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.
