兰州大学机构库 >数学与统计学院
基于II型删失数据下单调关联系统的统计推断
Alternative TitleStatistical inference for type II censored lifetime data of coherent system
王瑾
Thesis Advisor焦桂梅
2016-05-15
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword系统最小特征量 极大似然估计法 最优线性无偏估计法 最优线性无偏估计近似法 极大似然估计近似法
Abstract本文将序统计量的概率密度函数表达式与引入的系统最小特征量结合,得到系统的概率密度函数和可靠度函数,并用极大似然估计法(MLE)、最优线性无偏估计法(BLUE)估计部件服从位置-尺度分布族的分布参数,以工业上最为常用的Weibull分布为例,引入Tayor展开的思想,将上述两种方法转变为最优线性无偏估计近似法(ABLUE)和极大似然估计近似法(AMLE),重新对部件分布参数进行估计。最后用以上四种方法对某一系统在不同截尾数下分别进行参数估计,并用蒙特卡洛法模拟探讨了不同系统(即系统结构不同、系统部件数不同)、不同方法在不同截尾数下参数估计的情况。 研究表明,不同系统在截尾数逐渐增大时,各方法的估计值均越接近于真实值,且在同一截尾数下影响估计结果的主要是系统最小特征量,但没有证据表明系统部件数和系统最小特征量与最终的估计结果误差有明显的正/反比关系或其他联系。本文研究的四种方法没有哪一种是绝对最优的,要针对具体系统具体分析,但研究过程和结果显示ABLUE法在实际操作中最为方便,应优先被考虑。总的来说,系统部件数对估计结果没有什么明显影响,而系统最小特征量对参数估计值有重要影响,当截尾数越大时,该四种方法的差异就越小且估计值均趋近于真实值。
Other AbstractSeveral components can constitute a system in a certain way while each component in the system of life distribution parameters directly affects the reliability of the system. The research can be divided into two types by different sources of life data: component life data is known; component life is unknown. Most of the existing research is the first case,namely, using a method for different types of distribution in the life of existing data to estimate the distribution parameter. The second case is less. Especially due to the experimental conditions, component life can not be obtained while life data of the entire system can be obtained, namely using the system lifetime data to estimate component distribution parameters. This type of study is rare. Thus, the dissertation targets on the life of the system, introduces the concept of system minimum signature, combines the knowledge of order statistics and further studies coherent systems based on type II censored data location-scale distribution family parameter estimation problem. In this dissertation, the probability density function of order statistics, combined with system minimum signature, is to obtain the probability density function and the reliability function of the system. The author uses the maximum likelihood estimation (MLE) method, the best linear unbiased estimation (BLUE) to estimate the distribution parameters of the components subject to the location-scale distribution family, taking the most commonly used Weibull distribution in industry as an example. The idea of Tayor expansion is introduced. The above mentioned two methods are transformed into approximation of best linear unbiased estimation (ABLUE) and approximation of maximum likelihood estimate (AMLE), re-estimating component distribution parameters. Finally, a system parameters are estimated in the different censoring numbers by the above mentioned four methods, and explored by Monte Carlo simulation method in different systems (namely, structurally different systems, different number of system components), different ways at different censoring numbers parameters be estimated. Studies have shown that when the censoring number of different systems increases, the estimated value of each method are closer to the true value, and the main effect of the estimated results is the system minimum signature under same censoring number. However, there is no evidence that the number of system components and the system minimum signature hav...
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Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225226
Collection数学与统计学院
Recommended Citation
GB/T 7714
王瑾. 基于II型删失数据下单调关联系统的统计推断[D]. 兰州. 兰州大学,2016.
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