發(fā)布時間：2018-12-18 18:20

【摘要】：隨著時代的發(fā)展和科技的進步,人們對產(chǎn)品質(zhì)量及可靠性的要求越來越高.很多新的分析可靠性的技術(shù)和數(shù)據(jù)處理的方法不斷出現(xiàn),使可靠性統(tǒng)計面臨著許多新的問題.指數(shù)分布、Weibull分布、極值分布、Gamma分布等一些可靠性統(tǒng)計模型已經(jīng)被很多專家學(xué)者研究并利用到實際生活中.但每一種可靠性統(tǒng)計模型并不是對所有類型的數(shù)據(jù)模擬效果都是好的,所以我們需要找到適應(yīng)效果更好的分布對壽命數(shù)據(jù)進行模擬分析.本文針對上述問題展開討論:第一,逆高斯分布和Weibull分布是可靠性理論中的兩種重要的壽命分布模型,而T-X family方法是近年來拓展新分布中應(yīng)用較廣的一種方法.故而本文考慮由逆高斯分布與Weibull分布出發(fā),利用T-X family的方法構(gòu)建一個新的壽命分布,稱之為拓展的逆高斯分布(EIG).我們討論了它的一些基本性質(zhì),如密度曲線類型,危險率函數(shù)曲線、r階中心距及矩母函數(shù),偏度和峰度,隨機序和剩余壽命等.第二,基于所產(chǎn)生的新分布,我們還研究了它的參數(shù)估計問題.討論了新分布所含參數(shù)的極大似然估計和近似置信區(qū)間.針對已有數(shù)據(jù),利用TTT轉(zhuǎn)換分析數(shù)據(jù)危險率的形狀,并對數(shù)據(jù)擬合的可行性作了分析.進而用EIG分布模擬真實數(shù)據(jù),進行K-S擬合檢驗,分析討論結(jié)果.第三,近年來,缺失和退化數(shù)據(jù)處理方面的應(yīng)用研究大量出現(xiàn),使得可靠性理論得到迅速發(fā)展.疲勞數(shù)據(jù)常常有限,尤其是從節(jié)約費用時間角度上,即使使用特殊的疲勞試驗方法(加速壽命試驗),也得不到完整的樣本數(shù)據(jù),得到的大多是截尾數(shù)據(jù).因此有必要發(fā)展截尾數(shù)據(jù)下參數(shù)的統(tǒng)計推斷問題.2009年Kundu提出一個自適應(yīng)II型逐次截尾方案,較Ⅰ型和Ⅱ型逐次截尾方案,節(jié)省了總試驗的時間和測試失效單元的成本,提高了統(tǒng)計分析的效率,解決了I、II型截尾方案的許多缺點.本文將基于自適應(yīng)II型逐次截尾樣本,對新分布的參數(shù)進行極大似然估計,并運用真實數(shù)據(jù)進行模擬研究.
[Abstract]:With the development of the times and the progress of science and technology, the demand of product quality and reliability is higher and higher. Many new techniques for reliability analysis and data processing are emerging, which make reliability statistics face many new problems. Some reliability statistical models, such as exponential distribution, Weibull distribution, extremum distribution, Gamma distribution and so on, have been studied by many experts and scholars and used in real life. However, each reliability statistical model is not good for all types of data simulation, so we need to find a better distribution of adaptive effect to simulate the life data. In this paper, the following problems are discussed: first, inverse Gao Si distribution and Weibull distribution are two important life distribution models in reliability theory, and T-X family method is a widely used method to expand new distribution in recent years. Therefore, in this paper, starting from the inverse Gao Si distribution and Weibull distribution, a new life distribution is constructed by using T-X family method, which is called the extended inverse Gao Si distribution (EIG). Some basic properties are discussed, such as density curve type, risk rate function curve, r order center distance and moment generating function, skewness and kurtosis, random order and residual life, etc. Secondly, based on the new distribution, we also study the parameter estimation problem. The maximum likelihood estimation and approximate confidence interval of the parameters contained in the new distribution are discussed. According to the existing data, the shape of data risk rate is analyzed by TTT transform, and the feasibility of data fitting is analyzed. EIG distribution is used to simulate the real data, K-S fitting test is carried out, and the results are analyzed. Thirdly, in recent years, applications of missing and degenerate data processing have emerged in large numbers, which makes the reliability theory develop rapidly. Fatigue data are often limited, especially from the point of view of saving cost and time. Even if special fatigue test method (accelerated life test) is used, the complete sample data can not be obtained, and most of the data obtained are truncated data. Therefore, it is necessary to develop the statistical inference of parameters under censored data. In 2009, Kundu proposed an adaptive II successive truncation scheme, which saves the total test time and the cost of the test failure unit compared with the successive truncation schemes of type 鈪，

本文編號：2386291