Weibull小样本失效数据的贝叶斯可靠性分析  

Bayes Reliability Analysis of Weibull Small Sample Failure Data

作　　者：王春枝 申哲星 杨倬镔 WANG Chun-zhi;SHEN Zhe-xing;YANG Zhuo-bin(Department of Statistics and Mathematics,Inner Mongolia Finance and Economics University,Hohhot 010070,China)

机构地区：[1]内蒙古财经大学统计与数学学院,内蒙古呼和浩特010070

出　　处：《数学的实践与认识》2023年第10期151-159,共9页Mathematics in Practice and Theory

基　　金：国家社科基金项目(BMA180038)。

摘　　要：随着高性能复杂系统日益向“高质量、长寿命、小子样”等方向发展,在可靠性试验中经常出现小样本失效数据,传统的基于大样本的产品可靠性评估已不能满足试验要求.在两参数Weibull分布模型的基础上,对原始小样本数据采用灰色估计进行两参数估计,再利用蒙特卡洛方法进行随机抽样并将抽样结果纳入贝叶斯先验信息,通过贝叶斯公式得到后验分布,最终计算得到产品可靠度、失效概率、失效率等结果.最后经实例验证了该方法的有效性.With the development of high-performance complex systems towards the direction of“high quality,long life and small sample”,failure data of small sample often appear in reliability test,and sometimes failure data cannot be obtained.The traditional product reliability assessment based on large sample cannot meet the test requirements.To battle tank failure data of hydraulic shock absorber,for example,in the two parameter Weibull distribution model,on the basis of the original small sample data using the grey estimation for two parameter estimation,using the Monte Carlo method for random sampling and the sampling results into Bayesian prior information,posterior distribution is obtained by the Bayesian formula,finally calculate the product reliability and failure probability,failure rate,etc.An example shows that this method is suitable for the product reliability evaluation of small sample failure data,and an ideal result is obtained.

关 键 词：小样本 可靠性分析 两参数WEIBULL分布 贝叶斯方法 蒙特卡洛方法 

分 类 号：O213.2[理学—概率论与数理统计]