distribution products with small sampled missing data in constant-stress accelerated tests.Firstly,the likelihood function of the missing data is obtained by use of probability atom method.At the same time,the prior distribution of the unknown parameters in the likelihood function is set up according to their physics meaning.The super-parameters in the prior distribution functions can be estimated by the second Maximum Likelihood Estimation(ML-II) method.In the end A Monte Carlo study of the bias and mean square error of the estimators and a comparison with the properties of maximum likelihood estimators are carried out.