Issues In Education
Tossing Beanbags
By Mark A. Christobek
Management science instructors often use techniques and games to translate theoretical concepts into practical applications, especially those that might directly relate to the student's future employment. A simple experiment that involves the student manually tossing beanbags at a target marked on the classroom floor has proven instrumental in demonstrating concepts such statistical variability, statistical process control and process capability. This concept was first demonstrated by the Westat Consulting Group when SPC was introduced (or should we say, reintroduced) to American industry in the early 1980s. A brief description of the methodology follows:
A section of the room is cleared of desks and the remaining desks are arranged to allow the students to observe and participate in the exercise. Five pieces of masking tape are used to define the process; a sketch is provided (see Figure 1).
Figure 1
The first piece of tape (baseline), about 24 inches in length, is placed on the floor.
The second piece of tape (target), about 24 inches in length, is placed parallel to the baseline about 15 feet from the baseline.
The third piece of tape (measurement), about 72 inches in length, is placed perpendicular to the target, centered on the target (zero point), and is marked in inch increments from the target using both positive and negative numbers.
The fourth and fifth pieces of tape (specifications) are placed parallel to the target ±20 inches from the target.
Three students participate in the game. The first (operator) throws the beanbags at the target. The second (inspector) calls out the distance from the target line and picks up the beanbags after each throw. The third (recorder) marks each value on the control chart (overhead or spreadsheet).
The only instruction given the operator is to "hit the target." No information is given whether to throw with a low or high trajectory. Allowing the student operator to have a few practice throws will confirm the "best" throwing trajectory for the room. Each sample consists of five throws with the inspector evaluating the length of the throw (center of the beanbag) and picking up the beanbag. The measurements are recorded on a control chart overhead or in a spreadsheet.
Samples 1 through 4: No additional information is given the operator.
Samples 5 through 8: Prior to these samples, the instructor places motivational slogans around the room to encourage better quality output.
Samples 9 through 12: Prior to these samples, a twenty-dollar bill is taped to the target line as a financial incentive.
Samples 13 through 15: Prior to these samples, the LSL and USL are tightened (to ±10 inches) to see whether "tighter specs drive better quality." After the 15th sample has been collected, the process is stopped and control limits are calculated.
Samples 16 through 22: Prior to these samples, the class forms an ad hoc quality team and brainstorms ideas to reduce the amount of variability in the process. Training, automation, moving the operator closer to the target, and the use of a funnel or backstop are usually mentioned. The instructor then provides the class with the components for a backstop consisting of a sheet of Plexiglas (approximately 2'x3') and two wooden supports. The students determine how to best erect and position the backstop.
Samples 23 through 25: At this point, the instructor mentions that beanbag materials have been deemed too expensive, and that the purchasing department has identified a less expensive substitute raw material: plastic poker chips! After much objection by the operator, he/she must make drastic changes in their process trying to control the toss and inevitable rolling of the chips.
Control charts developed in a classroom setting are presented in Figures 2 and 3.
Figure 2: X-bar Chart for Beanbag Toss
Figure 3: R Chart for Beanbag Toss
Examination of the control chart will indicate the three distinct processes: (1) bean bags without backstop, (2) beanbags with backstop, and (3) poker chips with backstop. Students will also observe that the use of slogans, incentives and tighter internal specifications do nothing to help the process.
This game has been successfully used in undergraduate and graduate university settings as well as in industrial training environments. The background of the operator (hourly, management or student) or different floor surfaces (tile or carpet) do not impact the outcome of the game. Operators who have had experience tossing horseshoes or throwing darts only cause the control limits to become tighter, and they still have a hard time with the poker chips!
Students' actions while participating in this game are also observed and related to processes in industry. Perhaps the most common is the interaction between the operator and the inspector ("Give me a break, it wasn't that far off") or the inspector "cheating" by announcing a value closer to the target. Discussions are held with the class about these ethical concerns both during and after the game. Students also see that the actions of others not directly involved in the process (i.e. purchasing reducing their costs by switching vendors) can have a drastic effect on the bottom line profit of a company due to a reduced quality level of the processes.
Additional detailed information on this game can be obtained from the author at christobek.1@osu.edu.
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Mark A. Christobek is a visiting assistant professor in the Department of Management Sciences, Fisher School of Business, The Ohio State University.
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