Mathematical Sciences: Stochastic Processes Applied to Control, Reliability and Replacement

数学科学：应用于控制、可靠性和替换的随机过程

• 批准号: 8614888
• 负责人: Erhan Cinlar
• 金额: $ 4万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-10-15 至 1990-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8614888&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stochastic; Processes; Applied

The proposal addresses three major topics. The first one is that of modeling inter fitting circles or cylinders by random fields. This is necessary since the success of the operation of machines involving such components depends on the smoothness of the surfaces that are finer than what can be achieved by the manufacturing processes. The stochastic geometry and analysis of such spaces will be investigated. The second topic of the reliability and maintenance of complex devices will be investigated under the assumed dependence of the components, which will make the resulting theories more practical and applicable. The third topic will extend the idea of markovian dependence to one with infinite but exponentially fading memory.

该提案涉及三个主要议题。 第一个是 即通过随机拟合圆或圆柱来建模兴趣 领域的 这是必要的，因为 涉及这些部件的机器取决于 表面比可以实现的更精细， 制造工艺。 随机几何与分析 将对这些空间进行调查。 第二个主题是 复杂设备的可靠性和维护 在假设的组分依赖性下研究， 这将使所产生的理论更加实用， 适用因 第三个主题将扩展马尔可夫的思想 依赖于一个无限但指数衰减的记忆。