Deming's funnel: Difference between revisions

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[[wp:W. Edwards Deming|W Edwards Deming]] was an American statistician and management guru who used physical demonstrations to illuminate his management teachings. In one such demonstration he dropped multiple marbles through a funnel at a target, marking where they landed, and observing the resulting pattern. A sequence of "rules" are tested to try to improve performance. In each case, the experiment begins with the funnel positioned directly over the target.
[[wp:W. Edwards Deming|W Edwards Deming]] was an American statistician and management guru who used physical demonstrations to illuminate his teachings. In one such demonstration he repeatedly dropped marbles through a funnel at a target, marking where they landed, and observing the resulting pattern. He applied a sequence of "rules" to try to improve performance. In each case, the experiment begins with the funnel positioned directly over the target.


* '''Rule 1''': The funnel remains directly above the target.
* '''Rule 1''': The funnel remains directly above the target.
* '''Rule 2''': Adjust the funnel position by shifting the target to compensate for the miss. If the last shot missed 1 cm east, move the funnel 1 cm to the west of its current position.
* '''Rule 2''': Adjust the funnel position by shifting the target to compensate after each drop. E.g. If the last drop missed 1 cm east, move the funnel 1 cm to the west of its current position.
* '''Rule 3''': As rule 2, but first move the funnel back over the target, before making the adjustment. E.g. If the funnel is 2 cm north, and the marble lands 3 cm north, move the funnel 3 cm south.
* '''Rule 3''': As rule 2, but first move the funnel back over the target, before making the adjustment. E.g. If the funnel is 2 cm north, and the marble lands 3 cm north, move the funnel 3 cm south of the target.
* '''Rule 4''': The funnel moves directly over the last place a marble landed.
* '''Rule 4''': The funnel is moved directly over the last place a marble landed.


Apply the four rules to the set of 50 pseudorandom displacements provided (e.g in the Racket solution) for the dxs and dys. '''Output''': calculate the mean and standard-deviations of the resulting x and y values for each rule.
Apply the four rules to the set of 50 pseudorandom displacements provided (e.g in the Racket solution) for the dxs and dys. '''Output''': calculate the mean and standard-deviations of the resulting x and y values for each rule.
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