竞争失效产品部分加速寿命试验的统计分析

发布时间：2018-04-17 13:40

本文选题：竞争失效 + Pareto分布　；参考：《西北工业大学学报》2017年01期

【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。
[Abstract]:Based on the failure data of accelerated life test, it is necessary to use the relationship between product life and stress level to make statistical analysis of product life characteristics.But in engineering practice, acceleration models are not always known, such as newly developed products.In order to solve this problem, a statistical analysis method is proposed to study the life characteristics of competitive failure products by using partial accelerated life test.In this paper, the statistical analysis of constant stress partial accelerated life test of Pareto distributed competitive failure products is discussed under the condition of type I mixed truncation.In this paper, we give the maximum estimators of unknown parameters and acceleration factors (MLEs) and Bayesian estimators.By using Bootstrap method and Bayesian theory, the Bootstrap confidence interval of parameters and acceleration factors is obtained, and the maximum posterior probability density confidence interval is obtained.Finally, Monte Carlo method is used to simulate the mean relative error and the confidence interval of the parameters, and the effects of sample size and distribution ratio on the estimation accuracy are discussed.The results show that the ARE and MSE of the parameter MLE and be decrease with the increase of sample size, while the ARE and MSE of parameter be are smaller than those of MLE, and the ratio of sample distribution is negatively correlated with the ARE and MSE corresponding to the two estimates.The length of the HPD confidence interval of the parameter is smaller than that of the Stud-t confidence interval.
【作者单位】：西北工业大学理学院;西安邮电大学电子工程学院;
【基金】：国家自然科学基金(71401134、71571144、71171164) 陕西省自然科学基础研究计划(2015JM1003) 陕西省国际科技合作与交流计划项目(2016KW-033)资助
【分类号】：O213.2

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