本文選題：可靠性評(píng)估 + 三參數(shù)威布爾分布　； 參考：《河南科技大學(xué)》2014年碩士論文

【摘要】：隨著科學(xué)技術(shù)的發(fā)展，對(duì)航空航天系統(tǒng)、重要設(shè)備及產(chǎn)品的可靠性要求越來(lái)越高。因此，能夠準(zhǔn)確迅速地評(píng)估系統(tǒng)及產(chǎn)品的可靠性已經(jīng)顯得至關(guān)重要。近年來(lái)，由于三參數(shù)威布爾分布廣泛應(yīng)用于失效數(shù)據(jù)建模，，對(duì)三參數(shù)威布爾分布可靠性評(píng)估已成為熱點(diǎn)問(wèn)題�？煽啃栽u(píng)估主要包括參數(shù)估計(jì)、最優(yōu)置信區(qū)間評(píng)估及假設(shè)檢驗(yàn)。如何對(duì)三參數(shù)威布爾分布進(jìn)行有效準(zhǔn)確的可靠性評(píng)估將是本文研究的重點(diǎn)問(wèn)題。 本文提出了最小加權(quán)相對(duì)熵范數(shù)法和自助法進(jìn)行三參數(shù)威布爾分布的可靠性評(píng)估。首先，將試驗(yàn)壽命數(shù)據(jù)向量代入三參數(shù)威布爾分布可靠性函數(shù)，得到了可靠性理論值向量。再根據(jù)Johnson或Nelson方法，對(duì)壽命數(shù)據(jù)進(jìn)行非參數(shù)估計(jì)得到了可靠性經(jīng)驗(yàn)值向量�；诳煽啃越�(jīng)驗(yàn)值與理論值的相對(duì)差異信息，借助相對(duì)熵理論及范數(shù)理論，構(gòu)建了6個(gè)最小加權(quán)相對(duì)熵準(zhǔn)則來(lái)提取產(chǎn)品壽命可靠性試驗(yàn)中最優(yōu)威布爾參數(shù)的信息向量。通過(guò)自助法抽樣最優(yōu)威布爾參數(shù)信息向量獲得了大量生成信息向量，以模擬得到了參數(shù)概率密度函數(shù)。由參數(shù)的概率密度函數(shù)求解出了參數(shù)的估計(jì)真值及置信區(qū)間，即得到了三參數(shù)威布爾分布可靠性的估計(jì)真值函數(shù)及其最優(yōu)置信區(qū)間函數(shù)。最后，通過(guò)三參數(shù)威布爾分布的估計(jì)真值函數(shù)及其置信區(qū)間函數(shù)交集的面積確定了假設(shè)檢驗(yàn)中的否定域。模擬案例、直升機(jī)部件案例以及陶瓷材料案例表明，通過(guò)本文提出的最小加權(quán)相對(duì)熵范數(shù)法和自助法進(jìn)行的可靠性評(píng)估能夠反應(yīng)可靠性試驗(yàn)中的實(shí)際情況。通過(guò)最小加權(quán)相對(duì)熵范數(shù)法和自助法、極大似然法、矩法及概率權(quán)重矩法、貝葉斯方法在參數(shù)評(píng)估應(yīng)用上的對(duì)比，結(jié)果表明本文提出的最小加權(quán)相對(duì)熵范數(shù)法和自助法可靠性評(píng)估效果最優(yōu)。 采用三參數(shù)威布爾分布可靠性模型建模本文可靠性實(shí)驗(yàn)中收集的材料試樣失效數(shù)據(jù)，用最小加權(quán)相對(duì)熵范數(shù)法和自助法對(duì)該模型進(jìn)行可靠性評(píng)估。經(jīng)可靠性研究表明得到的可靠性經(jīng)驗(yàn)值向量與理論值向量相對(duì)差異較為明顯，本次試驗(yàn)采集到的失效數(shù)據(jù)誤差較大并且偏離了三參數(shù)威布爾分布。
[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.
【學(xué)位授予單位】：河南科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TB114.3

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