BASIC TOOLS
“Effective Six Sigma via Statistical Thinking”
by Willis Jensen
Introduction
Six Sigma is enjoying its moment in the limelight due
to the large number of “success stories” it has generated.
One only has to pick up the latest issue of a business
related magazine to find references to Six Sigma and the
impact it is having on companies all over the world.
While first conceived and implemented in a
manufacturing environment, its focus is expanding
beyond manufacturing to other diverse applications, such
as health care, finance, services, and government. There
is even speculation that Six Sigma can help save lives in
the war on terrorism. However, with all its success and
media attention, those in the Six Sigma “trenches” are
painfully aware that things are not always as rosy as they
are sometimes made out to be.
My attempt to discuss both the positive and negative
side of Six Sigma does not mean that I lack confidence in
the Six Sigma methodology. On the contrary, I have seen
tremendous success from applying the methodology and
its associated tools. My motive is simply to aid in the
continuous improvement effort. My own journey with Six
Sigma is not free of challenges. However, I have become
convinced that Six Sigma has the potential to transform
the way businesses attack and solve problems. I have
seen dramatic improvements in processes that have
helped increase employee morale and build stronger
customer satisfaction. I have seen the broader impact that
Six Sigma can have on an organization, making it more
data driven and focused on processes, instead of placing
blame on individuals. It certainly has potential to help
make “data-based decision making” more commonplace –
even where traditionally it has been ignored. I sincerely
hope that it does achieve its potential. I believe it can.
To fully achieve its potential, Six Sigma requires more
than just “talking the talk.” It has to be done right.
Effective utilization of Six Sigma requires much more than
doing a bunch of training and christening a bunch of
“belts.” It requires changing the mindsets of all the
individuals involved. It involves a different way of
thinking than what most people are accustomed to.
Effective utilization of Six Sigma methodology requires
outstanding use of statistical thinking.
Statistical Thinking
According to the Glossary and Tables for Statistical
Quality Control: 3rdEdition published by the ASQ
Statistics Division, statistical thinking is based on the three
following principles:
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1. All work occurs in a system of interconnected
processes.
2. Variation exists in all processes.
3. Understanding and reducing variation are keys to
success.
The principles of statistical thinking are straightforward
and make a lot of sense. However, applying them to
solve problems is a bit more difficult than it first appears.
In my experience teaching people the principles of
statistical thinking, I have learned that there is variability
in how well people truly understand the concept.
An important thing to remember is that statistical
thinking is a philosophy and does not have much to do
with the traditional view of statistics. I often ask students
what they think of when they hear the term “statistical
thinking.” Most of the time, the answers have to do with
the ability to analyze and interpret data. In fact, “statistical
thinking” may be somewhat of a misnomer, a more
accurate term in my view is “process-oriented thinking,”
but I digress.
For more information about statistical thinking, there
are a number of excellent articles and publications that
have been published by the Statistics Division. For
example, see the first and second special publications of
the ASQ Statistics Division, or Improving Performance
Through Statistical Thinking by Britz et al.
Six Sigma
While many may be familiar with the general idea
behind Six Sigma, there are many different definitions.
For example, Mikel Harry – widely considered one of the
influential founders of Six Sigma at Motorola - put it this
way:
“It is a business process that allows companies to
drastically improve their bottom line by designing
and monitoring everyday business activities in ways
that minimize waste and resources while increasing
customer satisfaction.”
George Eckes, an external consultant who helped
implement Six Sigma at GE defined Six Sigma in two
aspects: technical and cultural. The technical aspect deals
with the well-known target of 3.4 defects per million
units. The cultural aspect, which Eckes considers to be far
more important, is one of continuous improvement or as
he says, a “never-ending dissatisfaction with current
performance.”
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“Effective Six Sigma via Statistical Thinking”
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Pande, Neuman, and Cavanaugh define Six Sigma
as:
“A comprehensive and flexible system for
achieving, sustaining and maximizing business
success. Six Sigma is uniquely driven by close
understanding of customer needs, disciplined use of
facts, data, and statistical analysis, and diligent
attention to managing, improving, and reinventing
business processes.”
A recently published glossary in Quality Progress
defines Six Sigma as:
“A methodology that provides businesses with the
tools to improve the capability of their business
processes. This increase in performance and
decrease in process variation leads to defect
reduction and improvement in profits, employee
morale and quality of product.”
Because it encompasses so many different aspects, it
would be difficult to create a single definition that
everyone would agree with. Different people have
different ideas about what it means. However, all these
definitions have the same general idea – continuous
process improvement. This has long been a part of other
quality improvement efforts from the past.
This process improvement is achieved using the
DMAIC (Define, Measure, Analyze, Improve, and Control)
methodology. The “D” phase essentially defines the
process to be improved along with its major inputs and
outputs. The “M” phase measures the current level of
performance in the process and ensures that the
measurement system is adequate. This level is defined in
terms of a key output of the process, often called a
project Y. This project Y becomes a key metric and is
useful in determining whether or not there has been an
improvement in the process. The “A” phase analyzes the
relationship between the key inputs of the process and its
outputs. The “I” phase involves some form of
experimentation (many times in the form of a DOE) to
improve the process and verify the relationship between
key inputs and outputs. The “C” phase involves placing
controls for the critical inputs. This ensures that the
improved performance level of the process can be
sustained over time.
DMAIC uses many different tools for the various
phases. Many are statistical in nature, like control charts,
capability indices, measurement systems analysis, design
of experiments, multi-vari analysis and others. These
statistical tools can be used in all the phases. Other tools
also play a strong role in DMAIC methodology; process
maps, cause and effects matrices, failure modes and
effects analysis, control plans and others. Use of these
ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 2
tools to improve processes is not new; it has been part of
past quality control programs. What is different about
DMAIC is a stronger focus on maintaining the improved
process through a control plan. In addition, it provides a
strong link of the process to be improved and the
strategic plan of the organization.
The overall goal of DMAIC is find the critical inputs,
understand their relationship to the key outputs and then
control them to maintain an improved level of
performance in the process. If the methodology is used
correctly, the improved process generally results in some
financial benefit. This financial benefit is what holds such
a strong allure to the business community. It is the reason
for all the attention Six Sigma has received. Six Sigma has
made a strong link between the use of the tools and
financial results. It has done a good job of keeping in
mind the real reason for any improvement program, that
of making the organization better and more profitable.
For more information on Six Sigma, see references 6, 7
and 8 in the bibliography.
Relationship between Six Sigma and Statistical
Thinking
While companies tout Six Sigma as a methodology to
save money and improve operational performance, the
core philosophy behind any successful Six Sigma
program is statistical thinking. The two should be
inextricably linked to ensure that Six Sigma results are
real and lasting.
The critical inputs that are diligently sought through
DMAIC methodology are simply sources of variation in
the process. The idea is to understand the sources of
variability to improve and control the process. When
correctly applied, DMAIC then becomes a formalized
methodology for understanding and reducing variation principle #3 of the definition of statistical thinking.
A Six Sigma program is doomed to fail if it only
focuses on the financial results. Many Six Sigma programs
have overemphasized a focus on cost reduction. If
process improvement does not accompany that focus on
costs, any realized financial gains will only be temporary.
Processes will continue to perform at the same level.
Remember the definition of insanity is doing the same
thing we have always done and expecting different
results. To get the fundamental, long-term savings, you
have to focus on process improvement, not cost cutting. I
have seen many cost cutting programs disguised as Six
Sigma “process improvement” projects. While this may
yield temporary financial benefits, it undermines the longterm success of the Six Sigma program.
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“Effective Six Sigma via Statistical Thinking”
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When adopting a philosophy of statistical thinking in
conjunction with Six Sigma, the focus becomes
fundamental process change. It moves us away from
trying to massage the data to get the answers we want.
Statistical thinking helps us to focus on sustainable, longterm improvements. It is very compatible with a
philosophy of continuous improvement and Six Sigma
methodology. In fact, it is necessary to ensure success.
In addition, Six Sigma complemented with the
philosophy of statistical thinking adds a focus on only the
most important sources of variability (the critical inputs).
It helps us to reduce their negative impact. For any
particular process, there are many different sources of
variability. It is more effective to focus on those sources
that have the most dramatic impact on the output. We
can picture Six Sigma methodology as a funnel that acts
to narrow the list from all the potential sources of
variation to a manageable number. Figure 1 illustrates the
concept.
Figure 1 – “The Funnel”
Existing process
Potential sources of variability
D
M
A
I
C
Statistical Thinking is the
philosophy that says
sources of variability
exist in all processes
Critical sources
of variability
Improved process
Financial Results
Examples
I would now like to show some examples of where
failure to understand the principles of statistical thinking
can have an impact on a Six Sigma project. Before doing
so, I want to clarify that there are many reasons why a
project may not be successful. These can be separated
into two major categories (or levels) of failure:
Deployment and Technical. See Table 1 below for some
examples.
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Table 1 – Examples of Six Sigma failures
Level of failure
Examples
Deployment
Lack of resources, No upper
management support, Team dynamics
issues, Resistance to change, Failure
to link projects to strategic plan, No
accountability for results, No
champion support, Unclear project
goal
Technical
Misapplication of statistical tools,
Wrong interpretation, Wrong analysis,
Not finding right critical inputs, Using
wrong or bad measurement system,
Failure to control process, Not using
right metrics
Much of the Six Sigma literature focuses on the
deployment level. As an example, Eckes lists 10 reasons
why Six Sigma initiatives fail and how to avoid making
those mistakes. Nine of them deal with deployment
related issues. Only one deals with a technical issue –
that of confusing special vs. common cause variation.
Other Six Sigma literature has similar discussions (See #6
or #8 in list of references).
In the remainder of this paper, I will focus more on
the technical failures that can occur when utilizing Six
Sigma methodology. This choice of focus does not mean
I think the deployment side of things is not important.
Quite the contrary, I believe deployment failures must be
addressed as soon as possible. They have been the
downfall of many a Six Sigma program. The principles of
statistical thinking can certainly be applied to handle the
deployment issues. However, many practitioners of
statistics deal more with the technical issues because of
their technical background. That seems like a good place
to start looking for applications of statistical thinking to
Six Sigma.
Many technical failures could have been avoided had
there been a thorough understanding of the principles of
statistical thinking. The examples below highlight just
some of the technical failures that I have seen. Certainly
many more could be discussed here. Each one is
followed by a key learning.
Example #1
A project was aimed at reducing relocation costs for
employees. The team decided to use cost per relocation
as their project Y. Because they were so focused on costs,
they had a difficult time mapping the process. They had
trouble applying DMAIC because they were not focused
on the inputs and outputs of the process. The work
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of the team resulted in a series of cost cutting action
items.
Short-term savings were accomplished by changes in
company policies but there was no understanding of the
process. However, they were not able to see the impact
of those changes. The relocation process producing the
costs is still the same. In addition, there is no
understanding of the satisfaction level of the participants
of the process. Those involved in the process still have
the same problems they have always had.
An understanding of statistical thinking could have
prevented this situation. The team would have focused
on the process to be improved. More time would be
spent on mapping the process and determining the key
sources of variability in that process. This would result in
a better understanding of the process and sustainable
process improvement.
It is important with any Six Sigma project to use a
project Y that focuses on the process. In other words, the
project Y should be an output of the process. You will
notice that in Figure 1, the financial benefit is off to the
side. The financial result is not an output of DMAIC; it is
a result of the improved process.
Learning – Do not use metrics that have $ as the unit
of measurement
Example #2
One project leader was struggling to figure out how to
apply the principles to his project. After discussing the
project with him, it became obvious that the team already
had a solution in mind - outsourcing the manufacture of a
particular product. By outsourcing, they felt like they
could make the product with fewer costs.
In this case, DMAIC tools were being used, but the
leader was simply going through the motions. The tools
were not adding value to the project because they were
not improving a process. They were just implementing a
change. It was fruitless for the team to apply all the tools
simply to say they had used them.
Statistical thinking helps to focus on the process and
look at all possible solutions – or sources of variability. It
reduces the number of “just do it” or “solution in mind”
types of projects. It increases the number of things that a
team can consider doing to reduce variability and
improve processes.
Learning – Make sure you are trying to improve a
process, not a “just do it” project or a “solution in
mind” project.
Example #3
Some Six Sigma projects focus on the project Y at the
expense of other metrics. For example, a completed
project was not achieving its targeted level of
performance. The reason? Fixing a problem in one area
had caused problems in another area. The process was
sub-optimized. The team did not consider the impact of
their solutions on the other related processes.
This is a failure to recognize that all processes are part
of a system, that is, they are interconnected. I applaud the
choice of words in the definition of statistical thinking
“All work occurs in a system of interconnected
processes.” Sometimes we get caught up in the idea that
all work occurs in processes that we forget how
interconnected they really are.
Any Six Sigma project that strives to improve a process
must be aware of the potential impact on other processes.
This can be accomplished by using a good
counterbalance metric. A counterbalance metric simply
measures what could be negatively impacted by changes
in the project Y. For example, if the project Y were to
improve the production rate of a machine, a good
counterbalance metric would be the measurable quality
characteristics of the outgoing product.
Learning – Always include an appropriate
counterbalance metric that is measurable.
Example #4
On another occasion, someone wanted my help to
figure out how to do her statistical analysis in the Analyze
phase. She had already completed the Define and
Measure phases and had a list of key inputs to analyze. It
turns out that she was doing the analysis correctly but
was not getting any information from her results.
Upon further questioning, it was determined that the
inputs were not controlled. They were simply “noise
variables” and she had not come up with any way to
improve the process. She had to go back to find other
inputs that could be used to improve and control the
process. With some rework of the results of the Define
and Measure phases, she was able to find some
controllable inputs. The controllable inputs allowed the
project to achieve its goals and improve the process.
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ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 2
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“Effective Six Sigma via Statistical Thinking”
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Learning – Focus on the inputs that can be
controlled or inputs that can mitigate the effect of
noise variables.
Example #5
Two key components of DMAIC methodology are to
present the initial capability and final capability of the
project Y. The initial capability, occurring during the “M”
phase, simply measures the current level of performance
in the process. The final capability, occurring during the
“C” phase, measures the new level of performance in the
improved process. Many times this analysis is done with
capability indices such as Cp and Cpk. However, the
main tool should be simply a control chart. While
capability indices can be useful, do not overemphasize
them. For many non-manufacturing projects, the
capability indices mean little because there are no
customer specifications.
An effective project leader will always show a control
chart of the data and refer to that chart frequently to
show real improvement in the process. If a control chart
cannot be created, it is either because the data was not
collected or because the project is not really a process
improvement project. If data was not collected in the
past, the data collection should begin as soon as the
project starts.
Someone who understands statistical thinking will have
a strong focus on the control charts, the process view of
the data. They recognize that control charts should be
part of all Six Sigma projects.
Learning – Always plot the data for initial and final
capability. Do a control chart of all the data in
chronological order.
understand is this one: “a series of actions or operations
conducing to an end” (emphasis added). It is important
to make sure that people understand that when we talk
about a process, we are talking about a series or
sequence of steps with inputs and outputs. It is ironic to
think that there is variability even in the definitions of
terms like processes and variation. However, it is
important for us to be clear and consistent in our term
usage.
Second, we must realize that statistical thinking
(process-oriented thinking) is not natural. It may be easy
to understand the words but to actually apply them is a
completely different ballgame. It is a counter-intuitive at
times. Our educational system teaches us deterministic
principles, that there are facts and unchangeable things.
The scientific method, in its pursuit of testing hypotheses
and discovering new theories, encourages a deterministic
mindset – that there is a fixed truth. For individuals to
fully assimilate the principles of statistical thinking, they
have to relax their deterministic beliefs. This can take
some time getting used to.
A couple of things I have found, to help people learn
and better understand the concept of a process, are the
high-level process map and the fishbone diagram. An
example of a high-level process map is shown in Figure
2. This process map is just a “50,00 foot view” of the
process to be improved and includes a simple name. If
you cannot give a name to the process, you will not be
on the right track. Once the process is defined, you can
talk about the major inputs and outputs of the process.
Figure 2 – High level process map
Inputs
Solutions
To prevent these types of failures, the concepts of
statistical thinking need to be taught, reinforced, and
solidified in the minds of those involved in Six Sigma.
Below are four solutions that will help in the effort to
overcome some of the technical failures previously
mentioned.
First, we must have greater care in defining the terms
we use. One problem is that when we as statisticians talk
about processes and variation, people sometimes have
different operational definitions. To those not familiar
with statistical thinking, the word process can mean
something different. The dictionary has several different
definitions for the word “process.” One is “something
going on” and another is “a natural continuing activity or
function”. However, the one that we want people to
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Inputs
Process
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“Effective Six Sigma via Statistical Thinking”
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Figure 3 – Fishbone diagram
With the high level view in place, you can then begin to
talk about the specific steps of the process and talk in
more detail about specific inputs and outputs.
Generally, a process map is created by first listing the
steps and then listing the corresponding inputs and
outputs. However, it may be helpful to first list the inputs
(by way of the fishbone diagram) and then try to
organize them into steps. The idea is to get people to
think in ways they have not thought by considering all
the potential inputs.
On one occasion, someone was having a hard time
figuring out what to do next on her project. She had gone
through the steps but had not really come up with
improvements to make in the process. We went back to
the beginning of her work and I found very few inputs
on her process map. I encouraged her to do a fishbone
diagram, which doubled the number of inputs. With the
new inputs in hand, she learned that some of them were
crucial to improving the process.
Third, improve Six Sigma training curriculum. Statistical
thinking should be taught as the fundamental concept in
any form of Six Sigma training curriculum. This should be
done near the beginning of any training session before
talking about any of the DMAIC tools. In addition, in any
sort of training, we have to teach the purpose of the
tools, and not just the tools. We have to de-emphasize
the theory and calculations and focus on when and why
the particular statistical tool should be used. I like to tell
people to focus on the “spirit of the law” rather than the
“letter of the law” when applying Six Sigma methodology.
To learn the “spirit of the law” you have to provide
examples, examples, and more examples. Supplementing
training materials and instruction with a wide variety of
examples help to solidify concepts of statistical thinking.
ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 2
Lastly, we can be what Hahn has called the “Proactive
Statistician.” This involves anticipating problems and
seeking out solutions before the problems occur. This will
be a big change for many of us who are used to the
traditional “consultant” role of statisticians. It requires us
to do more value added activities. It requires us to play
more of a leadership role and take advantage of the
opportunities before us.
Conclusion
Statistical thinking is fundamental to the success of Six
Sigma. It plays a key role in bringing about true process
improvement. Application of the philosophy of statistical
thinking prevents many types of technical Six Sigma
failures.
While the business culture is changing and the
traditional role of statisticians is evolving, there is much to
cheer. Six Sigma represents a powerful means to help a
wider audience embrace and assimilate the principles of
statistical thinking. That has to be a good thing. We
should be excited about the role we can play in bringing
about that change. We have a responsibility to ensure
that we are really helping others better understand the
rather chaotic world around us. This will ensure a better
place for all of us.
References
ASQ Statistics Division (1996). Glossary and Tables for
Statistical Quality Control, Third Edition. ASQ Quality Press.
Balestracci, D (1998). Data ‘Sanity’: Statistical Thinking Applied
to Everyday Data. ASQ Statistics Division Special
Publication.
Britz, G., Emerling, D., Hare, L., Hoerl, R., Janis, S., and Shade, J
(2000). Improving Performance through Statistical Thinking.
ASQ Quality Press.
Britz, G., Emerling, D., Hare, L., Hoerl, R., and Shade, J (1996).
Statistical Thinking. ASQ Statistics Division Special
Publication.
Eckes, G. (2001). The Six Sigma Revolution: How General
Electric and Others turned Process to Profits. Wiley & Sons.
Hahn, G. (2002). Deming and the Proactive Statistician. The
American Statistician, Vol. 56, No. 4, 290-298.
Harry, M. J., Schroeder, R., and Linsenmann, D. R. (2000). Six
Sigma: The Breakthrough Management Strategy
Revolutionizing the World’s Top Corporations. Random
House.
Pande, P. S., Neuman, R. P., Cavanagh, R. R., and George, M. L.
(2000). The Six Sigma Way: How GE, Motorola, and Other
Top Companies are Honing Their Performance. McGraw-Hill.
Quality Progress (2002). Quality Glossary, Vol. 35, No. 7, 43-61.
USA Today, October 31, 2002
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