逐步Ⅱ型截尾步进应力部分加速寿命试验的统计推断  

Statistical inference of progressive typeⅡcensored under step-stress partial accelerated life test

作　　者：何剑 蔡静 徐开丽 韩荣 何飞 HE Jian;CAI Jing;XU Kaili;HAN Rong;HE Fei(School of Data Science and Information Engineerin,Guizhou Minzu University,Guiyang 550000,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550000

出　　处：《延边大学学报（自然科学版）》2024年第1期13-22,30,共11页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金(11901134)。

摘　　要：基于逐步Ⅱ型截尾样本,研究了逆Rayleigh分布在步进应力部分加速寿命试验下的统计分析问题.首先运用贝叶斯方法、极大似然估计方法和近似极大似然估计方法,得到了未知参数和加速度因子的贝叶斯估计(BE)、极大似然估计(MLE)和近似极大似然估计(AMLE),并运用极大似然估计的渐近正态性推导出未知参数和加速因子的渐近置信区间.其次,运用贝叶斯理论在平方损失函数和线性指数损失函数下给出了模型参数和加速因子的贝叶斯估计和最大后验密度(HPD)置信区间.最后,利用蒙特卡罗模拟对3种不同估计方法的精度进行了评估.数值模拟表明:贝叶斯估计的效果大体上优于极大似然估计和近似极大似然估计的效果;线性指数损失函数下的贝叶斯估计效果要优于平方损失函数下的贝叶斯估计效果;随着样本量的增加,3种估计方法的均方误差(MSE)和平均相对误差(ARE)均呈减小趋势;在同一组样本和同一种移除方案中,BE的HPD置信区间长度优于MLE的渐近置信区间长度.Based on the progressive typeⅡcensored samples,the statistical analysis of the inverse Rayleigh distribution under the step-stress partial accelerated life test is investigated.Firstly,Bayesian estimation(BE),the maximum likelihood estimation(MLE)and approximate maximum likelihood estimation(AMLE)of unknown parameters and acceleration factors are estiblished by using Bayesian method,maximum likelihood estimation method and approximate maximum likelihood estimation method,and their approximate confidence interval is derived by using the asymptotic normality of maximum likelihood estimation.Secondly,the Bayesian estimation and maximum posterior density(HPD)confidence interval of model parameters and acceleration factors are given by using Bayesian theory under square loss function and linear exponential loss function.Finally,the accuracy of three different estimation methods is evaluated by Monte Carlo simulation.Numerical simulation shows that the effect of Bayesian estimation is generally better than that of MLE and AMLE.The Bayesian estimation effect under the linear exponential loss function is better than that under the square loss function.With the increase of sample size,the mean square error(MSE)and average relative error(ARE)of the three estimation methods demonstrated a decreasing trend.In the same group of samples and removal scheme,the HPD confidence interval length of BE is better than the asymptotic confidence interval length of MLE.

关 键 词：逐步Ⅱ型截尾样本 逆Rayleigh分布 步进应力部分加速寿命试验 极大似然估计 近似极大似然估计 贝叶斯估计 

分 类 号：O213.2[理学—概率论与数理统计]