几何分布下含屏蔽数据复杂系统可靠度估计
发布时间：2019-05-18 22:28
【摘要】：系统由元件组成，因此元件的可靠性必然直接决定系统的可靠性。在对系统进行可靠性试验时，通常要收集系统寿命和系统失效原因这两项数据，来对系统的可靠性进行分析。然而在实际的试验过程中，往往由于设备或记录等客观因素，可能无法确切地观测到系统失效的原因，即造成系统失效的元件不能确定，而只能得到系统寿命数据和可能造成系统失效的元件的集合，这类试验数据称为屏蔽数据。 另外，也可能受试验成本等客观因素的限制，只能有少量的样本参与试验，这时由于样本信息较少，通常采用Bayes方法进行分析。目前利用Bayes方法对一般的由最小路径描述的复杂系统可靠性进行的研究分析并不多见。 本文基于屏蔽数据，在假定元件寿命服从几何分布的情况下，利用极大似然方法与Bayes方法，对由最小路径描述且元件相互独立的一般复杂系统的可靠性进行了研究。得到如下结果： 1.基于屏蔽数据，针对由最小路径描述的一般复杂系统，在元件相互独立且服从几何分布的假定下，给出了元件参数的极大似然估计，，进而得到元件可靠度的估计，以及平方损失下系统可靠度的估计。 2.在逐步增加II型截尾样本下，结合一般复杂系统在元件寿命服从相同及不同参数几何分布下的可靠度表达式，利用Bayes方法，得到平方损失下系统的可靠度Bayes估计及EB估计。
[Abstract]:The system is composed of components, so the reliability of the components must directly determine the reliability of the system. In the reliability test of the system, it is usually necessary to collect the data of system life and system failure to analyze the reliability of the system. However, in the actual test process, it may not be possible to accurately observe the causes of system failure due to objective factors such as equipment or records, that is, the components that cause the system failure can not be determined. However, only the system life data and the set of components that may cause system failure can be obtained, and this kind of test data is called shielded data. In addition, it may also be limited by objective factors such as test cost, and only a small number of samples can participate in the experiment. At this time, because of the lack of sample information, Bayes method is usually used for analysis. At present, it is rare to use Bayes method to study and analyze the reliability of complex systems described by the minimum path. Based on shielded data and assuming that the life of components obeys geometric distribution, the reliability of general complex systems described by minimum path and independent of components is studied by using maximum likelihood method and Bayes method. The following results are obtained: 1. Based on the shielded data, for the general complex system described by the minimum path, the maximum likelihood estimation of the component parameters is given under the assumption that the components are independent of each other and subject to the geometric distribution, and then the estimation of the component reliability is obtained. And the estimation of system reliability under square loss. 2. Under the condition of increasing the type II truncated sample step by step, combined with the reliability expression of the general complex system under the same component life and different parameter geometric distribution, the reliability Bayes estimation and EB estimation of the system under square loss are obtained by using Bayes method.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1;N941.4
本文编号：2480387
[Abstract]:The system is composed of components, so the reliability of the components must directly determine the reliability of the system. In the reliability test of the system, it is usually necessary to collect the data of system life and system failure to analyze the reliability of the system. However, in the actual test process, it may not be possible to accurately observe the causes of system failure due to objective factors such as equipment or records, that is, the components that cause the system failure can not be determined. However, only the system life data and the set of components that may cause system failure can be obtained, and this kind of test data is called shielded data. In addition, it may also be limited by objective factors such as test cost, and only a small number of samples can participate in the experiment. At this time, because of the lack of sample information, Bayes method is usually used for analysis. At present, it is rare to use Bayes method to study and analyze the reliability of complex systems described by the minimum path. Based on shielded data and assuming that the life of components obeys geometric distribution, the reliability of general complex systems described by minimum path and independent of components is studied by using maximum likelihood method and Bayes method. The following results are obtained: 1. Based on the shielded data, for the general complex system described by the minimum path, the maximum likelihood estimation of the component parameters is given under the assumption that the components are independent of each other and subject to the geometric distribution, and then the estimation of the component reliability is obtained. And the estimation of system reliability under square loss. 2. Under the condition of increasing the type II truncated sample step by step, combined with the reliability expression of the general complex system under the same component life and different parameter geometric distribution, the reliability Bayes estimation and EB estimation of the system under square loss are obtained by using Bayes method.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1;N941.4
【参考文献】
相关期刊论文 前3条
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2 刘英;师义民;王婷婷;;基于屏蔽数据的部件可靠性指标的贝叶斯估计[J];数理统计与管理;2010年05期
3 师义民;寇开昌;周巧娟;;定数双截尾样本下k/N(G)系统可靠性指标的经验Bayes估计[J];数学的实践与认识;2007年01期
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