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

9714035 Shlaes本基金用于研究利用广义线性模型（GLIMs）处理非正态响应变量的统计技术。目前广泛使用的几乎所有实验设计技术都是基于这样的假设，即响应变量的误差为正态分布，方差恒定。然而，在许多现实世界和工业情况下，实验数据不符合这些假设。非正常响应的例子包括二项响应（1-0响应，缺陷数据比例），指数/威布尔响应（故障时间和生存时间）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（GLIMs）将响应变量的可疑分布与线性预测函数联系起来。在这项拨款中，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GLIMs的应用和改进的工业实验设计方法将进行研究。如果成功的话，这项研究的结果将导致分析非正常数据的统计技术的改进。此外，可以开发改进的实验设计技术，利用有关误差真实潜在分布的知识。采用精心设计的统计测试方法进行工业实验，对于优化流程、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，最大限度地从有限的实验试验中获得信息。

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.