Design of Experiments project - 2011

Due date:	28 March 2011, or optionally on 31 March at class.
(PDF)	Project outline
Link	[{{{questions_link}}} Project outline ]
Link	[{{{solutions_link}}} Solutions]

<rst> <rst-options: 'toc' = False/> <rst-options: 'reset-figures' = False/> Intention

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This DOE (design of experiments) mini-project gives you an opportunity to learn about designed experiments in a more hands-on manner.

The project is *not long*, and should *not be elaborate*. You only have a few weeks to plan your experiments, perform them and then analyze the data. You will hand in a short report (about 4 pages) on your work. Some more examples are given below, but it could be something like optimizing a favourite recipe or dessert, a hobby or sport, or it could be related to work from another course project or your graduate research, which is ideal for 600-level students, or 400-level students doing research projects.

The intention is that you discover for yourself how important the following topics are in DOE. Once you have decided on a system to investigate you will be faced with:

* Which variables should we use? * What range should these variables cover? * How do we measure these variables (especially the response variable)? * What other variability is in the system, is it measurable, is it controllable? * Choosing the type of experimental design, center points, fractional designs, confounding pattern, and handling constraints. * How many experiments should be run, are replicates possible, and how to randomize the runs. * Understand what George Box means when he says: "*the best time to run an experiment is after the experiment*".

These are issues that are not easily reproduced or understood from assignment questions and exams.

Project topics

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You might be passionate about your hobby, for cooking, or your research area, *etc*, so coming up with a system to investigate shouldn't be a problem. However, some systems are too complex for the short time you have available, and you might have to cut back to something simpler. So below are some ideas that you can think about and modify, but please work on anything you are interested in, or anything you have ever wondered about.

• Yield of stovetop popcorn or `microwave popcorn <http://www.statease.com/pubs/popcorn.pdf>`_
• Rise height of bread
• Algae growth in an aquarium
• Gas mileage of a car
• Dissolving table salt
• The perfect meringue from egg-whites
• Time to melt ice
• Taste of pancakes (average of 4 tasters)
• Time taken to go down a ski slope
• Factors related to seed germination and growth (e.g. does Miracle-Gro work?)
• Growing plants from root cuttings
• Foam produced when pouring (soft) drinks into a glass
• Strength of wood glue bond
• Stain removal from clothes
• Hover time of a paper helicopter
• Flight time or distance of a paper plane or model plane
• Shot distance of tabletop hockey puck
• Factors related to paper towel absorbency, cost, softness, strength
• Burst time of soap bubbles
• Bounce height of tennis balls or golf balls
• Condensing water in a cup off a plastic sheet (camping trip)

You might be fortunate that you have access to a lab for another course, or that one of your other courses overlaps in some way. You may even have an industrial partner from your co-op or current research area (grad students) with whom you can work. For example, a blown-film line, an extruder, a configurable heat-exchanger. Try to work with these as much as possible.

Note that topics involving cooking and baking can be the most complex due to raw material variability and subjectivity of the outcome variable(s). However, if this is an area that you/your group is interested in, please meet with me to discuss how to control for these problems.

Finally, the system under investigation can be anything, however, you cannot merely copy-paste a problem that you found in a book, technical journal, website, or some other resource. You must be able to prove you planned and performed the experiments yourself; this means that you cannot reuse experimental data from a previous course project. If you are going to investigate a relatively simple system, such as dissolving salt in water, then ensure that your project is at the level of a 4th year university project, is comprehensive, and covers many factors. In general the number of experiments, the cost and the complexity of the experiments should be inversely proportional to the duration of each experiment.

If you have any ethical doubts (e.g. experiments on animals or people) then rather choose another system.

Group work

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You may perform this project by yourself, with one other person, or with two other people. Try to ensure that the system is of interest to all group members, and that you can all contribute to the work. 600-level students may work with one other person in the class.

It makes sense to use the same group members that you worked with in the assignments, since you will work on the take-home midterm around the same time as writing this project report.

The project report

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The final report is to be about 4 pages. The following guidelines will help you produce a great report:

• The report is a narrative that describes the problem you want to solve, outlines the factors experimented on, how you identified and controlled for disturbances and provides conclusions. You may choose to use some or all of these sections:

#. Describe your objective for the system under investigation. What is/are the outcome variable/s you are investigating; how are they measured? #. Outline the factors that you expect will influence the outcome variable. How will you measure the factors, over what range will you vary them? State how you expect each factor to affect the response(s); do you expect any interactions? #. Disturbances: which factors are known to affect the response but not being investigated here? How do you control for them? #. Plan an experimental program that will change the system's factors and control for disturbances. Be specific on how you chose your design. #. Execute the experimental program, logging all relevant details (e.g. experiments that are "weird", unusual events). Take photos/keep a log sheet. #. Analyze the experimental results using the tools introduced in the course. #. The conclusions, related back to your original objectives. What would be the next set of experiments you run?

• Place clearly drawn visualization plots in the report next to the text that describes, or refers to the figure.
• Place all source code in the appendix. I will generally assume you know how to analyze the data, so I don't have to see code. However, the code may be helpful, if your description in the report is unclear, or if I have doubts when grading the report.
• Appendices and extra information can be attached, specifically the original/scanned run sheet, and any photos from your experiments.
• The total report should not be longer than 7 pages.

Guidance

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• Feel free to email me with any questions.
• If you are uncertain if your system is suitable, run your idea by me before you go too far.
• Due to the short time line for this project you should consider systems where experiments take no longer than a day or two each, unless you can run all your experiments in parallel (e.g. growing plants).

Example of a previous project

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A good example of the style and type of report required is in Box, Hunter and Hunter, page 215 to 219 (second edition), pages 368 to 272 (first edition).

Time line

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16 March 2011, or earlier You may *optionally* hand-in a single page, and using bullet points, describe your system and its parameters. Also discuss disturbance factors you think will affect your results, and your **planned** experiment (i.e. points 1, 2 and 3 outlined above). I will provide general comments in person or by email.

The earlier you do this, the longer you have to perform (and perhaps repeat) any of your experiments. Many students in the previous class found this interactive help the most useful part of the course, because there are quite a few pitfalls in designing and analyzing experiments.

28 March 2011 (or 31 March, at your option)

	Hand-in of the final project report with the rest of the take home midterm.

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