Dealing With Variation In Measurements & Processes: Experiments For An Undergraduate Laboratory
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Dealing With Variation In Measurements & Processes: Experiments For An Undergraduate Laboratory Linda Vanasupa1, Heather Smith2 California Polytechnic State University, San Luis Obispo, California 1 Materials Engineering Department, 2Statistics Department Stacy Gleixner, Greg Young, Emily Allen San Jose State University, San Jose, California Department of Chemical and Materials Engineering Abstract Being able to obtain and analyze quantitative data are an essential components of any undergraduate education in science or engineering. At the most basic level, this begins with characterizing the measurement system using proper statistical techniques. Although most undergraduates in the sciences and engineering are required to take a course in statistics, the knowledge gained in the statistics course does not always find its way into practice. In this paper we will present 4 experimental modules that will enable the student to: 1. Assess the precision of a measurement system; 2. Determine if the system is stable with respect to a number of variables; 3. Quantify the amount of variation that exists within a particular sample; 4. Quantify the amount of variation from sample to sample (i.e., process variation). Our modules were applied to the measurement of silicon dioxide thickness from an oxidation process. However, they generally apply to any process that involves measuring a physical quantity. Assessing these sources of variation in a process form the foundation for more advanced techniques such as process control and experimental design. INTRODUCTION The ability to apply mathematics is recognized as a necessary skill for engineers [1]. Both engineers and scientists often use numerical data to make decisions. The data is often in the form of a measured quantity. As a result, it is essential for the engineer/scientist to clearly understand the measurement system—its precision and stability. It is also important for them to be able to quantify the stability of a process (e.g., a heat-treating process) and identify whether a process is stable. In industry, control charts are common tools used to quantify the variation resulting from a process and to monitor the stability of the process. This requires that students apply basic mathematics. Although undergraduate engineers and scientists often develop the ability to deal with data in a course on statistics, they are not always able to apply their understanding in the laboratory setting. The four laboratory exercises that we’ve developed are intended to address the need for students to have an opportunity to apply their mathematics knowledge in the context of their engineering major. In this paper, we discuss the specific goals of the modules, the details of the activities and the results of their implementation. OVERVIEW Our specimens consisted of silicon dioxide films grown on silicon wafers (-Silicon, 100cm diameter wafers). The oxidation process was conducted by the students in the context of a Microelectronics Processing Laboratory. The oxide thickness was the quantity
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