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

PDF (PC)

14

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

[1] 马秀平. 基于逆Xgamma分布的应力强度模型可靠度估计[D]. 安庆:安庆师范大学, 2022.
[2] 戴林送, 王枞. 基于广义逆威布尔分布的应力强度模型可靠度估计[J]. 统计与决策, 2020, 36(9): 25-29.
[3] 李珺, 闫在在. 逐次Ⅰ型混合截尾下基于FGM copula的应力强度模型可靠性估计[J]. 数学的实践与认识, 2022, 52(4): 183-195.
[4] 程从华. 基于截尾数据指数Pareto分布应力-强度模型的可靠性[J]. 数学学报(中文版), 2020, 63(3): 193-208.
[5] BHATTACHARYYA G K,JOHNSON R A. Estimation of the reliability in a multicomponent stress-strength model[J]. Journal of the American Statistical Association,1974,69(348):966-97.
[6] AKGÜL F G. Classical and Bayesian estimation of multicomponent stress-strength reliability for exponentiated Pareto distribution[J]. Soft Computing, 2021, 25(14): 9185-9197.
[7] FATIH K. Classical and Bayesian estimation of reliability in a multicomponent stress-strength model based on a general class of inverse exponentiated distributions[J]. Statistical Papers, 2018, 59(3): 1161-1192.
[8] JANA N, BERA S. Interval estimation of multicomponent stress strength reliability based on inverse Weibull distribution[J]. Mathematics and Computers in Simulation, 2022, 191: 95-119.
[9] WANG L, WU K, TRIPATHI Y M, et al. Reliability analysis of multicomponent stress-strength reliability from a bathtub-shaped distribution[J]. Journal of Applied Statistics, 2020, 49(1): 122-142.
[10] DEY S, MAZUCHELI J, ANIS M Z. Estimation of reliability of multicomponent stress-strength for a Kumaraswamy distribution[J]. Communications in Statistics Theory and Methods, 2017, 46(4): 1560-1572.
[11] AKGÜL F G. Reliability estimation in multicomponent stress-strength model for Topp-Leone distribution[J]. Journal of Statistical Computation and Simulation, 2019, 89(15): 2914-2929.
[12] RAO G S, BHATTI F A, ASLAM M, et al. Estimation of reliability in a multicomponent stress-strength system for the exponentiated moment-based exponential distribution[J]. Algorithms, 2019, 12(12), 246.
[13] NADAR M, ERÇELIK E. Reliability of multicomponent stress-strength model based on bivariate generalized exponential distribution[J]. American Journal of Mathematical and Management Sciences, 2023, 42(1): 86-103.
[14] SADEGH M K. Erratum to: Reliability of a coherent system in a multicomponent stress-strength model[J]. American Journal of Mathematical and Management Sciences, 2021, 40(4): 336-339.
[15] RASEKHI M, SABER M M, YOUSOF H M. Bayesian and classical inference of reliability in multicomponent stress-strength under the generalized logistic model[J]. Communications in Statistics-Theory and Methods, 2021, 50(21): 5114-5125.
[16] MAURYA R K, TRIPATHI Y M. Reliability estimation in a multicomponent stress-strength model for Burr XII distribution under progressive censoring[J]. Brazilian Journal of Probability and Statistics, 2020, 34(2): 345-369.
[17] KOHANSAL A. On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample[J]. Statistical Papers , 2019, 60(6): 2185-2224.
[18] PRATAP S D, KUMAR J M, YOGESH T, et al. Reliability estimation in a multicomponent stress-strength model for unit Burr Ⅲ distribution under progressive censoring[J]. Quality Technology & Quantitative Management, 2022, 19(5): 605-632.
[19] MAHTO A K, TRIPATHI Y M, KIZILASLAN F. Estimation of reliability in a multicomponent stress-strength model for a general class of inverted exponentiated distributions under progressive censoring[J]. Journal of Statistical Theory and Practice, 2020, 14(4): 58.
[20] JHA M K, DEY S, ALOTAIBI R M, et al. Reliability estimation of a multicomponentstress-strength model for unit Gompertz distribution under progressive Type Ⅱ censoring[J]. Quality and Reliability Engineering International, 2020, 36: 965-987
[21] KOHANSAL A, SHOAEE S. Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data[J]. Statistical Papers, 2021, 62(1): 309-359.
[22] DEBASIS K, AVIJIT J. Analysis of type-Ⅱ progressively hybrid censored data[J]. Computational Statistics and Data Analysis, 2006, 50(10): 2509-2528.
[23] 刘一鸣. 多部件系统应力强度模型的可靠性分析[D]. 西安:西北工业大学, 2019.
[24] 孙烨, 蒋京京, 王纯杰. 广义极值回归模型下现状数据的贝叶斯估计[J]. 广西师范大学学报(自然科学版), 2022, 40(1): 82-90.
[25] TIERNEY L, KADANE J B. Accurate approximations for posterior moments and marginal densities[J]. Journal of the American Statistical Association, 1986, 81(393): 82-86.
[26] 韦来生, 张伟平.贝叶斯分析[M]. 合肥:中国科学技术大学出版社, 2013.
[27] 罗君念,蔡静,张峰源.广义逆指数分布应力-强度模型的可靠性评估[J]. 湖北民族大学学报(自然科学版), 2023, 41(1): 102-108.
[28] HASTINGS W K. Monte Carlo sampling methods using Markov chains and their applications[J]. Biometrika, 1970, 57(1): 97-109.
[1] 陈钟秀, 张兴发, 熊强, 宋泽芳. 非对称DAR模型的估计与检验[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 68-81.
[2] 孙烨, 蒋京京, 王纯杰. 广义极值回归模型下现状数据的贝叶斯估计[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 82-90.
[3] 梁鑫, 陈小玲, 张兴发, 李元. 一类带有GARCH类误差项的自回归滑动平均模型[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 195-205.
[4] 李莉丽, 张兴发, 李元, 邓春亮. 基于高频数据的日频GARCH模型估计[J]. 广西师范大学学报（自然科学版）, 2021, 39(4): 68-78.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 袁静静, 郑宇钊, 徐晨枫, 殷婷婕. 非内吞依赖型生物大分子药物胞质递送策略研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(1): 1 -8 .
[2] 涂广升, 孔咏骏, 宋哲超, 叶康. 密文域可逆信息隐藏研究进展及技术难点分析[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 1 -15 .
[3] 杨杨阳, 朱震霆, 杨翠萍, 李世豪, 张舒, 范秀磊, 万蕾. 基于文献计量学分析的剩余污泥厌氧消化预处理研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 16 -29 .
[4] 许伦辉, 李金龙, 李若南, 陈俊宇. 基于动态生成对抗网络的路网缺失交通数据修复[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 30 -40 .
[5] 杨海, 谢亚琴. 基于Floyd算法的5G基站区域储能分配策略[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 41 -54 .
[6] 闫文文, 文中, 王爽, 李国祥, 王博宇, 吴艺. 基于AA-CAES电站和综合需求响应的供暖期弃风消纳策略[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 55 -68 .
[7] 甘友春, 王灿, 贺旭辉, 张羽, 张雪菲, 王帆, 喻亚洲. 考虑光热电站和柔性负荷的电氢热综合能源系统联合优化运行[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 69 -83 .
[8] 王旭阳, 王常瑞, 张金峰, 邢梦怡. 基于跨模态交叉注意力网络的多模态情感分析方法[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 84 -93 .
[9] 王卫舵, 王以松, 杨磊. 云资源调度的回答集程序描述性求解[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 94 -104 .
[10] 余谦, 陈庆锋, 何乃旭, 韩宗钊, 卢家辉. 基于矩阵运算加速的改进社区发现遗传算法[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 105 -119 .
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发