竞争失效产品部分加速寿命试验的统计分析 -- 西北工业大学学报,2017,35(1):109-115
论文:2017,Vol:35,Issue(1):109-115
引用本文:
师义民, 师小琳. 竞争失效产品部分加速寿命试验的统计分析[J]. 西北工业大学学报
Shi Yimin, Shi Xiaolin. Statistical Analysis for Partially Accelerated Life Tests with Competing Causes of Failure[J]. Northwestern polytechnical university

竞争失效产品部分加速寿命试验的统计分析
师义民1, 师小琳2
1. 西北工业大学 理学院, 陕西 西安 710072;
2. 西安邮电大学 电子工程学院, 陕西 西安 710121
摘要:
基于加速寿命试验的失效数据对产品的寿命特征进行统计分析时,需要利用产品寿命和应力水平之间的关系即加速模型。但在工程实际中,加速模型不一定总是已知的,例如新研制的产品。针对这个问题,提出了一种利用部分加速寿命试验研究竞争失效产品寿命特征的统计分析方法。在逐步Ⅰ型混合截尾下,讨论Pareto分布竞争失效产品恒定应力部分加速寿命试验的统计分析问题。文中给出了未知参数和加速因子的极大估计(MLE)和贝叶斯估计(BE)。利用Bootstrap方法及贝叶斯理论分别获得了参数和加速因子的Bootstrap置信区间(Stud-t)、最高后验概率密度置信区间(HPD)。最后运用Monte Carlo方法对各种估计的平均相对误差(ARE)、均方误差(MSE)及参数的置信区间进行了模拟计算,并讨论了样本量和分配比例对估计精度的影响。结果表明:参数的MLE和BE的ARE和MSE均随样本量增大而减小;而参数BE的ARE和MSE均小于MLE的ARE和MSE;样本分配比例和2种估计所对应的ARE和MSE呈负相关关系;在相同的置信度下,参数的HPD置信区间的长度小于Stud-t置信区间的长度。
关键词:    竞争失效    Pareto分布    恒定应力部分加速寿命试验    统计分析    蒙特卡罗方法    平均相对误差    均方误差    极大似然估计    Bayes估计    平方损失函数    置信区间   
Statistical Analysis for Partially Accelerated Life Tests with Competing Causes of Failure
Shi Yimin1, Shi Xiaolin2
1. School of Nature and Applied Sciences, Northwestern Polytechnical University, Xi'an 710072, China;
2. School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
Abstract:
Based on the failure data of accelerated life test to analyze the life characteristics of product, we need to use the relationship between product life and stress levels, that acceleration model. But in engineering practice, the accelerated model is not always known, such as the newly developed products. In order to solve this problem, a statistical analysis method is proposed to research the product life characteristics of competing failure based on the partially accelerated life test. Under Type-I progressive hybrid censoring, we discuss the statistical analysis for constant-stress partially accelerated life tests with competing failure modes and Pareto life data. The maximum likelihood estimation and Bayesian estimation of unknown parameters and acceleration factor are obtained. By using the Bootstrap and Bayes method, the Bootstrap confidence interval (Stud-t) and the highest posterior probability confidence interval (HPD) are presented. Finally, we use the Monte Carlo method to carry out the calculation of the average relative error(ARE) and the mean square error(MES) of various estimations and confidence interval of the unknown parameters. We analyze the influence of different sample sizes and distribution proportion on the accuracy of different estimation results. The calculation results, given in Table 1-Table 5, and their analysis show preliminarily that:(1) the AREs and the MESs of various estimations decrease with the samples size increase; (2) the AREs and the MESs of the BE are less than that of the MLE; (3) There is a negative correlation between the proportion of the sample distribution and the AREs and MSEs of two kinds estimates respectively; (4) at the same confidence level, the length of the HPD confidence interval for parameters less than that of the Stud-t confidence intervals.
Key words:    Competing causes of failure    Pareto distribution    constant-stress partially accelerated life tests    statistical analysis    Monte Carlo method    failure modes    the average relative error    mean square error    maximum likelihood estimation    Bayesian estimation    the square loss function    confidence intervals   
收稿日期: 2016-06-16     修回日期:
DOI:
基金项目: 国家自然科学基金(71401134、71571144、71171164)与陕西省自然科学基础研究计划(2015JM1003)及陕西省国际科技合作与交流计划项目(2016KW-033)资助
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作者简介: 师义民(1952-),西北工业大学教授、博士生导师,主要从事应用概率统计、可靠性理论及应用的研究。
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