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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (12): 122-129.doi: 10.6040/j.issn.1671-9352.0.2023.064

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定数截尾下步进应力部分加速寿命试验模型的统计推断

龙兵,蒋再富   

  1. 荆楚理工学院数理学院, 湖北 荆门 448000
  • 发布日期:2024-12-12
  • 基金资助:
    湖北省自然科学基金资助项目(2022CFB527);荆楚理工学院科学研究项目(QN202426)

Statistical inference of step-stress partially accelerated life test model under Type-Ⅱ censoring

LONG Bing, JIANG Zaifu   

  1. School of Mathematics and Physics, Jingchu University of Technology, Jingmen 448000, Hubei, China
  • Published:2024-12-12

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摘要： 在步进应力部分加速寿命试验下,基于试验数据分别用经典方法和贝叶斯方法得到分布参数、加速因子及可靠度函数的极大似然估计与贝叶斯估计。根据极大似然估计的渐近性理论构建分布参数和加速因子的近似置信区间。利用观测数据对被截尾单元的失效时刻进行预测,包括最好无偏预测和条件中位数预测。运用蒙特卡洛方法对各种估计量的均值和平均相对误差进行模拟计算,并讨论样本量对估计精度的影响。最后用文中的方法对一个数值例子进行分析。

关键词: 指数分布, 步进应力部分加速寿命试验, 极大似然估计, 贝叶斯估计

Abstract: Under the step-stress partially accelerated life test, based on the test data, the maximum likelihood estimation and Bayesian estimation of the distribution parameter, acceleration factor and reliability function are obtained by the classical method and Bayesian method, respectively. According to the asymptotic theory of maximum likelihood estimation, the approximate confidence intervals of the distribution parameter and the acceleration factor are constructed. The failure times of the censored units are predicted by using the observed data, including the best unbiased predictor and the conditional median predictor. The mean values and average relative errors of various estimators are calculated by Monte-Carlo method, and the influence of sample size on estimation accuracy is discussed. Finally, a numerical example is analyzed using the method presented in the paper.

Key words: exponential distribution, step-stress partially accelerated life test, maximum likelihood estimation, Bayesian estimation

中图分类号: 

  • O213.2
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