System Variance
This activity is an analysis and reflection of the glass bead game described by Deming (W. Edwards Deming, Out of the Crisis, MIT Center for Advanced Engineering Studies, Cambridge, 1986, pp 346 – 354). It is used to illustrate the impact of variation which exists within a system and the extent to which that variation limits the effectiveness with which individuals can be evaluated.
A container of 800 white marbles and 200 red marbles is the center piece of this activity. Students are told that their initial task is to quickly select 50 marbles (without regard to color) to prepare for packaging. They are given paper cups that are marked with a blue line. Their instructions are to fill the cup up to the blue line, which should result in 50 marbles. Each student takes a turn and then counts the number of marbles in the cup, recording the total number as well as the number of red marbles. One student is given a cup for which the blue line is drawn at a 30 marble level rather than 50. Everyone’s results are recorded on a variable control chart. Few students get exactly 50 marbles since the measuring device is very imprecise. Upper and lower control limits are calculated and drawn on the chart. The student with the defective cup will fall below the lower control limit. A discussion of why that one person did such a poor job soon results in the observation that defective equipment was the cause. Once that problem is solved there remains wide variation in the results, none of which can be attributed lack of effort or desire on the “worker’s” part but is a result exclusively of problems in the system. Students are given the opportunity to discuss the nature of those problems and to suggest solutions. Next, for each student’s results the proportion that are red is calculated and an attribute control chart is drawn.
This is the classical Deming exercise in which the inherent variation in the system causes a wide range of results. This lecture often begins with a list of workers along with the proportion of defective parts they produced in a fixed sample. Initially students are willing to rank the performances from the best (lowest percent defective) to the worst. After seeing that the variation in the proportion of red beads is similar to that in the proportion of defectives, they recognize that system variation should be a primary focus of attention rather than individual efforts. The defective measuring cup also illustrates nicely how special variation can be identified with control charts.
Students, as a follow up will post a reflection of this learning activity to the Assignment link in Blackboard with examples of system variation from their experiences.
