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The Nelson Funnel Experiment - MS Word Document

Tim Folkerts

Super Moderator
#2
OK,

I must be missing something. I have read Steve's paper and others, and I'm a reasonably bright guy, but I still don't get rules 2 & 3.

RULE 2 "If the marble rolled 2 inches northeast, we position the funnel 2 inches to the southwest of where it last was."

RULE 3 "If the marble rolled 2 inches northeast last time, we should set the funnel 2 inches southwest of the target."

To keep things simple, let's do one dimension: the target is 0, left is negative, right is positive.

Suppose we start by aiming for 0, but it ends up at +1
According to #2: aim the funnel at -1 to counteract the tendency of the marble to roll +1.
According to #3: aim the funnel at -1, since that is 1" left of the target.

Now suppose the marble ends up at -3 (i.e. it rolled 2" left from the location of the funnel.
According to #2: aim the funnel at +2. The marble rolled 3" left of the target, so we move 3" right of the last position: -1 +3 = +2
According to #3: aim the funnel at +2. The marble rolled 2" to the left of the starting location, so we set the funnel 2" to the right of the target.

AHA! I think I have it. Rule 3 is the "Let's start over from scratch" rule. What I should say for #3 after the second drop is "Look, whatever we were doing, it isn't working. We ended -3 last time, so let's just start over and aim for +3 and see how we come out." I have to "forget" that I had been aiming for -1 and that the marble actually only rolled -2 from where I was aiming.

So perhaps the rules could be modified to say

RULE 2 "If the marble ended up 2 inches northeast of the original target, we position the funnel 2 inches to the southwest of where it last was."

RULE 3 "If the marble
ended up 2 inches northeast of the original target, we should set the funnel 2 inches southwest of the original target."

Tim F
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#3
Yes, it took a long time for me to mull through rules 2 and 3 to realize the difference. I appreciate the alternate wording. It is subtle, but rule 2 will only result in a slightly larger circle (still bounded) while rule 3 will explode to infinity. It helps if you do physically rig up a funnel on a stand and walk through it. I never did get a real marble to "behave" well - the table was not perfectly flat and the marble would keep rolling towards any low spot in the table.
 
B

Bill Pflanz

#4
Steve Prevette said:
Yes, it took a long time for me to mull through rules 2 and 3 to realize the difference. I appreciate the alternate wording. It is subtle, but rule 2 will only result in a slightly larger circle (still bounded) while rule 3 will explode to infinity. It helps if you do physically rig up a funnel on a stand and walk through it. I never did get a real marble to "behave" well - the table was not perfectly flat and the marble would keep rolling towards any low spot in the table.
I know Deming routinely demonstrated the bead box experiment but did he actually ever do the funnel experiment? The reason that I ask is that it is possible that Deming was using a description of the funnel experiment to help people visualize what tampering caused.

In The New Economics Chapter 9, Deming talks about the marble eventually moving off into the Milky Way (infinitely far from your target). He references to mathematical solutions developed by Lord Rayleigh. Is it possible that his funnel experiment rules were derived mathematically rather than empirically?

The bead box is easier to demonstrate since the equipment (box, beads, paddle) are tightly controlled. I understood that Deming only had 2 boxes built and the statistical data that he presented at the end of the presentation was based on the one that he had used for years. As you noted, Steve, the funnel experiment is harder to control the outcome due to the variation of the table even if the same cloth and marbles were used.

Shewhart and Deming were mathematicians and statisticians and were comfortable with the mathematical theories that were developed to explain nature. In another thread, someone attached "The Influence of CI Lewis on Shewhart and Deming". Lewis was attempting to answer the philosophical question of what is knowledge. Most people hear the word philosophical and think of an intangible belief. Lewis tied the collection of data (information gained from experience) to use past history to predict future outcomes (knowledge). Mathematical models are then developed so that that the theory can be used in other areas. (Steve or others, correct me at any time.) Deming may have known enough of the mathematical theory that he really did not need the actual experiment to verify the effect.

I can only imagine how hard it must be to read Mind and the World Order. Before I even attempt to make that my summer reading, I may want to go back and read the article that I referenced a few more times.

Bill Pflanz
 
#5
Bill Pflanz said:
I know Deming routinely demonstrated the bead box experiment but did he actually ever do the funnel experiment? The reason that I ask is that it is possible that Deming was using a description of the funnel experiment to help people visualize what tampering caused.

In The New Economics Chapter 9, Deming talks about the marble eventually moving off into the Milky Way (infinitely far from your target). He references to mathematical solutions developed by Lord Rayleigh. Is it possible that his funnel experiment rules were derived mathematically rather than empirically?

The bead box is easier to demonstrate since the equipment (box, beads, paddle) are tightly controlled. I understood that Deming only had 2 boxes built and the statistical data that he presented at the end of the presentation was based on the one that he had used for years. As you noted, Steve, the funnel experiment is harder to control the outcome due to the variation of the table even if the same cloth and marbles were used.

Shewhart and Deming were mathematicians and statisticians and were comfortable with the mathematical theories that were developed to explain nature. In another thread, someone attached "The Influence of CI Lewis on Shewhart and Deming". Lewis was attempting to answer the philosophical question of what is knowledge. Most people hear the word philosophical and think of an intangible belief. Lewis tied the collection of data (information gained from experience) to use past history to predict future outcomes (knowledge). Mathematical models are then developed so that that the theory can be used in other areas. (Steve or others, correct me at any time.) Deming may have known enough of the mathematical theory that he really did not need the actual experiment to verify the effect.

I can only imagine how hard it must be to read Mind and the World Order. Before I even attempt to make that my summer reading, I may want to go back and read the article that I referenced a few more times.

Bill Pflanz
Let's see - slanting table - is that "common cause" or "special cause"?
common cause if moving the funnel may result in marble going to a different place (different surface conditions - bumps, grooves, highs, lows, etc)
special cause if the marble ends up in same place no matter where funnel is (one leg of table two inches shorter than the others)

I can imagine a table with both special and common cause effects on variation.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#6
Rule 2 of the funnel can definitely be calculated mathematically (the 40% increase in diameter of the circle). Rules 3 and 4 can be simulated in Excel (by the way, if anyone would like the simulation spreadsheets let me know). You could probably do rules 3 and 4 mathematically, Rule 4 is otherwise known as the random walk, or the drunken walk. Brownian motion.

I am finding Mind and the World Order to be worthwhile. It is especially interesting to look up CI Lewis in the index to Out of the Crisis, and then go read the referenced material. I don't understand how Dr. Deming made the leaps he did from the philosophical material to his works, but given the path has already been cut, it is fascinating to follow with 20/20 hindsight.

The Funnel Experiment is better done as a "thought experiment" rather than a physical experiment, and that is how Dr. Deming used it in his seminars. The lesson that comes out of the Funnel is slightly different than the Red Beads. The Red Beads show ineffective attempts to change a stable process - the process remains stable and nothing changes. The Funnel shows the result of tampering with a stable process. Yes, change actually results, but makes matters worse, not better.
 
J

Jim Howe

#7
I love this kind of thing! It takes me awhile to figure it out but eventually it makes sense. It reminds me of Heisenberg's "Principle of Uncertainty" where in he postulated that we can never be certain of the location of a subatomic particle because location changes with energy level and the act of observing (measuring) adds energy which causes a shift in location. Bu de de be du bub! :nope:
 
B

Bernoulli

#8
Re: The Deming Funnel Experiment - MS Word Document

Another paper in my library. $150 or no $150 I appreciate the opportunity to share.
I enjoyed reading this paper, and now understand better the Funnel experiment to application in the workplace. thank-you!!!!:
 
A

artichoke

#9
Re: The Deming Funnel Experiment - MS Word Document

It is subtle, but rule 2 will only result in a slightly larger circle (still bounded) while rule 3 will explode to infinity.
Rule 2, but by comparing the position where the marble ends up with the target (as Tim suggests), is the basis for feedback control systems (PID). These measure deviations from a set point. Automatic control systems reduce the gain or the proportional (P) effect of Rule 2, and add integral (I), to avoid "reset wind up" or a progressive drift off target. Derivative (D) may also be added, with great caution ... it has a negative effect on many systems such as temperature and level by increasing instability.

Rule 2 with a deadband is similar to Shainin's Pre Control. Without being able to tune the (human) controller, this can result in increased variation.
 
Z

zelwood

#10
Re: The Deming Funnel Experiment - MS Word Document

There's something fundamental about this thought experiment that I'm not getting. I've thought about it for a while. Maybe someone can clear this up.

I am also confused about Rules 2 and 3, as one of the original repliers was. Because all of the wording for the Rules I've read has been so ambiguous, let me give my interpretation as to what the Rules are supposed to be (as I currently understand them):

To simplify, we'll treat this as a one-dimensional line with '0' being the goal.

Our goal is to hit a set target at position 0.

Rule 2: We drop the ball through the funnel, with the funnel being at position A. The ball winds up at a position B. We move the funnel in a direction to compensate for the movement from A to B, in relation to the funnel. The new funnel location would equal [A + (A-B)] In other words, every time we move the funnel, the funnel's new location becomes our new "target", which we are trying to hit with the next drop. Basically, we have forgotten all about our original target, if I am understanding this correctly. Let's say the funnel is at 0, the ball winds up at +2. We move the funnel to -2. We drop the ball and it winds up at -5 (moving 3 to the left). We move the funnel to +1.

Rule 3: We drop the ball through the funnel, with the funnel being at location A. The ball winds up at a position B. We move the funnel to compensate for the distance from B to the original target X (which is 0). The equation for the new funnel location would be: (X - B ) In other words, every time we drop a ball, we measure the distance from the ball to the target and compensate for that distance, not taking into account the funnel's last position at all.

Does this make sense?

If my understanding is correct, what I don't understand is why there isn't a Rule that would be to me the most logical (although obviously still not as effective as Rule 1):

We drop the ball through the funnel with the funnel at position A. The ball winds up at position B. We take the difference between A and B and compensate for that difference with regards to the target. In other words, the new funnel location = [X- (A-B)]


Maybe that is actually a rule and I'm not understanding that one of them is that rule. Any comments? I think my main confusion is the ambiguity with which I've seen the descriptions of the rules written.

I'm writing a computer-based training module about these things, that's why I'm trying to understand this concept very well, even though I know it's just a thought experiment to get a basic point across.
 
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