Simulates the famous Deming funnel experiment which showed that an inappropriate reaction to common-cause variation will make matters worse. Using MINITAB's SPC commands, the data is displayed graphically so that the performance of a process can be evaluated and a proper course of action for improvement determined.
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In the actual demonstration, a funnel apparatus is constructed and placed above a piece of paper with a bull's-eye. The objective is to drop a marble or ball through the funnel on to the paper as close to the bull's-eye as possible. A pen or pencil is used to mark the spot where the marble actually hits. Usually, 20 or more drops are performed in order to clearly establish the pattern and extent of the variation about the bull's-eye.
The funnel represents the common-cause system. Despite the operator's best efforts, the marble will not land exactly on the bull's-eye each time. The operator can react to this variability in one of four ways. These four strategies by which the funnel can be controlled are: Do not move the funnel -- leave it where it is for all drops. Measure the distance the hit is from the bull's-eye. Move the funnel an equal distance, but in the opposite direction (error relative to the previous position). Measure the distance the hit is from the bull's-eye. Move the funnel this distance in the opposite direction, starting at the bull's-eye (error relative to the bull's-eye). Move the funnel to be exactly over the location of the last drop.
Simulation with MINITAB
The macro FUNNEL.MAC provides a 1000-marble-drop simulation for each of the 4 strategies above! For each strategy, the macro produces a high-resolution plot of the hits, which may be printed in the usual way. This macro requires MINITAB Release 9 (or above) with high-resolution graphics and a supported graphics device.
To run the macro, go toand type:
Click Submit Commands.
The funnel remains fixed, aimed at the target. In this case the target is located at the coordinates (0,0). X1 and Y1 are the coordinates of the point where the marble drops.
Move the funnel from its previous position a distance equal the current error (location of drop), in the opposite direction.
Move the funnel to a position that is exactly opposite the point where the last marble dropped, relative to the target.
Move the funnel to the position where the last marble dropped.
After executing the macro and reviewing the resulting plots, students can observe that: Strategy 1 has the lowest variability about the target. Strategy 2 looks similar to strategy 1 but has more variability. Strategy 3 has the look of a "bow tie" in its pattern. Strategy 4 wanders off the screen.
The primary lesson is that a stable common-cause process (such as that involving the funnel) should be left alone for best results; adjustments (strategies 2 - 4) will only result in worse performance. To improve performance, the funnel apparatus (common-cause system) itself must be changed. In the industrial setting, it is management's responsibility to provide resources and coaching to work on common-cause performance problems. The operator can only be held accountable for what is under his/her control.
We sum up by mentioning that, statistically, both strategies (1) and (2) are stable with variance sigma2 and 2 sigma2, respectively. Strategies (3) and (4) are unstable and will eventually wander off to infinity.
Deming, W. E. (1986) Out of the Crisis. Cambridge: Massachusetts Institute of Technology Center for Advanced Engineering Study, 327-332.