Article Type : Review Article
Authors : Sheng Pin Kuan
Keywords : Control chart; Common cause; Special cause; Funnel experiments
In the book “Four Days with Dr. Deming”, Dr. Deming
explained the problems of management and intervention with funnel experiments.
Managers often interfere with the system due to lack of statistical thinking
about system variation, causing the problem becomes more and more complex. For
example, in the quality meeting, the management level in the factory requests
the process with the highest defective percentage to propose an improvement
plan; in the business meeting, the manger requests the salesperson who got a
decline in sales volume to propose a countermeasure. However, in the long run,
the defective percentage is still high or low; the monthly sales volume is
still good or bad. In the past, mentors in the school ranked the students on a
weekly examination basis, and warnings were given to the students who had
stepped back (it should still be the same now). The students' rankings are
still there. Much of the variation in these data is the normal variation of the
system, which is the so-called Variation of the Common Cause. However, managers
intervene on these variations and take corrective actions to make the system
more complex. For example, process personnel hide defective products to make
the defective percentage looks good; business personnel falsely report sales
volume to make the book looks good; students go to the cram school to practice
the examination topics first to make the ranking progress. These phenomena are
common in our work or living environment. We should first understand whether
the system variation is caused from the Special Cause or only the Common Cause,
and then take appropriate actions.
"Close to
Academician": Liu Yuanzhang: China's "factory doctor." In the
article, Liu Yuanzhang, the father of Chinese quality, told a story [1]:
His first test was completed in 1957 at the
Shanghai State-owned Second Textile Machinery Factory. The main product of this
factory is the textile machine, one of which is the key component of the fine
grinding process. Liu Yuanzhang saw in the workshop that the operator who
worked on the grinding machine was an old master. Every time he finished
grinding one piece, he handed it over to the young master. After the young
master accurately measured the product size, he told the old master whether it
was thick or thin. Liu Yuanzhang draws the data measured by the young master
into a trend chart according to the processing order, and then asks the old
master to process it alone without the help of the young master, and then draws
the finished product data into a trend chart. It is clear from the charts that
the data of both processing fluctuates around the standard size. However, the
fluctuation of the processing time of the old master alone is obviously much
smaller than when they cooperate. The reason is that the old master is rich in
experience, when the young master is on the side, he interferes with the old
master’s operation. Liu Yuanzhang explained through this small example that
quality control is not a traditional simple statistical test. Instead, it
controls the factors affecting product quality in the production process
through the principle of mathematical statistics, so as to make the product
quality fluctuate in every link as much small as possible. Ultimately achieve
stable, high-quality production on the whole. In the book “Four Days with Dr.
Deming” [2], Dr. Deming explained the problems of management and intervention
with funnel experiments. Managers often interfere with the system due to lack
of statistical thinking about system variation, causing the problem becomes
more and more complex. For example, in the quality meeting, the management
level in the factory requests the process with the highest defective percentage
to propose an improvement plan; in the business meeting, the manger requests
the salesperson who got a decline in sales volume to proposes a countermeasure.
However, in the long run, the defective percentage is still high or low; the
monthly sales volume is still good or bad. In the past, mentors in the school
ranked the students on a weekly examination basis, and warnings were given to
the students who had stepped back (it should still be the same now). The
students' rankings are still there. Much of the variation in these data is the
normal variation of the system, which is the so-called Variation of the Common
Cause. However, managers intervene on these variations and take corrective
actions to make the system more complex. For example, process personnel hide
defective products to make the defective percentage looks good; business
personnel falsely report sales volume to make the book looks good; students go
to the cram school to practice the examination topics first to make the ranking
progress. These phenomena are common in our work or living environment. We
should first understand whether the system variation is caused from the Special
Cause or only the Common Cause, and then take appropriate actions.
The so-called
"funnel experiments" means that we have a funnel, which is mounted on
a table about half a meter high, there is a target on the table. Suppose we put
a marble into the funnel, regardless of the way we put it down, the marble will
roll down the funnel in a random way. Then it will fall from the bottom of the
funnel to the target and mark it with a pencil. We use some simple rules to aim
the funnel at the target, these rules are quite equivalent to some of the rules
we use in operating equipment, controlling processes or managing systems.
For the convenience to do the interpretation of the
statistical model and the simulation of the data, we illustrate it in the time
series of two dimension. With zero as the target value,
Rule 1: At the beginning, aim at the target value, and then the aiming position is not adjusted every time. The statistical model is as shown in Figure 1 and the following formula (Figure 1):
Figure 1: Rule 1.
Rule 2:
According to the difference between the last drop point and the target value
Figure 2: Rule 2.
Figure 3: Rule 3.
Rule 4: Aiming for the last drop, the statistical model is as shown in Figure 4 and the following formula (Figure 4):
Assume that each
marble has a random error
Figure 5: Trend Chart of Rule 1 ~ Rule 4.
Figure 6: Histogram of Rule 1 ~ Rule 4.
Rule 1: Aim at the target value each time
The purpose of
process control is to economically and effectively control product or process
quality. In other words, when the process has only common cause variation, do
not adjust or tamper with the process; when there are special because
variations in the process, do not ignore the corrective action. The purpose of
process control is to make the process under the statistical control, as shown
in Figure 1, so that its variation only originates from the common cause of the
process. In this way, it is possible to monitor the process that can be
perceived when special causes arise, and to remove the bad effects of the
product or process quality, and to retain the benefits of the product or
process quality.
Rule 2: Adjusted in reverse by the previous
aiming position
It can be regarded
as the system under the common cause of variation, due to the operations and
management personnel lack of understanding of the system, interfere with the
system, and make the system structural changed. Unless the system itself is
influenced by some predictable factors, rule 2 can be applied to adjust the
system to reduce its variation. For example, the air conditioner's automatic
temperature control system adjusts the amount of cold air as the room
temperature changed so that the room temperature is at a fixed temperature.
MacGregor once explained that the average change in the system is predictable,
and Rule 2 will have less variation than Rule 1. Therefore, when interpreting Rule
2, we must assume that the system is under the common causes of variation. The
following examples illustrate [3]:
·
Automatic process control often adjusts the process by the results of
the previous process status;
·
Operators always adjust the process compensatory with the difference
between measurement result and the target value;
·
The teacher of the junior high school in Taiwan always determines the
severity of the penalty by the student's test score;
·
When cooking, it is customary to taste salty, add water or salt to
neutralize salty, making the dishes that are served each time differently.
Rule 3: Adjustment return to the target value
As the compensatory
adjustment of Rule 2, the adjustment returns to the target value and then
adjusts the difference. When there are common causes in the system, the
variation will be greater than the adjustment method in Rule 2.
·
The salesman’s performance in the month is lower than the target of
100,000 yuan, and the next month's performance must reach the target plus
100,000;
·
Political ideology, in accordance with public opinion or votes,
reverse adjustment of governance;
·
Loss of gambling or stock investment, double gambling investment or
investment, hope to win back the money, the result is not a big lose or is a
big win, usually a big lose;
·
The current budget of the public agency has not been used up, in the
next period, we should use more to make up for it.
Rule 4: Aiming for the last drop
This is the most
common mode of intervention and is visible in almost all industries,
governments, and academic institutions. The following examples can illustrate:
·
The operator takes previous production result as the standard, and
follows the standard to produce, omits the original standard;
·
When the engineering change, only refer to the last version as the
basis for the change, without tracing the original design;
·
In the education and training situation, the old students teach new
students or a elder students lead his younger students, but those student
teachers without well-trained;
·
Budgeting is based on the result of the previous period and
multiplied by some percentage, without any plans;
A kind of TV program, the host gives the first
performer a title, the first performer is shown by hands without talking to the
second performer, the second performer do the same way to the next performer,
and so on. After a long run the final performer announces the title which he
thinks what is, usually very far away.
The funnel
experiment emphasizes that managers must use statistical thinking ways to
distinguish the variation of the process system caused by common causes or
special causes. If there are special causes, the managers should detect and
correct it. If the variation of process system due to common causes, the
managers do not interfere it, just study the process system capability is large
enough to improve it. These are traditional SPC methods such as, Shewhart
Control Chart, CUSUM Chart, and EWMA Chart, which are used to monitor the
process or system. However, engineering process control often uses some control
methods to adjust the process system when the process system is floating, so
that the process system does not deviate from the target or increase the yield
of the process system. In the field of automatic control has been applied for a
long time, generally referred to as Engineering Process Control (EPC). These
two areas are originated from different industrial patterns. SPC uses the
component industry as the object of application, while EPC uses the process
flow industry as the object. In recent years, the quality methods of these two
industries have not had much difference based on the development of mixed
industries. For example, in the IC industry, the pre-process is a process flow
industry, and the post-process is a component industry. Therefore, the
integration of SPC and EPC applications will be the trend of future process
control [4].
1. Yuanzhang
L. China's "factory doctor", Chinese People's Party newspaper
reporter Li Shuya. Close to Academician.
3. MacGregor
JF. A different view of funnel experiment. J Quality Technol. 1995; 22:
255-259.