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Where to put the Armor?

Where to put the Armor?. Math Olympiad 2011 Northwest Missouri State University Neil Hatfield. The Problem. The United States Air Force is experiencing a problem…they are losing air craft on missions. USAF knows that the loss of planes is not due to pilot error or malfunction.

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Where to put the Armor?

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  1. Where to put the Armor? Math Olympiad 2011 Northwest Missouri State University Neil Hatfield

  2. The Problem • The United States Air Force is experiencing a problem…they are losing air craft on missions. • USAF knows that the loss of planes is not due to pilot error or malfunction. • The loss of planes is due to the planes being shot down. • You (and your team) have been hired to solve this problem.

  3. The Job • You and your team will need to • Develop a research question that will help you solve the USAF’s problem. • Design and “employ” a plan for data collection • Note: the USAF (me) may or may not be able/willing to give you the data you want, but will give you the data that we can. • Analyze and summarize your data. • Interpret your results • Make sure to answer your team’s research question. • Make a recommendation to the USAF for where to put the armor. Keep in mind, we’re on a budget.

  4. Recommendations

  5. And the Answer is…. Where there are not any bullet holes. But that’s counter-intuitive!

  6. So where’s the Problem(s)? • Formulating the question(s)? • Designing and Employing Data Collection? • Analyzing and Summarizing the Data? • Interpreting the Results and Answering the Question?

  7. Data Collection • Where did our data come from? • Planes that were shot, but were able to return to base. • The data is statistically biased towards the planes that survived! • What we really want to know about are where the planes that did not return were shot.

  8. Adjusting for Bias • Let’s do some reasoning • If a part of a plane got shot… • And the plane made it back… • Then… • That part needs no additional armor. • So what about the spaces between the shots?

  9. Historical Background • Patrick Blackett • Director of Operational Research for the British Navy, 1942-1945 • He and his team solved this very problem. • Convoy Survival • Depth Charges

  10. What To Take Away • Thinking critically costs us nothing. • Not thinking critically can cost. • Common Sense isn’t always the best, or right, thing to do. • Data is dirty…what we get to work with may or may not help us answer the question.

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