多阶段复杂退化产品的可靠性统计模型  

Reliability Statistical Inference Model for Multi-Stage Degraded Products

作　　者：周子韩 凡红梅 缪思巧 唐家银 ZHOU Zihan;FAN Hongmei;MIAO Siqiao;TANG Jiayin(Department of Statistics,School of Mathematics,Southwest Jiaotong University;National Engineering Laboratory of Integrated Transportation Big Data Application Technology,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院统计系 [2]西南交通大学综合交通大数据应用技术国家工程实验室,成都611756

出　　处：《重庆师范大学学报（自然科学版）》2024年第1期74-85,共12页Journal of Chongqing Normal University:Natural Science

基　　金：教育部人文社会科学研究规划基金项目(No.20XJAZH009);西南交通大学2020本科教育教学研究与改革项目(20201033);西南交通大学2020年度研究生研究类教育改革项目(No.YJG4-2020-Y035);四川省教育厅高等教育人才培养质量和教学改革项目(No.JG2018-143);中央高校基础研究培育专题2021年度项目(No.2682021ZTPY018)。

摘　　要：针对多阶段退化产品,基于性能退化响应数据的回归统计拟合,建立变速率复杂退化可靠性评估模型。首先利用分段回归拟合对性能退化数据进行变点回归建模,推导变点分布的极大似然函数;其次鉴于模型的复杂性,变点估计的最大似然估计无法得到显式解,采用分层Bayes进行建模;然后结合MCMC(Markov chain Monte Carlo)算法中的Gibbs采样对模型进行参数诊断,依据Schwarz信息准则(Schwarz information criterion,SIC)构建经验似然比对模型的变点进行估计与检验;最后根据产品失效退化的定义,推导该失效模式下产品的可靠度函数。以手机运行的游戏性能数据建模分析,演绎说明了多阶段退化模型适应性强、可行性高的特点。与传统两阶段建模相比,多阶段退化建模考虑了各个阶段的退化信息,提高了数据利用率和产品的可靠性评估可信度。Based on regression statistical fitting of performance degradation response data,a reliability assessment model of variable speed complex degradation was established for multi-stage degraded products.First,piecewise regression fitting was used to model performance degradation data,and the maximum likelihood function of change point distribution was derived.Secondly,due to the complexity of the model,the mayimum likelihood estimation of change point estimation cannot be displayed.Therefore,layered Bayes model is used for modeling,and Gibbs sampling technique in Markov chain Monte Carlo algorithm is used for parameter diagnosis of the model.The change point of the model is estimated and verified by using Schwarz information criterion criterion and empirical likelihood ratio.Finally,according to the definition of product failure degradation,the reliability function of the product under the failure mode is derived.Based on Mate30 game performance data modeling and analysis,the multi-stage degradation model is proved to be highly adaptable and feasible.Compared with traditional two-stage modeling,multi-stage degradation modeling reduces unnecessary data waste and improves reliability of product reliability evaluation.

关 键 词：多阶段退化 变点 Schwarz信息准则 GIBBS采样 可靠性 

分 类 号：O212.3[理学—概率论与数理统计] TB114.3[理学—数学]