class: center, middle, inverse, title-slide .title[ # MTH 547 Design of Experiments ] .subtitle[ ## Project Ideation & Feasibility Workshop ] .author[ ### <br>Ying-Ju Tessa Chen, PhD <br><br> Associate Professor <br> Department of Mathematics<br> University of Dayton <br><br> <a href="https://twitter.com/ju_tessa"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z" /></svg> <span class="citation">@ying-ju</span></a> <br> <a href="https://github.com/ying-ju/"><svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" /></svg> ying-ju</a> <br> <a href="mailto:ychen4@udayton.edu"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z" /></svg> ychen4@udayton.edu</a><br> ] --- ## Workshop Goals **Key points:** * Generate promising project directions * Think in terms of *experimental structure* * No final decisions today * Ideas will evolve as we learn more DOE tools --- ## What Makes a DOE-Friendly Project? * Measurable response * Controllable factors * Ability to replicate * Potential for **multiple factors** * Feasible within the semester --- ## Individual Brainstorming .small[ **Instruction:** * Write down at least **3 topics or processes** you’re interested in * For each: * Possible response * At least one factor **Optional AI use:** You may use AI **before or during this step** to help generate or refine ideas. > Example prompts: > > * “I’m interested in designing an experiment about step count during daily walks. The response could be average steps per 30-minute walk. Suggest 2–3 controllable factors I could vary and explain why they might matter.” > * “I have a vague idea about improving sleep quality. Help me define a measurable response variable and two experimental factors that could realistically be controlled.” > * "Here is a tentative experiment idea: testing different study environments. Can you help me check whether this idea is suitable for a multi-factor experimental design and suggest possible factors and responses?" **Important:** AI suggestions are **starting points**. You must still judge feasibility and relevance. ] --- ## Group Sharing & Idea Expansion **Instruction:** * Share your ideas within your group * Combine or improve ideas * Add possible factors 👉 **No AI here** This is intentionally *human discussion*. You want peer reasoning, not chatbot convergence. --- ## Feasibility Voting **Criteria for voting:** * DOE-friendly * Interesting/meaningful * Realistic Each student votes → top 3 ideas per group. --- ## Design Thinking: Current vs Future Tools Split it visually: **What you know now** * One-factor designs * ANOVA * Diagnostics **What you will learn soon** * Multi-factor designs * Interactions * `\(2^k\)` factorial designs Message: > Today, you are allowed to think *ahead* of where we are in the course. --- ## Brainstorming Run 1: One-Factor Framing For each of the top 3 ideas: * Response * One factor * Levels * Replication 👉 **Optional AI use** You *can* allow AI to help articulate: * clearer response definitions * possible factor levels & ensure they are reasonable > Use AI only if your group is stuck. --- ## Brainstorming Run 2: Multi-Factor Expansion Now push depth. For each of the top 3 ideas: * What second factor matters? * Could there be interactions? * What would you *expect* to interact? 👉 **This is where AI can be powerful — but risky** > You may use AI to **suggest additional factors**, > but you must decide which ones make sense and justify your choices using experimental reasoning. --- ## Brainstorming Run 3: Practical Constraints * What limits runs? * What must be controlled? * What could be blocked? > A block is a source of variability that we cannot or do not want to study, but we can group experimental runs by to reduce noise in the response. Blocking is needed only if there is a known nuisance variable that **affects the response**, and **cannot be randomized away easily**. .small[ **Examples:** - Runs must be conducted on different days - Multiple machines must be used - Ingredients come from different batches - Different operators are involved ] If none of those constraints exist → no block needed. 👉 **No AI in this stage** --- ## How to Identify a Blocking Variable .pull-left[ **Ask yourself:** * Does this variable affect the response? * Am I interested in its effect? * Can I randomize across it easily? If: * affects response ✔️ * not of interest ✔️ * hard to randomize ✔️ → Good candidate for blocking ] .pull-right[ **Common blocking variables** - Day or time - Operator / person - Machine or batch - Location - Raw material batch - Subject (if repeated measures) ] <br> > If runs must be conducted on different days, day may be treated as a block. > If multiple machines are used but machine performance is not the focus, machine may be a block. --- ## Expectations Reminder Expected Requirements * **Core**: `\(\geq 2\)` factors + interaction consideration * **Advanced (optional)**: `\(\geq 3\)` factors, `\(2^k\)`, fractional factorial > You are not expected to use AI in your final project analysis unless explicitly allowed. --- ## What Happens After Today * Ideas refined; Pick one from your top three ideas * Designs evolve * More tools coming soon * You’ll have time to prepare your presentation ### Acknowledgment Parts of the workshop structure and example prompts were developed with the assistance of an AI language model (ChatGPT) and refined by the instructor.