本文選題：應(yīng)力-強(qiáng)度模型 + 瑞利分布�。� 參考：《吉林大學(xué)》2017年碩士論文

【摘要】：應(yīng)力-強(qiáng)度模型在機(jī)械裝置或電器元件的可靠性評(píng)估中應(yīng)用廣泛,其中,應(yīng)力定義為引起元件或裝置失效的載荷,強(qiáng)度定義為元件或裝置在承受外部載荷時(shí)能滿意地完成規(guī)定任務(wù)而沒有失效的能力,可靠性參數(shù)定義為影響失效的應(yīng)力沒有超過控制失效的強(qiáng)度的概率.本文研究的是應(yīng)力和強(qiáng)度均服從瑞利分布且?guī)в挟惓Ｖ档膽?yīng)力-強(qiáng)度模型的參數(shù)估計(jì)問題,用數(shù)學(xué)語言來表述,即研究可靠性參數(shù)R=P(YX)的估計(jì)問題,其中變量Y和X是相互獨(dú)立的,變量Y代表應(yīng)力,服從參數(shù)是λ的瑞利分布,變量X代表強(qiáng)度,樣本中帶有2個(gè)異常值,服從參數(shù)是θ和β的瑞利分布.在國外學(xué)者對(duì)帶有異常值的應(yīng)力-強(qiáng)度模型的研究中,對(duì)參數(shù)R的估計(jì)基本以經(jīng)典估計(jì)方法為主,運(yùn)用貝葉斯估計(jì)方法的研究文章相對(duì)較少,國內(nèi)學(xué)者對(duì)應(yīng)力-強(qiáng)度模型的研究基本不涉及試驗(yàn)樣本帶有異常值的情況.在本文中,將運(yùn)用貝葉斯估計(jì)的方法來研究參數(shù)R=P(YX)的估計(jì)問題,相較于經(jīng)典方法把未知參數(shù)看作是確定的常數(shù),貝葉斯估計(jì)把未知參數(shù)看作是隨機(jī)變量,利用樣本分布和先驗(yàn)分布的全部信息來進(jìn)行統(tǒng)計(jì)推斷.在本文中,參數(shù)R的貝葉斯估計(jì)將會(huì)在平方損失,0-1損失和對(duì)稱熵?fù)p失這三種損失函數(shù)下給出,并根據(jù)推導(dǎo)得到的結(jié)果進(jìn)行估計(jì)值偏差的數(shù)值模擬,然后比較這三種損失函數(shù)下得到的貝葉斯估計(jì)值的估計(jì)效果,最后得出結(jié)論,運(yùn)用貝葉斯估計(jì)的方法來研究帶有異常值的應(yīng)力-強(qiáng)度模型行之有效.
[Abstract]:The stress-strength model is widely used in the reliability evaluation of mechanical or electrical components, in which the stress is defined as the load that causes the failure of the components or devices.Strength is defined as the ability of components or devices to perform specified tasks satisfactorily without failure under external load. The reliability parameter is defined as the probability that the stress affecting failure does not exceed the strength of control failure.In this paper, we study the parameter estimation of stress-strength model with Rayleigh distribution and outliers, which is expressed by mathematical language, that is, the estimation of reliability parameter RPX.The variables Y and X are independent of each other, the variable Y represents the stress, the subordinate parameter is the Rayleigh distribution of 位, the variable X represents the strength, the sample has two abnormal values, and the subordinate parameter is the Rayleigh distribution of 胃 and 尾.In the research of stress-strength model with outliers abroad, the estimation of parameter R is mainly based on classical estimation method, but there are few articles using Bayesian estimation method.The research on the stress-strength model by domestic scholars basically does not involve the case where the test sample has outliers.In this paper, the Bayesian estimation method is used to study the parameter estimation problem. Compared with the classical method, the unknown parameter is regarded as a definite constant, and the unknown parameter is regarded as a random variable in Bayesian estimation.All the information of sample distribution and prior distribution are used for statistical inference.In this paper, the Bayesian estimation of parameter R will be given under the three loss functions of squared loss 0-1 loss and symmetric entropy loss.The results of Bayesian estimation under these three loss functions are compared, and the conclusion is drawn that it is effective to use Bayesian estimation to study the stress-strength model with outliers.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.8

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