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

小行星9714035 该补助金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。 几乎所有的实验设计技术在今天广泛使用的基础上的假设，即响应变量的误差是正态分布的恒定方差。 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。 非正态响应的示例包括二项响应（1-0响应、缺陷数据比例）、指数/威布尔响应（失效时间和存活时间）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关联函数相关联。 预测功能 在这项补助金中，将研究在工业实验中实施GLIM的技术。 将受益于GLIM应用和改进的工业实验设计方法的具体工业应用 将进行调查。 如果成功的话，这项关于GLIM的研究结果将有助于改进分析非正态数据的统计技术。此外，可以利用关于误差的真实潜在分布的知识来改进实验设计技术。 开发使用精心设计的统计测试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。 产品. 这些技术将允许更有效的实验，最大限度地从有限数量的实验性试验中获得的信息。

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.