基于随机效应的可靠性试验设计分析  

Analysis of Reliability Experiments with Random Effect

作　　者：方俊涛 宋丽莎 何桢[1] 何曙光[1] FANG Juntao;SONG Lisha;HE Zhen;HE Shuguang(College of Management and Economics,Tianjin University,Tianjin 300072,China;School of Management,Tianjin University of Traditional Chinese Medicine,Tianjin 301617,China)

机构地区：[1]天津大学管理与经济学部,天津300072 [2]天津中医药大学管理学院,天津301617

出　　处：《工业工程与管理》2023年第1期26-33,共8页Industrial Engineering and Management

基　　金：国家重点研发计划(2016QY02D0301);国家自然科学基金项目(71902139);教育部人文社会科学研究青年基金项目(18YJC630029)。

摘　　要：试验设计是改进产品质量的有效技术,通常假定试验输出服从正态分布且相互独立,通过拟合质量特性(试验输出)与影响因素(参数)的关系,优化产品或工艺参数,实现质量提升。然而,寿命数据通常是偏态的、截尾的,每个试验单元包含多个样本,因此基于分位值的研究更具实际意义和价值。多样本的试验单元给试验设计带来了组内差异,即参数估计中的随机效应。首先,基于此建立了随机效应可靠性模型,给出了基于随机效应的极大似然估计方法。然后,采用Gauss-Hermite积分求得了具有解析形式的似然函数。最后,以恒温器寿命试验为例,分析了影响寿命的显著因子,得到了具有稳健且高可靠性分位值的试验因子组合,可以有效降低恒温器早期失效,提升产品的可靠性。Design of experiments is an effective technology for quality improvement. The output response is assumed to be normally distributed with constant variance and observations are supposed to be uncorrelated between runs. Quality improvement is achieved through fitting functions of quality characteristics(output responses) and input variables(parameters). However,the distribution of lifetime data is commonly skewed and censored,and each test stand contains multiple items,so the focus is often on percentile lifetime which is more practical and valuable. These cause the differences between the items in a test stand,namely the random effect associated with the items of an experimental unit. First,the method of maximum likelihood was used to estimate the parameters of the reliability model with random effects.Then,the likelihood function with approximately analytical form was obtained by Gauss-Hermite quadrature. Finally,an industrial thermostat experiment was presented as an illustrative example. The significant factors affecting the thermostat lifetime and their settings with robust and high-reliability quantile were identified. Under the predictive model,the industrial thermostats early failures could be reduced.

关 键 词：可靠性试验设计 随机效应 寿命回归 显著因子 

分 类 号：C931[经济管理—管理学]