Research Planning Grant: Implementation of Generalized Linear Models for Designed Experiments with Nonnormal Response Variables

9714035 Slaes这笔赠款为通过使用广义线性模型(GLIM)处理非正态响应变量的统计技术的研究提供资金。今天广泛使用的几乎所有的实验设计技术都是基于这样的假设，即响应变量具有正态分布的误差且具有恒定的方差。然而，在许多现实世界和工业情况下，实验数据无法满足这些假设。非正态响应的例子包括二项响应(1-0响应，缺陷数据的比例)、指数/威布尔响应(故障时间和存活时间)和泊松响应(计数数据，缺陷数量)。通过使用数学链接函数，广义线性模型(GLIM)将响应变量的可疑分布与线性预测函数相关联。在这笔赠款中，将研究在工业实验中实施GLIM的技术。具体的工业应用将受益于GLIM的应用和工业实验设计的改进方法。如果成功，这项关于Glims的研究结果将导致分析非正态数据的统计技术得到改进。此外，可以开发改进的实验设计技术，利用关于误差的真实潜在分布的知识。使用精心设计的统计检验方法进行工业试验，对于优化工艺、有效利用资源和提高产品质量至关重要。这些技术将允许更有效的实验，最大限度地利用从有限数量的实验试验中获得的信息。

9714035 Shlaes This grant provides funding for the investigation of statistical techniques for dealing with nonnormal response variables through the use of generalized linear models (GLIMs). Almost all of the experimental design techniques in wide use today are based on the assumptions that the response variables have errors that are normally distributed with a constant variance. However, in many real-world and industrial situations, experimental data fails to meet these assumptions. Examples of nonnormal responses include binomial responses (1-0 responses, proportion defective data), exponential/Weibull responses (time to failure and survival times) and Poisson responses (count data, number of defects). Through the use of a mathematical link function, generalized linear models (GLIMs) relate the suspected distribution of the response variable to a linear prediction function. In this grant, techniques for the implementation of GLIMs in industrial experimentation will be examined. Specific industrial applications that would benefit from the application of GLIMs and improved methods for the design of industrial experiments will be investigated. If successful, the results of this research on GLIMs will lead to improved statistical techniques for analyzing nonnormal data. In addition, improved experimental design techniques which exploit the knowledge about the true underlying distribution of the errors can be developed. Industrial experimentation using carefully designed statistical test methods is vital to the optimization of processes, efficient utilization of resources, and improvement in the quality of products. These techniques will permit more efficient experimentation maximizing the information gained from a limited number of experimental trials.