Mathematical Sciences: "Nonlinear Modeling of Spatially Correlated Data: Preliminary Investigations"

数学科学：“空间相关数据的非线性建模：初步研究”

• 批准号: 9631877
• 负责人: Jacqueline Hughes-Oliver
• 金额: $ 1.8万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-15 至 1998-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9631877&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Modeling; Spatially

Jacqueline M. Hughes-Oliver North Carolina State University Data collection in the semiconductor industry is such that repeated measurements --- obtained over a spatial grid on a single wafer --- are the norm, not the exception. Following this proposed planning period, the projected research goal is the development of methodological advances for nonlinear modeling of spatially correlated data with nonstationary, nonnormal errors. This work is well motivated by two real-life applications, which both indicate immediate need for these advances. A major result of research on the analysis of repeated measurements is the discovery that careful representation of the correlation structure is not necessary, provided the number of experimental units far exceeds the number of repeated measurements. The cost of wafers in the semiconductor industry, however, prohibits collection of data for very many wafers. Hence, careful representation of the possibly nonstationary error covariance structure must be undertaken. This constitutes the first of the planning activities. Specific modeling and estimation techniques must also be investigated in light of the (new) correlation structures. These constitute additional planning activities. Realistic modeling of these semiconductor processes require relaxing the assumption of normality, and a willingness to consider nonlinear models. Planning activities include preliminary investigations of the complications arising from these generalities. The final activity is the development of the regular NSF proposal.

Jacqueline M. Hughes-Oliver北卡罗来纳州立大学的半导体行业数据收集是如此，重复的测量值 - 通过单个晶圆上的空间网格获得的重复测量是常态，不是例外。 在此拟议的计划期之后，预计的研究目标是开发与非组织性，非正常错误的空间相关数据非线性建模的方法学进步。 这项工作是由两种现实生活应用的充分动机，这两者都表明对这些进步的需求立即需要。 对重复测量分析的研究的主要结果是，只要实验单元的数量远远超过重复测量的数量，就发现无需仔细表示相关结构。 但是，半导体行业的晶圆成本禁止许多晶片的数据收集。 因此，必须仔细代表可能的非组织误差协方差结构。 这构成了第一个计划活动。 还必须根据（新的）相关结构来研究特定的建模和估计技术。 这些构成了其他计划活动。 这些半导体过程的现实建模需要放松正态性的假设，并愿意考虑非线性模型。 计划活动包括对这些概括引起的并发症的初步调查。 最终活动是常规NSF提案的发展。