Core Fundamentals of Six Sigma
By Shao Changqiang, Senior Statistician, 3M Singapore Pte Ltd
Introduction
Since its introduction first in Motorola, Six Sigma has received considerable attention recently as
more and more companies claim significant benefits through Six Sigma implementation. When
many companies eager to impress customers have begun to use the term “six sigma” to label
themselves, few really understand the core fundamentals of Six Sigma. As a professor once told
the author, Six Sigma is one of the most misunderstood strategies ever to hit business world. In
this paper, the author tried to demonstrate one of the core fundamentals of Six Sigma - statistical
thinking - a thought process guiding the implementation of Six Sigma.
Statistical thinking
Statistics is one of the most widely used tools. It has been applied to science and technology for
over a century. To many, statistics is complex and difficult. It scares many people by people’s
anxieties about math. The techniques may be sometimes complex, but the thinking is fairly
simple and easy to understand. When statistical thinking was applied to atomic phenomena,
quantum mechanics was formulated. Albert Einstein hoped that quantum mechanics would
eventually be replaced by something else. As he told his friend and associate, the greatest
physicist Niels Bohr, “I can’t believe God would play dice with the universe.” Bohr was reputed
to have responded, “Albert, if God wants to play dice, let him.” In spite of Einstein’s wishes,
quantum mechanics has not been replaced. If anything, it is now being applied more broadly.
When statistical thinking was applied to variation reduction in Western Electric Company in
1920s, Dr. Walter A. Shewhart gave the world his greatest contribution – control chart. That
started the modern quality management. Despite the amount of time which has elapsed, the true
purpose and hence the potential of his contribution is still little understood and greatly
undervalued.
The American society for Quality Statistics Division (1996) defines statistical thinking as a
philosophy of learning and action based on the following fundamental principles (see figure 1):
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All work occurs in a system of interconnected processes,
Variation exists in all processes, and
Understanding and reducing variation are keys to success.
Statistical thinking provides a philosophical framework for use of statistical methods. The
framework focuses on processes, recognizing variation, and using data to understand the nature
of variation and then reduce it. Without knowledge of statistical thinking, practitioners often
apply inappropriate statistical methods, which lead to poor decisions and mistrust of statistics.
Without understanding variation, our best efforts may make matters worse. As Dr. Deming says,
“Best efforts, without profound knowledge, ruin the system.”
How Customers Define Quality
I just bought a new washing machine (the previous one broken down just one month after the
warranty and repairing it just did not seem worth it) from a big electric shop. I was told that it
would be delivered to my home between 2:00-6:00pm the next day. That way I had to waste my
time waiting at home the whole afternoon. And the machine finally arrived at around 8:00pm. I
would rather be told the machine be delivered at 8:00pm.
We know from our experience that every product or service we purchase will vary from item to
item. Small difference from item to item may be acceptable, while large difference is not
acceptable. Thus business ordering is always accompanied by specifications. “We’ll be there
between noon and 5:00;” “Your meal will be delivered between 6:30 and 7:00;” “The diameter
must be within 20 – 40 um.” This kind of specifications greatly helps people conducting
business, but at the same time, leads people to think that meeting specification is achieving
quality. A classical example with an automobile company has been used widely to demonstrate
the fallacy of meeting specification limits is achieving quality.
An automobile company worked very hard to provide high value to its customers. This company
had cars equipped with transmissions from two different sources. One source was its own plant
and the other was from a Japanese subcontractor. Marketing people found that customers were
requesting the Japanese transmissions. Initial investigations showed that the warranty cost on
cars equipped with Japanese transmissions was lower and it ran quieter and smoother. This
surprised lot of people as both plants used the same engineering drawings in manufacturing the
transmissions. The engineers from this company decided to investigate further. They took apart
the transmissions of several cars of each type. They measured all parts on their own
transmissions and found that the parts varied in size but all within specifications. But when they
measured the parts on the Japanese transmissions, they couldn’t find any differences in the
dimensions of the parts from one transmission to another with the instruments at hand. They had
to be sent to a scientific lab for measurement. It turned out to be that the Japanese transmissions
had much less variation around the target values for a number of important characteristics. The
Japanese didn’t stop working on reducing their variation even though all characteristics were
within the specifications!
The lesson this company learned shattered its long-held belief that meeting specifications was
achieving quality. It realized that meeting specifications was not sufficient. It needed to continue
striving to get closer and closer to the target, well inside the specification limit. Dr. Genichi
Taguchi, who was awarded a Deming Prize in 1960, developed a graph to capture this concept. It
is now well known as the Taguchi Loss Function (see figure 2). The curve tells us that the
farther we get from the target, the loss to the society increases. If we order pizza to be delivered
to our meeting room at 1:00pm, we can easily adapt our schedule if it is delivered a few minutes
early or late. If it comes 10 minutes early or late, it may be a bit more difficult to adjust our
schedule. Thirty minutes early or late, we are most unlikely to adapt to the meeting schedule.
Thus the loss to us is greater and the farther the service gets from the target. Specification limits
do not reflect this increasing loss. If the specification limits for Pizza delivery are +/-10 minutes,
that means anything between these goal posts is equally acceptable, ten minutes late is
acceptable but 11 minutes late is totally unacceptable. That obviously is not how we as a
customer perceive the value of the service. The performances of two pizza hut restaurants are
shown here (see figure 3). Both meet specifications, or in other words, zero defects. As a
customer, you certainly prefer supplier A. One of the author’s experiences vividly demonstrated
this concept:
A couple years ago, I went to Japan to attend a conference. One morning I wanted to take the
train (bullet train) to visit a joint venture. As I didn’t know Japanese, I was quite worried which
station to get off. My very considerate counterpart told me: “Don’t worry yourself about the
name of the station, look at your watch, get off the train at 7:26.” Of course, to have a safe
arrival, I must also need a reliable watch. Luckily, I was wearing a Japanese watch.
Just think the economy of a single sentence in your plans, no further descriptions, and no
alternative plans in expectation of delays. How much time will be saved and how much
frustration will be avoided? Those who travel a lot sure have a lot of stories to tell about their
frustrations due to delays of their trains or flights.
The same concept can be applied to any situations. If the month-to-month sales fluctuate a lot,
the whole supply chain, from procurement of raw materials, manufacturing capacity planning,
inventory, warehouse, to the delivery to the final customers would be difficult to schedule. Look
at a simple planning example (see figure 4). Most people choose B when being asked. The
problem is the yield will vary around 90%. The cycle time will also vary around 6 days. To be
safe, some choose C. But how safe is safe? …The bigger the variations of yield and cycle time,
the more difficult for the planning. …To get the calculation correct is simple, but to apply in real
life takes knowledge about variation.
Quality to a customer is uniformity. If the train is scheduled to arrive at 7:26, it arrives at 7:26. If
you promise to deliver washing machine at 8:00, too early or too late won’t delight the customer.
The sales go up tremendously one month and go down to the valley next month causes
substantial problems. The definition of World – Class Quality is “On Target with Minimum
Variance.”
Variation Exists Everywhere
All work is a process and all processes have variations. Think of a process that makes a kind of
product (see figure 5). There are countless factors which affect the quality characteristics of that
product. The materials are not exactly the same quality, machines and work methods are not used
in the same manner, environment is constantly changing, inspection methods are not identical. If
none of these variations existed, all products would be identical and there would be no varying of
quality like the occurrence of defectives and non-defectives.
As far as the products we make are concerned, it is almost impossible that every product turns
out to be exactly identical. Let’s consider when you buy a product, or a service, or you are
engaged in a service operation, or a manufacturing process, or administrative process, etc. Does
it always work smoothly, the same way, take the same amount of time so that you can either do,
or experience, a perfect job? Or does it work fine one day, but have nasty surprises for you the
next? That is variation. Variation makes things difficult and nasty, unpredictable, untrustworthy.
Bad quality means too much variation, good quality means little variation. If these variations are
reduced, defectives or problems will certainly decrease. This is a simple, strong principle which
holds true regardless of types of product or kinds of methods involved.
In the financial world, sigma is used to measure the risk of an investment. In manufacturing
industry, sigma is used to measure the variation. We can see the common point for both
engineers and fund managers: Engineers are paid to reduce variation, that is to reduce sigma;
Fund managers are paid to reduce risk, that is also to reduce sigma.
Six Sigma is all about reducing variation. But, how do we reduce variation?
Understanding Variation
The Western Electric Company in 1920s wanted to make their telephone components as same as
possible.
“…The harder they tried to achieve consistency and uniformity, the worse were the effects. The
more they tried to shrink variation, the larger it got. They were naturally also interested in
cutting costs. When any kind of error, mistake, or accident occurred, they went to work on it to
try to correct it. It was a noble aim. There was only one little trouble-their worthy efforts did not
work. Things got worse…they were failing to understand the difference between common causes
and special causes. And that mixing them up makes things worse. … Sure we don’t like mistakes,
complaints from customers, customers… but if we weight in at them without understanding, then
we make things worse.” - Dr. Deming
A wonderful device for understanding variation is the Funnel Experiment. The funnel is mounted
on the top aiming at the center as shown in figure 6. We then drop the balls through the funnel.
Our objective is to have all the balls end up right in the center of our target. We drop 40 – 50
balls. The balls will form a distribution (see figure 6) which is very common in real life
situations, a bell-shaped curve, or normal distribution. Most of the balls fall in the center of our
target. Some fall in slots near the center, and few falls in slots farther away from the center.
We can treat the center slot as the target value of a customer need. You already know that quality
is on target with minimum variation. You look at the performance in figure 6. Customers may
not like the variation presented in the results. Why not develop a strategy to have all the balls fall
closer to the target? No one is going to blame us for trying. In fact, in real world a boss would
ask us to improve results, An obvious strategy is to adjust the funnel whenever a ball misses the
target. If a ball ends up to the right of the target, the funnel will be adjusted the same amount to
the left. That is to say if a ball ends up 2 slots right of the center slot, the funnel will be adjusted
2 slots left to its original position. Our reasoning is that with this adjustment the ball would have
hit the target on the next try.
If we follow this strategy, adjust the funnel each time when miss the target. We then drop 40-50
balls. The results will be also a normal distribution as shown in figure 7 (see figure 7). Clearly,
the variation is getting bigger; quality is getting worse when we work harder – adjust whenever
we miss the target! Think about testing a gun, you aim and shot, if you miss the target, the gun or
aiming mechanism will be adjusted. Does this improve the accuracy or lessen it? Most people
may say that adjustment helps the accuracy. But remember that there are many things that cause
a gun to miss its target. Each bullet has a slightly different shape, the gunpowder in each bullet is
packed differently, air current is constantly changing, etc. Adjusting after one shot is exactly like
what we did when we adjusted the funnel each time we missed the target.
It must be a bit of shock to realize that some of our best efforts to make things better are making
things worse. The problem is we always tend to work harder under current style of management!
Let’s put this experiment another way: Suppose your job is to hold a cup to catch the falling balls
(see figure 8), the more the better. The procedure may state that you shall hold the cup right at
the target, and you will catch most balls. We all know by now that natural variations form a
normal distribution as shown in Figure 6. The balls may fall on your left or right, but most of
them will end up in your cup if you don’t move your cup. If you move your cup to the left or to
the right, you will catch less.
The concept is simple, but when comes to the real life application. Few can resist the temptation
to move their cup to try to catch the falling balls.
Suppose you hold your cup at the center and a ball happens to be falling on your left. Will you
move your cup to your left? Many people without knowledge of variation may move the cup to
the left wishing to catch the next falling ball. You may not adjust the cup since you know that the
cup is in the center - on target. You will catch the most if you don’t move your cup from the
target.
But your determination to stick to your belief may change when the rule becomes “if you catch
one ball, you get $100(reward).”
You may give up your belief when the rule changes to “if you miss one ball, you lose $100
(punishment).”
Most people just cannot resist their temptation to adjust even though they well understand that
adjustment only makes things worse.
Do you see some similarities in current styles of management? If the numbers changes for the
better compared to last month, reward them. If the numbers changes for the worse compared to
last month, punish them. How many times you hear people say, “We need the carrot and the stick
in managing people.”
The Funnel Experiment holds many valuable lessons for us. You may argue that this is just
simulation. We don’t do these kinds of things in our real life.
Unfortunately, actions like that happen all the time, every day, in every organization at high
levels and low. Let’s take a look at the following real life examples.
A big semiconductor plant has a wire-bonding process (see figure 9). Gold wire is used to
connect die to the lead-frame. High power is applied to melt the gold wire to a small ball which
is then applied to the pad of the die. If this ball does not stick to the pad strong enough, it may lift
off and cause “open”. Ball-shear strength is measured to check whether the strength is strong
enough. Customers require that the Ball-shear strength must be no less than 30g.
It is easy to increase Ball-shear strength by increasing the power. When increase the power, the
ball gets bigger. It sticks to the pad stronger. The problem is when the ball gets bigger. Small
alignment deviation may cause the ball touch two pads and cause “short”.
The QA department set a limit at 45g. That means if the Ball-shear strength is less than 45g,
machines must be shutdown and, maintenance people are called to correct the problem.
Customers are impressed by this policy as the action limit is 15g higher than the specification
limit.
The problem was that the Ball-shear strength variation was too big, which caused lower cpk
value. The author tried to find out the causes. It turned out to be that the 45g limit was not
statistically determined limit. The author talked to the operators and maintenance people.
Author: “if the Ball-shear strength is less than 45g, what would you do?”
Operator: “I just shutdown the machine and inform maintenance people”
Turn to the maintenance people
Author: “What would you do if you are called in?”
Maintenance people: “Most of the time we don’t know why Ball-shear is low. We simply
increase the power.”
Operator: “Increase power makes the balls too big and that causes a lot of “shorts” since the
balls may touch two pads. I have to decrease the power.”
They were just doing similar things like what we did when we adjust the funnel. Increase power
when ball-shear is too low; decrease the power when the ball is too big. When control limit was
changed from 45g to 35g which was statistical determined based on the process. Variation was
reduced by 22%. Machine downtime was reduced from 4% to 2%. And surprisingly, the final
electrical test on “open” and “short” was also reduced and saving on this was about half a
million a year. All by doing less. When savings come from working smarter not harder, that is
real improvement.
Most people may say that adjustment help accuracy. All of us have adjusted something to bring
it back in line. We have taken it as a matter of faith that this would make things better. But
lessons show that this would make things worse. Over-adjustment of a stable system invariably
makes things worse. This deserves a special name – tampering.
The famous saying from Western Electric Company, “if it ain’t broke, don’t fix it” is probably
because those people were sick of all these kinds of over-adjustment, or in other words,
tampering.
A senior manufacturing manager once said: “if I were to start a new company, I would only hire
two employees, a man and a dog. The man would be there to feed the dog, and the dog would be
there to keep the man from touching the machines.”
This does not guarantee this manager is doing the right things! Tampering is not limited in shopfloor people. The following case may happen in any company.
Joe is a plant manager. He has a weekly meeting reviewing the performance. Based on his
experience, it is too bad if the defective rate is more than 5%, and it is quite good if the defective
rate goes below 3%(see figure10). Typically, he highlights the point which is above 5%, and
then asks someone, “what happened?” In asking for explanations, and demanding actions
based on that point, the scenario may go like this:
“What happened?!”
“I don’t know! I will go and see”
“Why this happens? What’s going on?”
“I am looking, I am looking, I am looking….”
“Don’t stand there, do something!”
By doing something, they are actually tampering, overreacting to variation, which often just
increases variation and cost.
However, what do they learn? Whenever they ask, “what happened?” and “do something”, the
defective rate goes down. They feel effectiveness and happy except that “What happened?”
happens again and again. For years, the defective rate remains the same. Even worse, when
praise is given for a good job, the defective rate goes up the following week! They learn that to
be effective, you must get tougher. They learn false lessons and put in false solutions.
When we put the same data in a control chart, it shows a stable process (see figure 11). When a
process is stable, common causes dominate the process. The way to improve the process is
working to improve the system, not adjusting the existing system. Real improvement will start
when we focus on the system improvement. Shewhart’s breakthrough in understanding variation
is the distinguishing the common and special causes. Special cause of variation should be
investigated and corrected. Common cause of variation should not be tampered. Very different
actions are called for depending on whether cause of variation is common or special. Control
charts help to distinguish common and special causes and provide guidance for the type of things
to do which will lead to real improvements.
I used to work with an organization. Near the end of each year, I looked at the budget which
was, say $800,000. If I found over $200,000 left, my next move was to try to spend it even I
didn’t really need it. Because if I didn’t spend it, my next year’s budget would be $600,000; If I
found I had spent more than $800,000, I would stop spending regardless the real need and
started preparing report to explain why over-spending.
I learned very fast. To avoid all these kinds of troubles, I would apply one million when my real
need was $800,000. The Ministry of Finance also learned very fast. They knew that I applied
more than what I really needed. They cut across the board by, say 20%: If you applied one
million, they gave you $800,000. If you applied 2 million, they gave you 1.6 million. This policy
encouraged me to apply even higher…. Till the number became unreasonable, an angry officer
from the Ministry of Finance came down. We went back to the original number, $800,000. Then
we started the game again!
This evil cycle will continue unless we change the policy. You cannot blame me as I was just
trying to survive in the system.
Just imaging how much energy and resources wasted here because we don’t understand
variation. It accomplishes nothing except to give the false sense that we’re taking actions. It
leads to higher costs, increase variation, and more wasted effort. Dr. Lloyd S. Nelson articulated
this fact succinctly, “Failure to understand variation is a central problem of management.”
3M Woodlands Plant’s Roadmap to Six Sigma
In his recent visit to Woodlands Plant (Singapore), 3M CEO, Jim McNerney recognized
Woodlands Plant as the benchmark in applying Six Sigma methodology even before the
deployment of Corporation Six Sigma. The roadmap taken is a typical example of applying
statistical thinking and statistical methods in manufacturing processes.
Educate plant population on statistical thinking and statistical methods. The most efficient
way to change the way people do things is to change the way people think. Statistical thinking
provides a lens through which we understand and optimize our organization. Statistical methods
are just the natural flow of the thinking. All employees are trained with basic understanding of
variation and control charts. The author experienced unlearning is even more difficult. There are
a lot of bad teachings in this area.
Set-up standard approach. The Pyramid (see figure 12) approach is well communicated to the
whole plant population. Understand customers’ needs, establish capable measurement system,
determine appropriate sampling structure, set up control charts, and report process performance
(cpk/ppk). Each process must follow this step by step with just in time training of the tools
needed in each step.
Leadership Team put their power behind the knowledge. As many agree that leadership is
vital for the success or failure of implementing Six Sigma, the Woodlands Plant leadership team
not only supports but also participates in Six Sigma. They are statistically minded managers.
They don’t ask questions that may make matter worse. They ask the right questions that lead to
real improvements.
People from worldwide over come to learn Woodlands Plant’s best practices. A group of visitors
visited our plant. They were shown everything and their questions were answered. At the end of
the tour, they might not learn what the difference of Woodlands Plant from many others they had
visited. Subtle difference makes huge difference as demonstrated in the case of a semiconductor
plant. Statistical thinking and statistical methods are used wisely in this plant. Without
knowledge of statistical thinking, they may have nothing to learn from Woodlands Plant’s
practices.
Conclusions
Of all the issues I’ve worked on with engineers and managers over the years, the control chart,
which is one of the applications of statistical thinking, has probably had the most profound
impact, made the most drastic changes in their view of the world. The main purpose for which
Shewhart created it was to provide guidance for the type of things to do which will lead to
improvement, to make things better, and stop doing things which make things worse. Yet, 70
years later, Dr. Deming lamented: “We may need another half century to fully appreciate Dr.
Shewhart’s contribution.” The sad, and costly, fact is that control charts are only used for
monitoring purpose if not misused. The usage is still hopelessly narrow and limited compared
with Shewhart’s understanding in his great book [5] of 70 years ago.
Dr. Hoerl from GE, in his recent discussion [7] wrote: “ …I actually believe that statistical
thinking, i.e., the statistical thought processes that are developed in the BB, is the single most
important aspect of their overall training. These thought processes include viewing all work as a
process, understanding the practical implications of variation, basing opinion on data whenever
possible, and mental rigor required to utilize a systematic, disciplined approach to improvement.
The tools are relatively easy to convey if you can develop this mental discipline of statistical
thinking first.”
Professor Goh from NUS said in the SQI Symposium: “…indeed it would not be unreasonable to
state that a Six Sigma initiative stands or falls, ultimately, on the extent to which statistical
thinking and statistical tools are truly understood and seriously applied.”
Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and
write. – H. G. Wells
[1] Brian L. Joiner. Fourth Generation Management: The New Business Consciousness.
McGraw-Hill, Inc., 1994.
[2] Deming, W. Edwards. Out of the Crisis. Cambridge, MA: MIT Center for Advanced
Engineering Study, 1986.
[3] Deming. W. Edwards. The New Economics: for Industry, Government, Education.
Cambridge, MA: MIT Center for Advanced Engineering Study, 1993.
[4] Henry R. Neave. The Deming Dimension. Knoxville, TN: SPC Press Inc., 1990
[5] Walter A. Shewhart. Economic Control of Quality of Manufactured Product. ASQ, 1980.
[6] Wheeler, Donald J. Understanding Variation: The Key to Managing Chaos. Knoxville, TN:
SPC Press Inc., 1993.
[7] Roger W. Hoerl. “Six Sigma Black Belts: What Do They Need to Know?” ASQ Journal of
Quality Technology, October 2001.