Dennis Gilliland and Roy EricksonDept. of Statistics and Probability
This proposal asks for support for a computer laboratory consisting of an instructor's workstation, slave monitors to display the instructor's screen, and sixteen workstations for students. Each workstation will accommodate two students.
The basic premise that underpins this proposal is that instruction is improved by having teaching faculty take advantage of a classroom which has the capacity for demonstration of statistical ideas on computers and the subsequent interaction of students with the computers. The interaction may take place in class or after class depending upon the wishes of the instructor. The success of the teaching laboratory will depend on the ability of the Department and the professors to provide appropriate demonstrations and computer experiences for the students.
Basic courses will be improved by incorporating already developed software into the teaching models. The basic notion of variability will be demonstrated through random selections from specific distributions. The effect of sample size and the central limit theorem will be illustrated. Whereas these courses have typically taught large sample methods for calculating confidence interval estimates, software that enables evaluation of exact confidence intervals will be illustrated and may be made available to students. The bootstrap method can be incorporated into courses as a modern method made accessible only through the use of computers.
The statistics course for quality and productivity improvement will provide a key test for the proposed teaching laboratory. The principal investigator is responsible for this course and has three interactive computer teaching modules in preliminary stages of development for use in the course, once the teaching laboratory is equipped.
One module concerns capability analysis for multi-dimensional characteristics. A series developed by the principal investigator is programmed to handle the two-dimensional case. Some companies use software for two-dimensional capability analyses that depends upon less efficient numerical integration or Monte Carlo methods for computations.
The second illustrates the fundamentals of elementary control charting. Students choose from several production processes, make runs, and perform capability analyses. Some processes are in control, others have trends in mean, others have trends in variance, and others are chaotic. Another feature allows for the simulation of specified in-control and out-of-control (e.g., drifting mean or variance) processes to estimate operating characteristics such as Average Run Length under various charting techniques and control systems.
The third module illustrates the importance of organized experimentation, such as in a 2^3 factorial. Students choose from several processes with three predictor variables (factors) and are asked to explore the response surface. The purpose is to find levels of the predictor variables for a production run with a specified target for the output. Before having had lectures and readings on the design of experiments, students are given the opportunity to explore the response surface with up to 16 observations. They generally do inefficient, one-at-a-time experimentation. A production run of 100 parts is scored on the basis of CP index, CPK index, percentage of parts out of tolerance, and Taguchi loss. After lectures on the design of experiments, students interact with the processes more intelligently and see the immediate impact of their education on the choices of factor levels for their runs. An important lesson is learned later when 2-level fractional factorials work well on processes that have little curvature in their response surfaces and fail when significant curvature exists.