广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (2): 120-130.doi: 10.16088/j.issn.1001-6600.2023041902

• • 上一篇    下一篇

逐步Ⅱ型混合截尾下Lomax分布多部件应力强度模型的可靠性分析

龙芳, 蔡静*, 朱艳   

  1. 贵州民族大学 数据科学与信息工程学院, 贵州 贵阳 550000
  • 收稿日期:2023-04-19 修回日期:2023-06-03 发布日期:2024-04-22
  • 通讯作者: 蔡静(1980—), 女, 山东淮坊人, 贵州民族大学教授, 博士。 E-mail: 114528176@qq.com
  • 基金资助:
    国家自然科学基金(11901134)

Analysis of Reliability in a Multicomponent Stress-Strength Model for Lomax Distribution under Progressive type-Ⅱ Hybrid Censoring

LONG Fang, CAI Jing*, ZHU Yan   

  1. School of Data Science and Information Engineeting, Guizhou Minzu University, Guiyang Guizhou 550000, China
  • Received:2023-04-19 Revised:2023-06-03 Published:2024-04-22

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摘要： 基于逐步Ⅱ型混合截尾样本,研究Lomax分布多部件应力强度模型的可靠性分析问题。假设应力和强度具有不同形状参数和共同尺度参数,利用极大似然理论及迭代方法获得可靠度函数的极大似然估计(MLE),并给出渐近置信区间;然后,运用贝叶斯理论,借助Tierney-Kadane(TK)近似方法、MCMC算法,讨论平方误差损失函数下未知参数及可靠度的贝叶斯估计,给出其最大后验密度可信区间(HPD);最后,利用Monte-Carlo模拟方法对估计结果进行对比分析。模拟结果显示:贝叶斯估计整体上优于极大似然估计,并且随样本量的增大,2种估计的均方误差(MSE)均逐渐减小,HPD可信区间的效果优于渐近置信区间。

关键词: 逐步Ⅱ型混合截尾, Lomax分布, 多部件应力强度可靠性, 极大似然估计, 贝叶斯估计

Abstract: Based on progressive type-Ⅱ hybrid samples, the reliability analysis of Lomax distributed multicomponent stress-strength model is studied. Assuming that stress and strength have the same scale parameters and different shape parameters, the maximum likelihood estimation of the reliability function is obtained by using the maximum likelihood theory and the iterative method when the scale parameters are unknown and the asymptotic confidence interval is given. By using Bayesian theory, Tierney Kadane (TK) approximation method and MCMC algorithm, the Bayesian estimation of unknown parameters and reliability under the square error loss function is discussed, and the maximum a posteriori density confidence interval (HPD) is given. Finally, Monte-Carlo simulation method is used to compare and analyze the estimated results. The simulation results show that the Bayesian estimation is better than the maximum likelihood estimation on the whole, and the mean square error (MSE) of the two estimates decreases gradually with the increase of the sample, and the effect of (HPD) confidence interval is better than the asymptotic confidence interval.

Key words: progressive type-Ⅱ hybrid censoring, Lomax distribution, multicomponent stress-strength reliability, maximum likelihood estimation, Bayesian estimation

中图分类号:  O213.2

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