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The Cards Wager Assignment: Betting Homework Points on Statistical Process Control

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016





Conference Session

Supply Chain and Logistics in Manufacturing Education

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Mathew Schaefer Milwaukee School of Engineering

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MATHEW SCHAEFER is Associate Professor of Mechanical Engineering at Milwaukee School of Engineering. Prior to his academic work, Dr. Schaefer worked for G.E. Medical Systems and for Briggs & Stratton Corp. He earned his B.S. and M.S (Mechanical Engineering) and Ph.D (Materials Science) from Marquette University. His experiences in metallurgy, design, and failure analysis come from work in industry, projects and teaching at MSOE and projects completed as an independent consultant. He has taught courses both at university graduate/undergraduate level and has taught on-site professional development seminars.

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Suppose one weekend you are at the Bellagio Casino playing blackjack and the pit boss comes over and makes a proposition. It seems one of the dealers has been cheating and switched some cards in his shoe (a “shoe” holds 6 standard decks of cards). The pit boss tells you the bad shoe is either at table 1 or table 2, at the far end of the casino. The other table has a good shoe, which contains standard cards. The pit boss, being a gambling type, makes you the following offer; If you correctly pick which one is the bad shoe he will pay you $300. If you pick and are incorrect you owe him $150. Do you take the bet?

This problem serves as an outstanding analogy for teaching concepts of statistical process control in a junior level mechanical engineering course in Manufacturing Processes. This hypothetical wager serves as an extra credit problem in which students literally wager homework points for an opportunity to take a shot at the extra credit problem.

Students want to maximize their homework grade just as corporations want to maximize their profits. Trying to make a profit requires some risk up front and some intelligent monitoring of the manufacturing processes used to make a product. Process monitoring costs money. Investing more in process monitoring leads to greater confidence that “good product” is being made but only if the process data is analyzed intelligently.

Statistical process control is all about determining if some real population (parts or cards) matches some ideal population. For “The Cards Wager Assignment” above, students may choose to wager ($150 = 15 homework points) for the chance to win extra credit homework points ($300 = 30 points). But the heart of the problem is that students may also pay extra to look at cards from the shoe. Every 10 cards chosen costs 1 homework point. More cards inspected may lead to a more confident answer. However, spending too much on looking at cards will cut into their potential homework grade profits. The best option for the student is to look at just enough cards and analyze their data intelligently to make a confident choice.

This is an optional assignment; students are not forced to risk losing some of their homework points and as such there is no rule for inspection strategy or how to analyze their data. Some use control charts and other statistical methods to analyze their cards. A few have chosen to skip inspection altogether and take a blind guess. This assignment always generates a great deal of interest and questions in class even for the students who don’t choose to risk the bet.

Schaefer, M. (2016, June), The Cards Wager Assignment: Betting Homework Points on Statistical Process Control Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.26101

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