混合分布模型中序性质和维修策略的一些研究

项目名称： 混合分布模型中序性质和维修策略的一些研究

项目编号： No.11501162

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 凌晓亮

作者单位： 河北科技大学

项目金额： 18万元

中文摘要： 混合分布模型广泛应用于可靠性理论、 生存分析等概率统计的相关领域。本项目研究混合分布模型中的序性质和维修策略问题。. 首先，我们研究在随机时间处剩余寿命和休止时间的一些随机比较性质和年龄性质。考虑在随机环境下工作系统的n个元件，我们研究随机环境对这n个元件的多元剩余寿命和多元休止时间的影响。. 其次，我们研究具有随机次数维修的可修系统中的一些随机比较和年龄性质问题。并且，我们考虑当元件来自异质总体时，如何定义和研究最小维修。. 最后，我们考虑退化系统在连续监视情形下基于状态的维修模型。在维修后，系统状态都是随机分布的。基于每次维修后的状态，我们研究一系列维修活动之间的序性质和老化关系。. 本项目对于更好理解混合分布模型的构造机理有重要的意义，也为混合分布模型在可靠性理论和生存分析中的应用奠定一定的理论基础。

中文关键词： 最小维修；混合分布；剩余寿命；随机比较；退化系统

英文摘要： Mixture distribution model has been widely used in reliability theory, survival analysis and some other areas related to probability and statistics. This project studies ordering properties and maintenance policy of mixture distribution model. . Firstly, we study some stochastic comparisons and aging properties of residual lifetimes and inactivity times at random time. Consider n components of a system which operates in a random environment, we study the influence of random environment on multivariate residual lifetimes and multivariate inactivity times of these component . . Secondly, we study some stochastic comparisons and aging properties of the repairable system with minimal repairs whose number of repairs is a random variable. Moreover, we consider how to define and study minimal repairs for components in heterogeneous population. . Lastly, we consider condition based maintenance model for degrading system under continuous monitoring. After maintenance, the states of the system are randomly distributed. We study the ordering and aging relationship among a sequence of maintenance actions based the random state after maintenance. . The research on this topic is of great significance for a better understanding of the mechanism of the mixture distribution model, it also provides some theory basis for application of mixture distribution model in reliability theory and survival analysis.

英文关键词： Minimal repair;Mixture distribution;Residual lifetime;Stochastic comparison;Degrading system