THE FIRST TWO RULES OF THE FUNNEL

~ 15 min reading · ~ 105 min at Neave’s pace

MAJOR ACTIVITY 3–h

Before we begin, a few words about the nature and purpose of the Funnel Experiment, some of which you will recognise as having been just as relevant to the Red Beads Experiment. As there, sooner or later it will become obvious to you that some of the strategies used and actions carried out are, depending on the circumstances, rather foolish! But that is precisely what’s intended. Both experiments are very simple—so simple that the difference between good and bad practice becomes plain for all to see. However, after the Funnel Experiment had been presented, both Dr Deming in his enormous seminars and I in my smaller-scale ones would then ask the delegates to tell us of examples of what had now become clear to them as costly and damaging bad practices in their own lives, their own experience, their own workplaces, their own organisations. And invariably the delegates would come up with dozens of such real-world examples analogous to the bad practices of which they were now aware through what they had just learned from the Funnel Experiment. Often they had carried out such practices themselves—not because they were bad people but because they hadn’t previously realised that the practices were so bad. Now they did. Thus, as with the Red Beads Experiment, the purpose of the Funnel Experiment is to alert you to the truth of such matters, so that in future you will be able to figure out more successfully what is good practice and what is not: what to do and what to avoid. As you go through the experiment, when similarly you think of practical examples in your own experience of what the Funnel Experiment is teaching, make a note of them since they will be of help when you get to today’s final Activity.

It is easy to think of real-life illustrations of the Funnel Experiment in many contexts. For example, consider my school bus again. Suppose the bus driver (who actually was my uncle!) was really keen to arrive at my bus-stop at exactly 8.30 am—which thus became his target. How might he use past experience to help him do that? Or we could think in terms of a manufacturing process. Suppose the nominal width of a socket, made by injection moulding, is 2.30 cm. How might one use information about past measurements of such sockets to try to manufacture future sockets closer to the nominal value?

With reference to the two illustrations just mentioned, the numbers on the funnel’s and marble’s tracks can relate to minutes in the case of the bus arrival time and tenths of a millimetre for the width of the socket. So the “target” of either 8.30 am or 2.30 cm is represented by 30 on the track, while the 29 refers to 8.29 am or 2.29 cm, 31 to 8.31 am or 2.31 cm, 34 to 8.34 am or 2.34 cm, etc.

The First Two Rules of the Funnel

An obvious way to attempt to improve results from a process is to compare the current outcome (today’s bus arrival time or the width of the socket just manufactured) with the nominal or target value, a comparison which may suggest an adjustment to try to improve the next outcome. In our “flattened” version of the Funnel Experiment, this adjustment will be represented in what follows by the movement of our funnel along its track—to the left if we want to try to make the next outcome respectively earlier or smaller, or to the right if we want to make it later or larger. Thus, if the bus arrives today at 8.33 (three minutes late), perhaps the bus driver should set out three minutes earlier tomorrow. (I am assuming that my uncle is keen to please me rather than anybody else!) Or, if the socket just made measures 2.33 cm (0.03 cm too wide), we can adjust a control on the machine to reduce the average diameter of future sockets by 0.03 cm. In either case, the equivalent movement of our funnel is a distance of 3 squares (minutes or tenths of a millimetre, etc—whatever units we are using) to the left along its track. Thus we compensate for the amount that the current outcome is off-target by moving the funnel by that same amount in the opposite direction. This type of compensation strategy is in fact the second of what both Drs Nelson and Deming referred to as the four Rules of the Funnel. Here we are demonstrating it first because it corresponds to what was happening first in the Ford example on page 5. We shall introduce the other three Rules in due course.

Whatever is tried, the fact remains that different things (be they bus journeys, manufactured sockets, or anything else) are almost always different! This is because, as we are now well aware, all processes have their common-cause variation as well as possibly some additional special causes of variation.

With the equipment as described, when the marble is dropped through the funnel it will finish up either to the left or right of the funnel or sometimes directly underneath it. There is no need to use anything very complicated to model the variation between the funnel’s current position and where the marble finishes up. Anything reasonable will produce the main messages to be learned from the experiment. So that’s why you have your two dice. You’ll throw the dice and add up the two numbers showing: let’s call that the dice-score. Since the faces on the dice range from 1 to 6, obviously you will get a dice-score of between 2 and 12. Then use the dice-score in conjunction with the following little table to decide where the marble finishes up relative to the funnel’s current position. Thus e.g. if you throw two ones, so that your dice-score is only 2, you place the marble 5 (= 7 − 2) squares to the left of the funnel’s current position. Or if you throw a 3 and a 5, with dice-score 8, then you place the marble one (= 8 − 7) square to the right of the funnel.

Dice-score 2 3 4 5 6 7 8 9 10 11 12
Marble relative to funnel 5 left 4 left 3 left 2 left 1 left Under 1 right 2 right 3 right 4 right 5 right

From now on I shall use the colour-coding in this little table to help you find your way around: the funnel in blue, and the dice-score in brown. The marble’s position (and thus the outcome or result) will be in red.

In this example, since of course the preferred outcome is always that target of 30 (corresponding to the bus arriving at 8.30 or to a socket diameter of 2.30 cm), you may as well start by putting the funnel at what would appear to be the “obvious” position, i.e. 30:

The 20–40 track with the funnel marker above the target square 30, and no marble yet — the starting position for Rule 2.
Describe this diagram

The 20–40 track with the funnel placed above square 30, the bullseye target. Nothing has been dropped yet: this is simply where Rule 2 starts.

You throw your dice. If you are fortunate enough to get a dice-score of 7 (e.g. by throwing a 2 and a 5), the table shows that the marble finishes up directly under the funnel—dead on target!

The same track with the funnel marker above square 30 and the marble marker also above square 30 — a dice-score of 7 leaves the marble directly under the funnel, dead on target.
Describe this diagram

The same 20–40 track, with the funnel above square 30 and the marble resting on square 30. A dice-score of 7 means “under”: the marble finishes directly beneath the funnel, on the target-point.

But suppose you’re not that lucky. Perhaps your dice fall as a 6 and a 4, giving you a dice-score of 10. Then the table shows that the marble finishes up 3 squares to the right of the funnel, i.e. 3 to the right of 30 giving 33—that’s 3 too big. What a pity!

The same track with the funnel marker above square 30 and the marble marker above square 33 — a dice-score of 10 puts the marble 3 squares to the right of the funnel.
Describe this diagram

The same 20–40 track, with the funnel still above square 30 and the marble resting on square 33. A dice-score of 10 means “3 right”: the marble finishes three squares to the right of the funnel, three too big.

So let’s try to make the next outcome a little smaller, to attempt to get it closer to that target value of 30. That was indeed the “logic” behind what was happening at Ford. As discussed earlier, according to Rule 2 (which, recall, was Ford’s First Strategy) the bus driver would then leave the depot 3 minutes earlier tomorrow, or we would adjust the control on the injection moulding machine down by 0.03 cm. So equivalently you move the funnel by 3 squares to the left along its track, i.e. from 30 to 27. (From now on I shall not keep referring directly to those two illustrations, as otherwise the description will become very lengthy.)

The same track with the marble still above square 33 and the funnel marker moved left to square 27 — Rule 2’s compensation, moving the funnel by the same amount the outcome was off-target, in the opposite direction.
Describe this diagram

The same 20–40 track, with the marble still on square 33 and the funnel now above square 27. The outcome was 3 too big, so Rule 2 moves the funnel 3 squares in the opposite direction, from 30 to 27.

Rule 2 of the Funnel (Ford’s First Strategy)

A particularly appealing way of considering this strategy (i.e. Rule 2 of the Funnel) is that it tells you to move the funnel to the position (27) where, if only it had been there when the marble was just dropped through it, you would have just obtained the preferred target outcome of 30! With the funnel placed there, the dice-score of 10 led you to move the marble 3 squares to the right of the funnel; so you would then have had the marble at the target, 30.

The 20–40 track with the funnel marker above square 27 and the marble marker above square 30 — the bullseye target. Illustrates Rule 2: had the funnel been placed at 27 when the dice-score-10 throw was made, the marble’s 3-right displacement would have landed it on the target.
Describe this diagram

The same 20–40 track, with the funnel placed above square 27 and the marble resting on square 30 (the bullseye target). This is the Rule 2 thought-experiment: with the dice-score of 10 that was just thrown, the marble lands 3 squares to the right of wherever the funnel was. So if the funnel had been at 27, the marble would have come to rest on 30 — exactly the target. Rule 2 therefore says: move the funnel from its present position to wherever it would have needed to be in order for the just-completed throw to have hit the target.

Now, in order to record the progress of Rule 2 in an organised fashion, both to study its behaviour and, later on, to compare it with the other three Rules of the Funnel, you will need to carry out some systematic book-keeping! So let me get you started with your own track and whatever you are using for your funnel and marble. I’ll use our familiar symbols for the funnel and the marble, and also ◎ for the target (30 in our illustrations).

We’ll use my own dice-scores to start with so that you can follow my illustration exactly: you’ll be able to start throwing your own dice very soon! Work through these demonstration stages carefully on your own track so that you can be sure about what to do when I leave you on your own. Take it steadily at first—remember (as my mother used to tell me!): “more haste, less speed”.

Use the interactive below to step through Rule 2. The first 5 stages use the author’s worked example (dice-scores 10, 8, 6, 7, 4); from Stage 6 onward your own randomly-generated dice are used.

OK, over to you—continue the experiment through a total of up to 40 stages. (Keep an eye on my timings though: if you get short of time then be content with fewer stages.)

Suggestion: If you are working in a small group rather than on your own, I suggest that each of you produce your own data. You can learn a great deal by comparing your different sets of results to discover which features are similar to each other and which are not. However, particularly if you are studying on your own, there are two runs of the whole experiment summarised in the Appendix for you to compare with your own results. Do your own experiment first though!

Finally, summarise the outcomes that you’ve just generated in a histogram. The “outcomes” are the resting positions of the marble, i.e. the positions of ● in the yellow-shaded rows in your table. However, now that you have as many as 40 data-values to include in the histogram, we need to think more carefully than before about what would be an efficient way to produce it.

Rule 1 of the Funnel (Ford’s Second Strategy)

I’ll postpone discussion on the outcomes from this strategy (which you’ll recall is what Drs Nelson and Deming called Rule 2 of the Funnel) until you’ve repeated the whole exercise using an easier strategy.

In contrast to Rule 2, let’s now be relatively idle by simply putting the funnel at 30 and leaving it there, irrespective of the outcomes, i.e. of where the marble finishes up. This strategy, which is Rule 1 of the Funnel, is of course equivalent to the Ford personnel switching off their automatic compensation device (which was their Second Strategy). So you’ll have some idea about what to expect in what follows!

As suggested above, on page 42, I recommend that you don’t bother to throw your dice any more but just use the same dice-scores as you obtained the first time. I mentioned two advantages of doing this on page 42, above.

In this case where you don’t move the funnel at all, you may be able to stop using the track almost straight-away. As I’ve just said, you simply put the funnel at 30 and leave it there. Referring back to my original five dice-scores which were 10, 8, 6, 7 and 4, these corresponded respectively to the marble finishing up 3 right, 1 right, 1 left, directly under and 3 left of the funnel. So, with the funnel stuck at 30, you can immediately see that the marble finishes up at 33, 31, 29, 30 and 27 respectively:

The 20–40 track with the funnel marker pinned above the target square 30 and the marble marker above square 33 — Stage 1 of Rule 1 using the worked-example dice-score of 10 (marble lands 3 squares to the right of the funnel).
Describe this diagram

The same 20–40 track, with the funnel pinned above the target square 30 and the marble resting on square 33. This is Stage 1 of Rule 1 played with the worked-example dice-score of 10: the marble lands 3 squares to the right of the funnel. Under Rule 1 the funnel stays put at 30 for every subsequent stage as well, so the marble’s positions can be read off directly from the dice-scores — 33, 31, 29, 30, and 27 for the first five throws.

As you can see, with Ford’s Second Strategy (Rule 1) you also no longer need the two rows which were under each yellow-shaded row in the Ford’s First Strategy (Rule 2) version of the book-keeping (see page 42 and then your table on page 44): they were only there to work out where that strategy (Rule 2) would move the funnel. Now, of course, the funnel stays put at 30. So, with everything being so much simpler than before, I think you’ll find it very easy to do the book-keeping this time!

So now summarise your new data in a histogram as before.

Discussion

Compare the two histograms you’ve drawn on pages 45 and above. As you’ll probably have realised already, the histogram that you’ve just constructed is somewhat more tightly clustered around the desired value of 30 than the previous one was. The difference may not be dramatic, but it’s certainly there. So this process performs better than the previous one: there is less variation. Yet this process was the “lazy” one. It is much less complicated, much quicker and easier to operate. With this strategy (Rule 1) we haven’t “tweaked” the process at all. We’ve put in less effort—and got better performance! With Ford’s original strategy (Rule 2), we worked harder but got worse performance. Some people seem to think that there’s a kind of rule of life stating that the harder we work, the better are our results. But, as Dr Deming often pointed out, it’s better to do nothing than to do the wrong thing! He was definitely an advocate of “Work smarter, not harder”! (See the 10th of the 14 Points on Day 5 page 8.)

I asked you a question in Activity 3–c (page 6) about the Ford automatic compensation example. Hopefully, you will now understand why I promised you would be able to answer that question before completing this Major Activity. Unless you produced a very peculiar set of scores from throwing your dice, you should see some similarities between the two histograms you’ve just drawn and the histograms which came from the Ford example on page 5—not in detail, of course, but broadly in terms of comparing one with the other. As there, the first histogram is more widely spread out than the second one, showing that the harder work (and, in Ford’s case, the extra expense of the automatic compensation equipment) actually increased the variation—making things worse, as Dr Deming pointed out.

So, to summarise, we have just seen that it is Rule 1 of the Funnel which has produced the better results. It was the original strategy, Rule 2, which produced the poorer results. The statistician’s advice to Ford (middle of page 5) was indeed wise.

Let’s now move on to …