三参数威布尔分布的可靠性研究

发布时间：2018-05-05 14:46

本文选题：可靠性评估 + 三参数威布尔分布　；参考：《河南科技大学》2014年硕士论文

【摘要】：随着科学技术的发展，对航空航天系统、重要设备及产品的可靠性要求越来越高。因此，能够准确迅速地评估系统及产品的可靠性已经显得至关重要。近年来，由于三参数威布尔分布广泛应用于失效数据建模，，对三参数威布尔分布可靠性评估已成为热点问题。可靠性评估主要包括参数估计、最优置信区间评估及假设检验。如何对三参数威布尔分布进行有效准确的可靠性评估将是本文研究的重点问题。本文提出了最小加权相对熵范数法和自助法进行三参数威布尔分布的可靠性评估。首先，将试验寿命数据向量代入三参数威布尔分布可靠性函数，得到了可靠性理论值向量。再根据Johnson或Nelson方法，对寿命数据进行非参数估计得到了可靠性经验值向量。基于可靠性经验值与理论值的相对差异信息，借助相对熵理论及范数理论，构建了6个最小加权相对熵准则来提取产品寿命可靠性试验中最优威布尔参数的信息向量。通过自助法抽样最优威布尔参数信息向量获得了大量生成信息向量，以模拟得到了参数概率密度函数。由参数的概率密度函数求解出了参数的估计真值及置信区间，即得到了三参数威布尔分布可靠性的估计真值函数及其最优置信区间函数。最后，通过三参数威布尔分布的估计真值函数及其置信区间函数交集的面积确定了假设检验中的否定域。模拟案例、直升机部件案例以及陶瓷材料案例表明，通过本文提出的最小加权相对熵范数法和自助法进行的可靠性评估能够反应可靠性试验中的实际情况。通过最小加权相对熵范数法和自助法、极大似然法、矩法及概率权重矩法、贝叶斯方法在参数评估应用上的对比，结果表明本文提出的最小加权相对熵范数法和自助法可靠性评估效果最优。采用三参数威布尔分布可靠性模型建模本文可靠性实验中收集的材料试样失效数据，用最小加权相对熵范数法和自助法对该模型进行可靠性评估。经可靠性研究表明得到的可靠性经验值向量与理论值向量相对差异较为明显，本次试验采集到的失效数据误差较大并且偏离了三参数威布尔分布。
[Abstract]:With the development of science and technology, the reliability requirements of aerospace systems, important equipment and products are becoming higher and higher. Therefore, it is very important to evaluate the reliability of systems and products accurately and quickly. In recent years, due to the wide application of three-parameter Weibull distribution in failure data modeling, the reliability evaluation of three-parameter Weibull distribution has become a hot issue. Reliability evaluation includes parameter estimation, optimal confidence interval evaluation and hypothesis test. How to evaluate the reliability of three-parameter Weibull distribution effectively and accurately will be the key problem in this paper. In this paper, the minimum weighted relative entropy norm method and the self-help method are proposed to evaluate the reliability of the three-parameter Weibull distribution. First, the experimental life data vector is substituted into the three-parameter Weibull distribution reliability function, and the reliability theory value vector is obtained. According to the Johnson or Nelson method, the reliability empirical value vector is obtained by nonparametric estimation of the life data. Based on the information of the relative difference between the reliability experience value and the theoretical value, six minimum weighted relative entropy criteria are constructed to extract the information vector of the optimal Weibull parameter in the reliability test of the product by using the relative entropy theory and the norm theory. A large number of generated information vectors are obtained by sampling the optimal Weibull parameter information vector by self-help method, and the parameter probability density function is obtained by simulation. The estimated true value and confidence interval of parameters are obtained from the probability density function of parameters, that is, the estimated true value function and the optimal confidence interval function of the reliability of three-parameter Weibull distribution are obtained. Finally, the negative domain in hypothesis testing is determined by the area of the intersection of the estimated truth function and its confidence interval function of the three-parameter Weibull distribution. The simulation cases, helicopter components cases and ceramic materials cases show that the reliability evaluation based on the least weighted relative entropy norm method and the self-help method presented in this paper can reflect the actual situation in the reliability test. The comparison between the minimum weighted relative entropy norm method and the self-help method, the maximum likelihood method, the moment method, the probability weight moment method and the Bayesian method in the parameter evaluation. The results show that the minimum weighted relative entropy norm method and the self-help method are optimal for reliability evaluation. Three parameter Weibull distribution reliability model is used to model the failure data of material samples collected in the reliability experiment in this paper. The reliability of the model is evaluated by the minimum weighted relative entropy norm method and the self-help method. The reliability study shows that the relative difference between the reliability empirical value vector and the theoretical value vector is obvious. The error of the failure data collected in this experiment is large and deviates from the three-parameter Weibull distribution.
【学位授予单位】：河南科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114.3

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