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Description
The concept of distribution is one of the core ideas of probability theory and inferential statistics, if not the core idea. Many introductory statistics textbooks pay lip service to stochastic/random processes but how do students think about these processes? This study sought to explore what understandings of stochastic process students develop as they work through materials intended to support them in constructing the long-run behavior meaning for distribution.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.
My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.
ContributorsHatfield, Neil (Author) / Thompson, Patrick (Thesis advisor) / Carlson, Marilyn (Committee member) / Middleton, James (Committee member) / Lehrer, Richard (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2019
Description
This paper explores the consequences of cleaning rescue ropes with common disinfectants and cleansers in order to assess their usability in cleaning ropes contaminated with blood borne pathogens. Using a modified version of an industry-standard testing procedure and in-depth statistical analysis, it characterizes the effect each chemical has on the mechanical properties of the rope. The experiment measured the strength and elastic properties of rope core fibers soaked in different chemicals and at different concentration levels. The data show that certain common solutions for cleaning equipment are, in fact, damaging to the equipment and thus dangerous to the users. Even products marketed for climbing ropes were found to be potentially hazardous. The results also demonstrate a curious phenomenon occurring within the washing process that causes a shift in the elastic properties of the fibers, prompting additional research. Further work is needed to expand the breadth and depth of these results and to make effective recommendations to the rope industry and rescue professionals regarding rope care and maintenance.
ContributorsDenike, Andrew Nicholas (Author) / Middleton, James (Thesis director) / Liao, Yabin (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The purpose of this paper is to provide a new and improved design method for the Formula Society of Automotive Engineering (FSAE) team. There are five tasks that I accomplish in this paper: 1. I describe how the FSAE team is currently designing their car. This allows the reader to understand where the flaws might arise in their design method. 2. I then describe the key aspects of systems engineering design. This is the backbone of the method I am proposing, and it is important to understand the key concepts so that they can be applied to the FSAE design method. 3. I discuss what is available in the literature about race car design and optimization. I describe what other FSAE teams are doing and how that differs from systems engineering design. 4. I describe what the FSAE team at Arizona State University (ASU) should do to improve their approach to race car design. I go into detail about how the systems engineering method works and how it can and should be applied to the way they design their car. 5. I then describe how the team should implement this method because the method is useless if they do not implement it into their design process. I include an interview from their brakes team leader, Colin Twist, to give an example of their current method of design and show how it can be improved with the new method. This paper provides a framework for the FSAE team to develop their new method of design that will help them accomplish their overall goal of succeeding at the national competition.
ContributorsPickrell, Trevor Charles (Author) / Trimble, Steven (Thesis director) / Middleton, James (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2015-05
Description
Statistical process control (SPC) is an important quality application that is used throughout industry and is composed of control charts. Most often, it is applied in the final stages of product manufacturing. However it would be beneficial to apply SPC throughout all stages of the manufacturing process such as the beginning stages. This report explores the fundamentals of SPC, applicable programs, important aspects of implementation, and specific examples of where SPC was beneficial. Important programs for SPC are general statistical software such as JMP and Minitab, and some programs are made specifically for SPC such as SPACE: statistical process and control environment. Advanced programs like SPACE are beneficial because they can easily assist with creating control charts and setting up rules, alarms and notifications, and reaction mechanisms. After the charts are set up it is important to apply rules to the charts to see when a system is running off target which indicates the need to troubleshoot and investigate. This makes the notification part an integral aspect as well because attention and awareness must be brought to out of control situations. The next important aspect is ensuring there is a reaction mechanism or plan on what to do in the event of an out of control situation and what to do to get the system running back on target. Setting up an SPC system takes time and practice and requires a lot of collaboration with experts who know more about the system or the quality side. Some of the more difficult parts of implementation is getting everyone on board and creating trainings and getting the appropriate personnel trained.
ContributorsSennavongsa, Christy (Author) / Raupp, Gregory (Thesis director) / Dai, Lenore (Committee member) / Materials Science and Engineering Program (Contributor) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Formula SAE is a student design competition where students design and fabricate a formula-style racecar to race in a series of events against schools from around the world. It gives students of all majors the ability to use classroom theory and knowledge in a real world application. The general guidelines for the prototype racecars is for the students to use four-stroke, Otto cycle piston engines with a displacement of no greater than 610cc. A 20mm air restrictor downstream the throttle limits the power of the engines to under 100 horsepower. A 178-page rulebook outlines the remaining restrictions as they apply to the various vehicle systems: vehicle dynamics, driver interface, aerodynamics, and engine. Vehicle dynamics is simply the study of the forces which affect wheeled vehicles in motion. Its primary components are the chassis and suspension system. Driver interface controls everything that the driver interacts with including steering wheel, seat, pedals, and shifter. Aerodynamics refers to the outside skin of the vehicle which controls the amount of drag and downforce on the vehicle. Finally, the engine consists of the air intake, engine block, cooling system, and the exhaust. The exhaust is one of the most important pieces of an engine that is often overlooked in racecar design. The purpose of the exhaust is to control the removal of the combusted air-fuel mixture from the engine cylinders. The exhaust as well as the intake is important because they govern the flow into and out of the engine's cylinders (Heywood 231). They are especially important in racecar design because they have a great impact on the power produced by an engine. The higher the airflow through the cylinders, the larger amount of fuel that can be burned and consequently, the greater amount of power the engine can produce. In the exhaust system, higher airflow is governed by several factors. A good exhaust design gives and engine a higher volumetric efficiency through the exhaust scavenging effect. Volumetric efficiency is also affected by frictional losses. In addition, the system should ideally be lightweight, and easily manufacturable. Arizona State University's Formula SAE racecar uses a Honda F4i Engine from a CBR 600 motorcycle. It is a four cylinder Otto cycle engine with a 600cc displacement. An ideal or tuned exhaust system for this car would maximize the negative gauge pressure during valve overlap at the ideal operating rpm. Based on the typical track layout for the Formula SAE design series, an ideal exhaust system would be optimized for 7500 rpm and work well in the range
ContributorsButterfield, Brandon Michael (Author) / Huang, Huei-Ping (Thesis director) / Trimble, Steven (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Materials Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05