the six sigma process

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The Six Sigma Process

In this module we introduce the Six Sigma process. Many companies have tailored this process to meet

their specific needs and so have their own version of the process. We will use a fairly generic process

that should serve you well even if your company process is a bit different.

Reference

• This module is based The Six Sigma Handbook , by Thomas Pyzdek, published by McGraw-Hill, and Six

Sigma for Dummies, by Craig Gygi, Neil DeCarlo, and Bruce Williams, published by Wiley Publishing, Inc.

Slide two

The primary references for this module are shown on the slide, but I’ve also been influenced by other

things I’ve read and learned over the years.

Why study the Six Sigma process?

• You need a common process that may be used to guide all quality improvement projects in the

Company

• The Six Sigma process is the state-of-the-art process for doing “problem solving” projects, and those

projects are the heart of quality improvement

• The Six Sigma process is PROVEN

Slide three

We mentioned in our quality management module that a company needed to create a common quality

culture so that all its associates know how to interact and work within that culture. Over the last few

years, a Six Sigma process has served as that culture for many of the top global organizations. As a

result, we have learned a lot about the process and how to make it work extremely well. I am sure we

will continue to improve it in future years, but I believe it is very good for professionals to have a solid

understanding of the state-of-the-art process today. This process is a proven process that has had a

great impact in many different companies around the globe.

4

Outline

• Motivation and background

• Define

• Measure



• Analyze

• Improve

• Control

Slide four

Since you are enrolled in this course you probably do not need additional motivation to convince you to

study the Six Sigma process. Nonetheless, we will provide a couple of slides of motivation and

background before launching into the standard define, measure, analyze, improve, and control steps of

a typical Six Sigma project.

5

Examples of the Impact of Six Sigma

• General Electric: $7 - $10B in 5 years

• Dupont: $2.4B in 4 years

• Bank of America: $100Ms, cycle time improvements greater than 50%, errors reduced by an order of

magnitude in 3 years

• Motorola: $2.2B in 4 years

• Caterpillar: Paid for itself the first year

Slide five

We have listed some examples of the impact of the Six Sigma process on some high profile

manufacturing and service organizations. The magnitude of these results justifies the statement that Six

Sigma was of strategic importance for these organizations. It is easier to obtain information about Six

Sigma impacts from larger and higher profile companies than others. However, it will be easy for you to

see as we go through this module that the tools and methods of Six Sigma would apply to any

professional organization, large or small. It will also be easy to see that they apply to manufacturing

companies, service organizations, and healthcare organizations. I obtained the information on

Caterpillar from their website and thought it was interesting that a $35 billion a year company could

implement Six Sigma and have it pay for itself in the first year. This is important since companies are

sometimes reluctant to implement a Six Sigma process for fear that it will take a while to start payingback. I think sometimes the companies themselves are too patient with the process and should demand

more. In late 2005, I started to work with a $50 million a year company on the implementation of a

quality revolution via a Six Sigma process, and so I know that it works in smaller firms. This particular

firm is already a leader in its industry but wants to get even better. It is true that the implementation

may be a little different since a smaller firm that cannot afford the dedicated resources like the larger



companies listed in the slide. We will try to point out some of these differences as we go through this

module.

6

How Did Six Sigma Get Its Name?

If the area under the curve represents

1,000,000 parts, then the area Under

the curve but OUTSIDE the

specification limit bars is 3.4 parts.

The area between the specification

limits is actually +/- 4.5 σ, not +/- 6 σ.

The 1.5 σ difference allows for some

“noise” in the process.

Slide six

It is interesting to note that in a statistically pure sense Six Sigma is really 4.5 Sigma. The slide will help

us explain why that is true. In statistics, Sigma is a Greek letter that is commonly used to mean the

standard deviation for a normal probability distribution. Assuming such a distribution, there are many

probabilistic statements that we may make. For example, if we were to take the area under the bell

shaped curve from plus one standard deviation to the right of the center line (which is the mean) to one

standard deviation to the left of the center line, it would contain 68% of the total area under the bell

shaped curve. If we were to subdivide the entire area under the curve into one million equal parts, andthen place vertical specification limits at plus 4.5 sigma and -4.5 sigma as illustrated in the chart, then

3.4 of the equal parts would fall outside the upper and lower specification limits, but still under the

curve. This is the statistical basis for the Six Sigma process. If you were to measure the area outside plus

or minus Six Sigma, you would find only 0.002 of one unit out of the one million equal units mentioned

above. So why the difference between Six Sigma and 4.5 sigma? The 1.5 sigma difference is to allow for

an inability to keep a process perfectly centered at all times. So it allows our real-world distribution to

slide to the left or the right and still maintain the 3.4 defects per million standard. So now you know

that Six Sigma got its name by really being 4.5 sigma!

7

Definition of Six Sigma

• “Six Sigma is a problem-solving methodology for minimizing mistakes and maximizing value”

• Source: Six Sigma for Dummies, Gygi et al.

Slide seven



Here we have a simple definition of Six Sigma that emphasizes both minimizing mistakes and maximizing

value, implying that Six Sigma can be used to impact both the bottom line and the top line for a

company. Let’s contrast this definition to the two others that follow.

8


• “Six Sigma is a rigorous, focused and highly effective implementation of proven quality principles

and techniques that aims for virtually error free business performance”

• Source: The Six Sigma Handbook , Pyzdek.

This second definition of Six Sigma adds additional insights into some of the “how” of Six Sigma by

introducing quality principles and techniques, but notice that there is no reference in this definition to

anything on the top line. Both of these first two definitions come from the practitioner environment.

Let’s look at a third definition that a group of academics put together.

9


• “Six Sigma is an organized parallel -meso structure to reduce variation in organizational processes by

using improvement specialists, a structured method, and performance metrics with the aim of

achieving strategic objectives”

• Source: “Six Sigma: Definition and Underlying Theory” by Schroeder, et al.

Roger Schroeder is the academic director of the Juran Center for Leadership in Quality at the Universityof Minnesota. When this center was being formed, the University sought 10 donors to each give

$100,000 to create a $1 million endowment to start the center. Dr. Juran was one of the first donors

that they approached. He liked the idea so much, that he gave the entire $1 million in order to get things

going! The center engages in a variety of activities to support its primary theme of leadership and

quality.

One of its activities is a bi-annual Summit that is really geared to practicing professionals in industry. I

was fortunate to receive a $4000 faculty Fellowship to attend the 2006 summit. The Fellowship covered

the $3500 registration fee and deferred some of my travel expenses. It was a very impressive

conference, and I would encourage you to go if you ever have the opportunity.

One of the co-authors of the paper referenced in this slide is a professor named Kevin Linderman. Kevin

earned his Ph.D. degree in operations management from the Weatherhead School of Management

before joining the faculty at the Carlson School of Business at the University of Minnesota. I was

fortunate to serve as his doctoral advisor and continue to work with him.



This definition sounds more like what an academic would write, but it has its virtues. The parallel

structure to which it refers means the structure outside the normal departmental, hierarchical structure

in organizations. We have mentioned earlier that a Quality Council typically forms this structure. The

meso word in the definition simply means that it reaches over all vertical levels in the organization.

You may remember our definition of total quality management talked about extending to all employees

from the top to the bottom of the organization, so this means the same thing. This definition adds still

more content by talking about improvement specialists, a structured method, and performance metrics.

Those of you with some familiarity of the Six Sigma process would agree, I believe, that these are

accurate descriptions.

One of the most important differences in this definition from the earlier two is the reference to

achieving corporate strategic objectives. You may recall in the quality management module that I talked

about how some companies have divorced their quality management process from their corporate

strategy. Clearly, these authors have made that connection and close an important loophole in the

earlier definitions. So even though this definition is a longer definition than the other two, I believe it is a

better definition with greater content than the other two.

10

Outline


• Define

• Measure

• Analyze

• Improve

• Control

We now turn to the first of the five widely recognized steps of a Six Sigma project: define. When

Motorola originally developed the Six Sigma process, it actually consisted of eight steps. The first step

was to recognize, meaning that we needed to recognize a need. The last two steps after control were to

sustain and institutionalize. Today, the control step generally includes the activities associated with

sustaining and institutionalizing.

11

Defining Projects

• Finding the right problems

• Defining them correctly – one bite at a time



can possibly hurt our company. Because cost reductions are so safe, top executives feel very

comfortable focusing Six Sigma efforts on cost reduction.

Many companies place a very strong emphasis on both customer and employee satisfaction. We will

study customer satisfaction in a later module and you will see why this is so important. A number of

years ago I had the opportunity to work with the CEO of Lubrizol Corp. At the time, the chairman andCEO was Dr. Lester Coleman who had a passion for quality. Dr. Coleman and I ran an executive workshop

entitled Total Quality Management: A Top-Down Approach through the Weatherhead Executive

Education program. He hosted me for an extended visit to his headquarters office and shared many

insights with me about Lubrizol’s approach to quality. During the session, he explained to me that the

company performed a customer satisfaction survey for every customer every year and did the same

thing for every employee. These two metrics were widely regarded as the two most important metrics

driving the company’s success. The financial performance of the company was seen to be the result of

achieving these metrics, as opposed to a driving force in and of itself.

Dr. Coleman was so secure as a professional and so passionate in his beliefs in quality that he

empowered the corporate Quality Council at Lubrizol with the final authority for corporate decisions.

This meant that if the council made a decision different from what Dr. Coleman would make for a

particular problem, their decision would rule. He explained to me that the company had undergone a

major reorganization and that a number of people who were running businesses and producing sound

financial results were replaced with new people because the prior individuals were not running the

businesses using the kind of quality principles that the company felt important to its long-term success.

When we study statistical process control later in the semester, we will study the quantitative definition

of process capability. Many in the automotive industries believe that the obsessive application of the

concept of process capability is what led the Japanese automotive companies to their superior quality

position in the industry. So certainly Six Sigma projects aimed at improving process capability make a lot

of sense and are very popular.

Many companies who have succeeded in implementing a Six Sigma culture find themselves in a strong

growth mode. Thus, another area or focus of Six Sigma projects is output capacity. To the degree that

capacity can be increased without having to add expensive capital equipment that often requires long

lead times to acquire, we can be ahead of the game.

Cycle time has been a common measure of performance in industry for a long, long time. It can be

applied at different levels in the process. The most detailed level is typically the cycle time for producing

a part in a machine. In such applications, it is defined as the average time between the same point in thetime cycle for producing a part. So if we chose the point as the final inspection and acceptance of the

part at a workstation, the cycle time is the average time from doing this for one part until the next. It has

been generally assumed that the shorter we can make the cycle time the greater the velocity of

inventory movement through our system. Improving this velocity should simultaneously improve

customer service and reduce inventory carrying costs. In recent years, the lean manufacturing

movement has challenged whether, in fact, this occurs. We could reduce the cycle time for machining a



projects. To me, this is a problem with the implementation of TQM but not with the substance of TQM. I

grant, however, that the Six Sigma movement has placed the financial impact front and center and as a

result gained wider acceptance than the TQM process.

A typical Six Sigma project should be a challenging project that is not easily done, and that cannot be

done within one department. If it can be done within one department, or by one person, we shouldsimply do it that way since that would be the easiest way. In most companies, projects of that scope do

not provide great leverage for improving the company’s performance as compared to projects that are

more challenging and complex and cross multiple department boundaries.

In addition to a rigid requirement for financial impact, another hallmark of Six Sigma projects is very

aggressive goals. A common metric is to improve an existing process by 70%; clearly this is a very

ambitious goal. In the corporate strategy field, this would be called a Big Hairy Audacious Goal (BHAG).

While I believe that it is important to set aggressive goals for Six Sigma projects, I think it's also

important to point out that most managers will be very happy if we achieve 20 or 30% improvements

even though our goal was 70. I believe the reason goals as ambitious as 70% are proposed is to really

put pressure on the team to try to find a revolutionary improvement, as opposed to an incremental

improvement. I have heard professionals who work in a hard-core Six Sigma environments lament the

fact that many good projects that might save 20 or 30% are rejected at the outset because they do not

meet a higher standard. So such projects don't get done and the organization doesn't enjoy the benefits

from them. A counter argument is why would you do those projects if there are other projects you can

do that generate 70% improvements? While I believe a company should exercise some flexibility in

choosing projects and so sometimes projects with goals less than 70% improvement might be selected, I

think it is a good thing to keep the hard edged financial goals in place for Six Sigma projects.

14

Slide fourteen

Some of the references that I

studied to learn about Six Sigma

suggest a project lifecycle as

illustrated in this slide. So we

start with a practical problem,

and cast it in the context of a Six

Sigma project. Once we can state

it in Six Sigma terms, we thentranslate it into a statistical

problem for which we can find a

statistical solution. The solution

allows us to establish a control

plan based on the solution, which

can then be translated into a



practical solution that achieves the desired results. As we study Six Sigma, we are probably more flexible

than this diagram would suggest. So we would probably use the word analytical in place of statistical,

and analytical would include quantitative and technical analysis as well as just logical analysis using

simple tools of quality.

15

Slide fifteen

The most publicized

implementations of Six Sigma

have come from large

companies that garner more

press than the smaller ones.

These large companies have

created a hierarchy of so-

called Six Sigma belts. The

different belts that I have

heard about start with a

yellow belt at the lowest

level, followed by a green

belt, then a black belt, and

finally a Master Black belt. If

you are interested in learning

more about the definition for each belt you may consult the website of the American Society for Quality

at www.asq.org. A common requirement for a black belt is that the person must have led at least one

Six Sigma project. As the slide above shows, it is a management responsibility to define the Six Sigma

projects that need to be done to support the business, and then the belts take over in the detailed steps

of the Six Sigma project. Finally, the results are handed over to the process owner for implementation

and control to enjoy the benefits of the project team achievements.

In the larger companies, it is common for black belts to work exclusively on Six Sigma projects and to

have no other job responsibilities. So you could say these are essentially internal consultants. For

smaller firms, it would be very difficult to dedicate resources in this fashion. Certainly, a smaller

organization could implement the Six Sigma process without having to dedicate employees full time to

serve as belts. The more important aspect is to implement the approach and methodologies of Six

Sigma, regardless of who in your company does the implementation.

16

Assessing Business Needs

• Voice of the customer (VOC)



– Customer needs, expectations about your products, services

• Voice of the business (VOB)

–Needs and expectations of the business, including owners and participants

• Problems exist when VOC and VOB are misaligned

When we are defining Six Sigma projects, we need to consider both the voice of the customer and the

voice of the business in order to support our selection of the right projects. The voice of the business

might be telling us that we need higher profits. One way to achieve this would be to simply raise prices.

The problem with such a strategy is that the voice of the customer may be telling us we need to lower

prices. So perhaps a better project in this situation would be to look at the largest cost elements of our

products and try to figure out a way to lower those costs substantially, so that we could simultaneously

lower our prices for customers and improve our profit margins for a business.

17

The Business Case Template for Project Identification

“As a company, our __________ performance for the ______ area is not meeting _________. Overall,

this is causing _________ problems, that are costing us as much as $____ per _____.”

One of the Six Sigma references I consulted suggested that every project proposal should have a

business case made for it. The reason for this is to cause people to think in business terms rather than in

personal terms. Many of us may have pet projects that we have wanted to do for years, but these may

not be the best projects for the business to undertake. So if we are forced to make a business case for

our pet project, we may see the weaknesses in that case so that we don't even propose it. Suchprescreening saves everybody time. The statement in this slide is a template for a business case

statement.

18

Business Case Example

“As a company, our repair parts availability performance for the customer service area is not meeting

customer expectations. Overall, this is causing lost sales and goodwill problems, that are costing us as

much as $500k per year.”

Use silent brainstorming techniques to develop business cases.

This slide contains a good example of a business case statement to support the submission of a Six

Sigma project proposal for consideration. As you can see, the statement above is a more forceful

statement then simply suggesting we should look into our repair parts operation.

19



The Project Definition Process

• Start with the Six Sigma Equation

y = f(x) + ε

• y is the business outcome

• f is the function by which business inputs are transformed into outputs

• x represents the inputs used to create the output; people, equipment, money, materials, information

• The ε is the error or uncertainty in the transformation process

Slide nineteen

In an earlier slide, we introduced the big business Y’s as the foci for Six Sigma projects. This slide helps us

to understand why we used the letter y. An ideal Six Sigma project starts with the general equationshown in this slide. Y stands for the business outcome that we are trying to achieve. F is the function by

which business inputs are transformed into the process outputs. Typically, this function has many inputs

so we can have many different x values to consider. The Greek letter epsilon represents the uncertainty

or error in the transformation process. A common goal for a Six Sigma project is to reduce or eliminate

epsilon, and to achieve the outcome with fewer inputs. In other words, we seek to improve the

efficiency of the process. A Six Sigma project team should be able to specify the outcome, the inputs,

the transformation process, and the nature of the error or uncertainty in the process at a very early

stage.

20

The Steps in the Project

Definition Process

1. Determine the y: what are you trying to improve?

2. Identify the associated processes and their physical locations

3. Determine the baseline performances of each y chosen

4. Identify the cost and impact of the problem

5. Write the problem statement

6. Write the objective statement

7. Ιdentify and recruit candidates for the project team



8. Obtain approvals and launch

Slide twenty

With the background concepts for the define step in the Six Sigma project in mind, we can now look at

the specific steps in the project definition process. Eight simple steps are spelled out in this slide. We will

look at each one of these in turn.

21


Definition Process

1. Determine the y: what are you trying to improve?

• Carefully choose and define the y

• If there are more than two y’s, you may need to subdivide the project

Slide twenty-one

The first step is simply being able to articulate what outcome you're trying to improve. Are we trying to

reduce the scrap rate for a process? Are we trying to reduce the number of errors made in picking parts

from our warehouse for customer orders? Are we trying to reduce the number of errors made in the

documentation that we ship with our product? The selection of the outcome is critical because it will

focus all the project team’s efforts as a result. In many cases, as the project team starts to discuss the

project, it will become broader and broader in scope. The reason for this is that the team members

know a lot about the process that is being studied. They have a natural tendency to engage in objective

creep, which means that more and more elements of the process are included in the project. The team

has to resist this temptation. A simple test will often help the team discover if their objectives are

becoming too broad. If the number of outcomes that they seek to influence becomes more than two, it

probably means that the project should be subdivided into two or more smaller projects.

Companies that implement Six Sigma feel that it is better to do a series of short, hard-hitting projects

that get completed in a short amount of time with a modest amount of resources and then move on to

another set of projects. So they put a lot of effort into defining a series of small projects that add up to

the impact of one large project. Using the small project approach, they can use different teams for

different parts of the project so as to fit the best people to the needs of the smaller projects, and toallow a greater variety of people to participate in the process. It's also true that if information is

revealed from earlier projects that suggest that continuing in this direction is going to yield fewer

benefits than expected, we can simply stop this line of investigation. Of course, a possible price to be

paid for this strategy is a loss of continuity from project team to project team. The quality leadership

team should try to see to it that this doesn't happen.



22


Definition Process

2. Identify the associated processes and their physical locations

• Identify the processes involved in creating the y

• Create at least a high level process map for each using flow chart techniques, or a SIPOC diagram

(suppliers, inputs, processes, outputs, customers)

• Identify the locations of the processes

Slide twenty-two

In the normal Six Sigma project, the outcome to be sought is obtained through the behavior of one ormore processes. So the second step in the project definition process is to briefly spell out what these

operational processes are. In addition to simply listing them and identifying their locations, a

recommended approach is to create some sort of a high-level process map for each process. This can be

done utilizing a flowchart which we will study in our tools of quality module. A more elaborate form of a

simple flowchart that has gained favor in Six Sigma projects is called a SIPOC diagram. This diagram

identifies the customers of a process, the outputs they receive, the processes used to create the

outputs, the inputs that the processes use, and the suppliers for those inputs. Even in small company

environments, it is common that these elements are located in different geographies and so

coordination becomes an issue.

Some companies have developed some fairly elaborate techniques in the construction of these

diagrams.

One technique is to move the flowchart symbol into a column that represents a particular department.

The flowchart then appears to jump back and forth between departments, but it gives all involved a

clear picture of which department is responsible for which steps in the process. We will talk more about

how to use such tools in a later module.

23


Definition Process

3. Determine the baseline performances of each y chosen

• How bad is bad?



• Measure and plot performance (a control chart might be used to show the behavior over time)

Slide twenty-three

Once the big picture is clear and the processes have been identified, the next step is to assess their

health. How bad are the processes? If they are performing at world-class standards, then perhaps we

need to look elsewhere for our Six Sigma project ideas. The team may want to obtain any

documentation of the process performance from the process owners. This could include statistical

process control charts, a tool of quality that we will study later. Assuming that the team decides that

there are opportunities for improving one or more of the processes involved in producing the outcome

we seek, we can move to the next step in the definition process.

24


Definition Process

4. Identify the cost and impact of the problem

• Is it worth doing?

• Hard savings - reduce expenses to produce a financial improvement

• Soft savings (or gains) - are financial benefits that may occur as a result of your project, but cannot be

directly measured and related to your work; an example is improved customer satisfaction leading to

additional business

• Potential savings - are hard savings but require action to achieve; an example is a re-design of aproduct that has not yet been implemented, but should produce a material savings

Slide twenty-four

Now we come to the real question; is this project worth doing? To answer the question, the Six Sigma

process suggests that we consider the three potential areas of impact shown in the slide. First, do we

believe there are some hard savings from this project in the form of reduced costs or expenses that are

likely to result from our efforts? If so, is the magnitude of those gains large compared to the costs of

doing the project? The second area to consider is so-called soft savings or gains. As an example, suppose

you are implementing an ERP system that allows you to closely track your production as it moves

through your facility. This better tracking allows you to answer customer inquiries about the progress of

their orders more exactly. It does not necessarily help you get their orders done faster, better, or

cheaper, but it does allow you to communicate the status of the orders more accurately to the

customers. This could cause your customers to decide that your firm is a better managed firm than your

competitors and it might make them less likely to switch to a competitor. This is a potential benefit, but

it cannot be guaranteed. If you implement the system and provide better information to your customers

and your business picks up, it may still be difficult to claim that it was because of the improved



communication rather than other things going on in your business. The final area for consideration is

potential savings. Suppose you are doing a study of order entry errors made by order entry personnel

when processing fax orders. You discover that a number of your customers have the capability of doing

EDI. However, you don't currently have the software to support it. You do a financial analysis and

discover that if you purchased it, it would help improve your accuracy and that you would need fewer

order entry people. The combination looks economically viable, but you have to implement the process

in order to make the gain. When your team presents its findings to the quality leadership team of your

company, your team should always include all the potential benefits in order to make the strongest case

for consideration of implementing your ideas.

25


Definition Process

5. Write the problem statement concisely

• Description of problem and metric used

• Where the problem is occurring by process name and location

• The timeframe over which the problem has been occurring

• The size or magnitude of the problem

Slide twenty-five

The fifth step in the problem definition process is to write a concise problem statement. We have anexample in the next slide, but you will see that our concise statement is much longer than the

alternative that we present. So even though we say concise, we do want the elements listed in this slide

to be included. This standard format helps decision-makers compare potential projects so that they can

make good choices of which to staff and support. In some instances, overzealous writers of problem

statements might tell us many details of specific situations that have led them to propose a Six Sigma

project. Such statements will not be as concise as if we follow the template in this slide, and will make it

more difficult for the quality leadership team to understand exactly what is being proposed.

26


Definition Process

5. Write the problem statement concisely

• Poor problem statement – our customer service levels on repair parts are too low and must be

improved



• Better problem statement – our customer service levels on repair parts average 78 per cent for high

volume parts, and 86 per cent for all others. These are below the target levels of 95% across the board.

Based on production records, they have resulted in interruptions of 10 per cent of our jobs in order to

process emergency orders, causing us to set up the interrupted job twice at an average cost of $500 per

job. Based on customer quotes that were rejected due to length of time needed to fill the order, we

estimate that we could increase revenue by $500k per year, and profit by 35 per cent of that if we could

achieve our target.

Slide twenty-six

We provide a not so good example of a problem statement in this slide and then a better example.

Notice that the poor problem statement is general and vague; it provides no ability for the reader to

assess the potential impact of addressing the problem. The second statement, although it is longer than

the first, is a much more forceful statement that does allow the reader to at least consider what the

impact might be under different assumptions about the effectiveness of the solution. I think it is easy to

see from this example that a good template should be used in your company to guide the development

of problem statements.

27


Definition Process

6. Write the objective statement

• How much is enough?

• Entitlement – is the best performance that a process as currently designed has delivered in actual

operation

• The Hidden Factory – is all the indirect or overhead expense needed to do things the way you do

them; for example, rework stations

• Breakthrough Improvement – a standard rate for Six Sigma projects is 70 per cent

• Write an aggressive objective statement that specifies both the metric improvement and the time to

achieve it

Slide twenty-seven

After we write a problem statement, the next step is to write an objective statement. Here the critical

question is how aggressive should be objective statement be? In addition to the standard suggestion of

a 70% improvement, there are some other ideas in our slide. The first idea is the concept of entitlement.

Suppose that the project is focused on reducing the scrap rate of the manufacturing process. Currently,

the average scrap rate for the process is 2% of all the units produced. But if we look at daily production



records for the process, we find that at one point in time for a few weeks the process averaged a scrap

rate of only one half of 1%, or 0.5%. The 0.5% rate is the entitlement rate. Since the process has

demonstrated that it is capable of producing this rate, our objective is to figure out how to make it do

this all the time rather than just on a rare occasion.

A second aspect to consider involves the concept of the hidden factory. The hidden factory is all theindirect or overhead operations that are required because of the way you currently do business. For

example, suppose that you have not developed any computerized methods of ordering replenishment

orders in your purchasing department. As a result, you have to have a purchasing agent review every

purchase order before it's released to a supplier for processing. It would probably be pretty easy to

develop some intelligent purchasing reordering rules that would take care of 70 or 80% of the orders

that you place on your suppliers, and that could be done directly by the computer with no human

intervention. The end result of this could be to substantially reduce the number of purchasing agents

needed to do all these purchase order reviews; in other words the elimination of some of the hidden

factory. You might say we are merely transferring the hidden factory from the purchasing department to

the information systems group to do the programming. Notice, however, that the software has to bedeveloped only once whereas the purchasing agent reviews go on and on.

Notice the last bullet on this slide. It is important to put some bounds around the project objective, so

you should not only specify the metric improvement but also the amount of time you expect it to take to

achieve it. This puts some pressure on the project team to maintain a brisk schedule throughout the

duration of the project. The timeline does not need to be at breakneck speed timeline, but it should

keep the pressure on the project team.

28


Definition Process

7. Ιdentify and recruit candidates for the project team

• Process experts from each of the processes involved

• Be sure they can devote the time to the project

• At least one person with broad expertise in the problem solving process and the various tools that can

help

Slide twenty-eight

If every step in the project definition process so far appears to meet the standards in effect in your

company, you can now consider potential team members for the project. Depending on the culture in

your company, you may need to get permission from each person's supervisor in order to approach

them about serving on your team. You want to get the best possible people to serve on your project



team. It may very well be the case, however, that a number of your first choices are already booked

heavily on other projects. This may either cause you to delay the timing of your project kickoff or to

accept other choices for your project team. Be careful and do not accept team members for your team

that you do not believe can do the job.

A few years ago, I needed an instructor for the new joint degree program between the engineeringschool and the management school that I was managing. This particular need was for an engineering

professor and so I obtained a recommendation from one of the department chairs in the engineering

school. Since I had a number of friends on the engineering faculty, I called one of them and asked for his

opinion of the recommendation that I had received. He told me that he thought the chairperson who

made the recommendation was trying to solve the chairperson’s problem and not my problem, since

the faculty member who had been recommended was not widely regarded as a good instructor. I kept

searching.

Another important point is to make sure that the people on the team can devote adequate time to the

project. A final point is to make sure the team has a Six Sigma or quality expert on the team. If your

company is a small company and does not have the resources to have certified belts on staff, you can

still have a resource person who does bring wide and deep knowledge about the problem-solving

process and the various tools available.

29


Definition Process

8. Obtain approvals and launch

• Get buy-in early!

• The process owner is key!

• Have an executive sponsor to remove obstacles, provide resource support as needed, and keep the

pressure on the team to perform

Slide twenty-nine

With our staffing lined up, we are almost good to go. What remains is to obtain the approval of the

quality leadership team for your project and launch. Even though this is the step where you seek formal

approval, you should typically have discussed this project with the process owner and appropriate

members of the quality leadership team long before now. You should have received encouragement

from those conversations in order to proceed to this point. The process owner is the individual who has

formal authority over the biggest piece of the process being studied, even though this is unlikely to be

the entire process. If this individual is very positive and passionate about your project, then your

chances for success are greatly improved. A good executive sponsor can make a huge difference in how



easy or hard it is to make progress on a project. In our teambuilding module, we discussed the duties

and responsibilities of the executive sponsor.

30

Outline


• Define

•Measure

• Analyze

• Improve

• Control

Slide thirty

We spent a lot of time on the design phase of the Six Sigma process. That's okay because the define

phase is probably the most important phase of the Six Sigma process. It is very, very important that we

get it right. Assuming we did, we are now ready to move on to the measure phase.

31

The Importance of Measurement

• "If you can't measure it, it's not worth doing." - Fred Smith, Federal Express Corporation

• If it doesn’t get measured, it doesn’t get better!

• There is a science of measurement, called metrology, that we will introduce in a later module entitled

“Quality Measurement and MIS”

Slide thirty-one

In our quality management module, we talked about the prominent role that measurement had played

in the quality management process. We used a very similar slide to this one in that module. We note in

the slide in this module that we will be introducing the science of metrology later in the course. We alsotalked about the psychology of measurement in a quality management module. I have an example from

the healthcare field to further illustrate this psychology that I thought you might find interesting. Many

years ago, when I first introduced the total quality management course into our curriculum, I was able

to get the director of quality management for the Cleveland Clinic to come and visit with my class. He

was a physician at the clinic who had taken on the role of quality director. His approach appeared to be

very laid back at first glance. He explained to us that for a particular DRG the clinic would have a



standard care path. This is simply a recommended program of treatment for that particular disease.

Suppose that patients for a particular DRG that includes a surgical procedure are supposed to receive a

particular medication within two hours after the surgery if the patient exhibits a certain marker (for

example, extremely high blood pressure). What the director and his staff would do is simply measure

the proportion of patients who were receiving the medication if they were supposed to, and also the

proportion of patients receiving it within the proper time frame. They would feed this information back

to the caregivers who were involved in the patient care process. Then they would measure the same

variables again. He reported for whole series of these before and after measures, where the only

intervention was to provide a report that summarized the measurements. In every case, the after

measures showed a dramatic improvement that approached perfection. In a number of cases, the

before measurements were surprisingly low. Obviously, in a medical environment such as this, the staff

is extremely professional so that this gentle feedback process had a profound effect. Nonetheless, the

example illustrates the power of measurement and feedback.

32

Measurement and Statistics

• Definition of statistics – making sense out of data!

• British Prime Minister Benjamin Disraeli once said: “There are three kinds of lies: lies, damn lies, and

statistics.”

• He probably never got a Six Sigma Black Belt!

Slide thirty-two

The use of statistics is often an important feature in the measure, analyze, and improve steps in the SixSigma process. So we introduce it here at the measure step since it is very common to use statistical

measurements as a part of this process. I should note that the definition of statistics shown in this slide

is my definition and not that of a Ph.D. statistician. I should also mention that for students who have had

and remember their basic statistics course, the following section of this module will be a simple review.

If you have not had statistics, this will be a gentle introduction but you will need to become more

knowledgeable in statistics if you expect to be a strong performer in a Six Sigma process.

33

Sample versus Population

• Population is all members of a particular group; i.e. all males working at a particular company

• Sample is a subset of the population; i.e. all males working as machinists at the company

Slide thirty-three



One of the most powerful aspects of statistics is that we can estimate the characteristics of a large group

by only measuring those characteristics for a small group. The small group is called a sample and the

large group is called the population. We have to be careful about the manner in which we select a

sample or it may not be representative of the population. Whenever we can compute a measure based

on a sample we call it a statistic. If we have the measurements for the entire population and we do a

computation, we call it a population parameter.

34

Discrete versus Continuous Data

• Discrete data can take on only a limited number of values; for example, the number of rooms in a

house is discrete

• Continuous data refers to things that can be measured as finely as our measuring instruments can go;

for example, height can be measured in feet, inches, centimeters, millimeters, etc. as fine as our

measuring instruments can measure it

Slide thirty-four

For anything that we measure, due to the limitations of our measuring instruments, our measurements

are actually discrete. However, phenomena that we want to measure may naturally exist as either

discrete or continuous data. If we want to know how many students are in our class; that is clearly a

discrete measure. We count the number of students and it has to be an integer such as 20 or 34 or some

similar number. If we had fine enough instruments to measure the temperature in our classroom

whenever we are meeting, it could be measured on a somewhat continuous scale. Even though we

normally quote temperatures on a discrete scale, so we might say it's 75° outside today. In reality, it may

be 74.9358°, but our measuring instrument is a digital instrument that only displays integer values of the

temperature. For statistical purposes, it is useful to know whether the data we're working with are

discrete or continuous.

35

Teaching by Example

• In the slides that follow, we will use the data we collected from the class members at a prior client

company consisting of their height, weight, and sex to illustrate statistical measurement and analysis

concepts

Slide thirty-five

Since there were 24 men in the class and only eight women, in some of the illustrations that follow we

will only use the male portion of our data.



36

Slide thirty-six

We entered the data from our 32 students into an Excel spreadsheet as shown in this slide. We will treat

the height and weight values as being continuous, and the sex variable as discrete. We have coded the

discrete variable with a one for a woman and a zero for a man.

37

Descriptive Statistics

• Descriptive statistics are used to describe something that we have measured so as to summarize the

measurements in some fashion

• Two broad categories are:

–Measures of central tendency

–Measures of dispersion (variation)



Slide thirty-seven

The first thing we will do with our data is compute some simple descriptive statistics that include both

measures of central tendency and of dispersion or variation.

38

Measures of Central Tendency

• Average or mean

• Median

• Mode

Slide thirty-eight

Three common descriptive statistics that measure the central tendency from a set of data are the mean,

median, and mode. We will illustrate each in the following slides.

39

Average or Mean

• The average or mean of a set of numbers is computed by adding all the numbers together, and then

dividing by the number of numbers

Slide thirty-nine

The arithmetic mean is the same arithmetic mean that you learned about in elementary school.

40



Slide forty

The 24 men in our data set average 71.15 inches in height, and have an average weight of 197.16

pounds. You can verify these results by adding the values shown in the slide and dividing by 24 in each

case since there are 24 males.

41

Median

• The median is the middle value in a sorted set of values if there are an odd number of values

• It is the average of the two middle values, if there is an even number of values in the set

Slide forty-one

In general, the median value is just the middle value of a sorted list of numbers. In case there is an even

number of values, we average the middle two to determine the median.

42



Male Data Sorted by Height

Slide forty-two

For our sample data, we sorted the male data from lowest to greatest height. Since we have 24 values,

we will have to average the middle two to determine the median. To do that, we count down to the

12th and 13th values in the list, and average them as shown in the slide. The result is a median value of

72 inches.

43

Mode

• The mode is the value in the set of values that occurs most frequently

• It is sometimes confusing because there can be multiple modes, or no mode in continuous data if

every measurement is unique

• Not as useful as mean and median

Slide forty-three



The mode is defined as the value in the data set that occurs the most frequently. It is not considered as

useful as the mean or medium, because there can be multiple modes or no mode at all if every value in

the data set is unique.

44

Male Data Sorted by Height

Slide forty-four

For the male data sorted by height, the modal value is 72 and this value occurs nine times in the data.

45

Measures of Dispersion or Variation

• Range

• Mean Absolute Deviation

• Standard Deviation



Slide forty-five

We will consider these three simple descriptive statistics for measuring variation in the data. Sometimes

when I am explaining measures of variation to people in companies who do not like statistics, they

accuse me of just creating confusion that is unnecessary. So I have come up with a simple example that I

share with them to try to illustrate the importance of variation. I asked them to imagine a bottling andpackaging operation that is filling 12 ounce longneck bottles with their favorite beverage, capping the

bottles, and putting them in cases of 24 bottles each for delivery to our local beverage store. The filling

operation is so fast that we have two people who take the filled bottles and place them in the case

containers. Each person of the two takes every other bottle. Now suppose that be pouring operation

functions as follows. It dispenses 6 ounces of liquid into the first bottle, and then dispenses 18 ounces

for the second bottle. Of course, this overflows the second bottle and some of our precious liquid spills

out and is lost. This pattern of first 6 ounces and then 18 ounces continues so all the odd-numbered

bottles have 6 ounces and all the even-numbered bottles are full to the cap. Now you go to your local

beverage store to pick up a case of your favorite drink. Do you want your case to contain all odd-

numbered bottles or even numbered bottles? In terms of the average, our process is perfect. It isdispensing an average of exactly 12 ounces of beverage per bottle. You can see that variation is a serious

problem in this example. No matter what Prime Minister Disraeli thinks, I think statistics can be

practically useful, especially if they keep me from buying a case of odd-numbered bottles.

46

Range

• The range is the difference between the largest value and the smallest value in a set of data

Slide forty-six

The range is the simplest of the three values and is the difference between the largest value and the

smallest value in a data set.

47



Slide forty-seven

We again use the male data sorted by height, and notice that the smallest value is the first value at 65

inches. The largest value is the last value and is 75 inches. So the range is simply the difference between

these two or 10 inches.

48

Mean Absolute Deviation

• The mean absolute deviation (MAD) is computed by first computing the average of the set of values

• Next the difference between the average and each value is computed; if the difference is negative, it is

changed to positive

• Then the positive differences are added together

• Finally, the total of the differences is divided by the number of values to get the average

Difference



Slide forty-eight

To compute the mean absolute deviation, we began by computing the difference between the mean

value and each individual value in the data set. Then we add up all those differences and divide by the

number of differences to obtain the average difference between the mean and the individual values.

The higher it is, the greater is the variation in the data. Let's look at an example in the next slide.

49

Slide forty-nine

Recall that the average height of the males was 71.15 inches. In the column above headed “Plus

Difference” we have computed the difference between 71.15 inches and the height of each male in the

data set. Notice that we have taken the absolute value of each difference so that all the differences are

positive values. At the bottom of the column, we have summed the differences and then divided by the

number of differences or 24 to obtain the mean absolute deviation value of 1.98. Compared to the

mean value of 71.15 inches, this does not seem to suggest a great deal of variation in the data.

50



Standard Deviation

• To compute the standard deviation, you start out similarly to the mean absolute deviation

• Instead of taking the positive difference between the average and the individual values, you compute

the squared difference

• Then you add all the squared differences, and divide by the number of differences minus 1

• Finally, you take the square root of that result

• Don't worry if this doesn't make sense now, we will learn how to interpret this value later

Slide fifty

Even if you have had statistics and are familiar with the standard deviation, you have to wonder how

statisticians came up with this value. The process to compute it is described in this slide, but it's easier to

follow with an example so we will go on to the next slide.

51



Slide fifty-one

We start the process of computing the standard deviation similarly to the process for computing the

mean absolute deviation. So first we compute the difference between the average value and each of the

individual values. But then we square each difference, as shown in the column above that is labeled

“Difference Squared.” If you go back to our mean absolute deviation slide and look at the column

labeled “Plus Difference,” you'll see that values in our difference squared column in this slide are simply

the values from the “Plus Difference” column squared. Next, we sum the squared differences in this

column to obtain the total of 149.11. Notice that we divide this sum by 23, the number of squared

differences minus one. When we compute a statistic such as the standard deviation, we subtract one

from the number of values so as to correct for the loss of 1° of freedom. We have only one more

operation to do, which is to take the square root of the value we just computed. This gives us a value of

2.55 inches as the standard deviation of the height of the males in our data set. Again, comparing this to

the mean value of 71.15 inches, we would not conclude that there is not a lot of variation in the data.

52

Why Do We Care About The Standard Deviation?



• If the data come from a normal or bell-shaped curve, we can make statistical statements about the

variation in the data as follows:

– 68.3% of the values should be between +/- one standard deviation or σ

– 95.4% of the values should be between +/- 2σ

– 99.7% of the values should be between +/- 3σ

Slide fifty-two

So we know how to compute the standard deviation, but why should we care? Well, we did learn in the

bottling example above that variation was important and the standard deviation is a measure of

variation. If our data come from a normal probability distribution and we know an estimate of the mean

and the standard deviation of the distribution, we can make statements such as those shown in this

slide about how the values behave. The Greek letter sigma (σ) is generally used in statistics books to

represent the standard deviation. For the normal distribution that we showed in the chart early in this

file, if we measure the area under the curve from minus one standard deviation to the left of the mean

or target value to plus one standard deviation to the right of the mean or target value, it will contain

68.3% of the total area under the curve. The ability to make this kind of statement is why we care about

the standard deviation.

53

Exploring Relationships Between

Variables

• Correlation

• Regression

Slide fifty-three

Sometimes we are interested in exploring the relationship between two or more variables. For such

instances, we employ statistical correlation and regression modeling.

54

Correlation

• Correlation coefficient measures the degree of relationship between two variables

• The range of values for the correlation coefficient is from -1 to +1

• A value of 1 means that the two variables are perfectly, positively correlated

• A value of 0 means there is no correlation between the two variables



• A value of -1 means that the two variables are perfectly negatively correlated

• On computer printouts, the correlation coefficient is generally abbreviated with the letter r

Slide fifty-four

We use a measure called a correlation coefficient to measure the degree of relationship between two

variables. The relationship is said to be a positive relationship if as the first variable increases the second

variable also increases. The relationship is said to exhibit negative correlation if as the first variable

increases, the second variable decreases. Two variables that exhibit perfect positive correlation will have

a correlation coefficient of one. Similarly, two variables that exhibit perfect negative correlation will

have a correlation coefficient of minus one. Let's look at some sample correlation coefficients for our

data.

55

Slide fifty-five

When we enter a data set that has several variables in it into a statistical software package, we can ask

the computer to compute a correlation matrix such as that shown in the slide. Notice that all three of



our variables are listed down the side as well as across the top. So we are going to compute the

correlation coefficient for every possible pair of relationships. In the process, we compute the

correlation coefficient for each variable with itself, which results in the perfect 1.0 positive correlations

down the diagonal of the matrix. We are more interested in the values off the diagonal. If we read the

first line of the matrix under the column headed WT, we see that the correlation between height (HT)

and weight (WT) is 0.454. This is a positive correlation, which is what we would expect. The taller a

person is, the more we would expect them to weigh.

Reading one column further to the right in the same line, we see the correlation between height (HT)

and sex (SEX) is a -0.613. Remember that we coded this variable with zero for a male and one for a

female. So the higher the value of the sex variable, the shorter the person is likely to be because it is a

female.

56

Regression

• Regression analysis is used to estimate the mathematical relationship between two or more variables

• The goal may be to understand the relationship and/or to predict values of one variable based on the

other(s)

• The variable we are trying to predict is called the dependent variable

• The variables we are using to predict it are called independent variables

• The correlation coefficient is used to measure the "goodness" of fit, or strength of relationship

between the dependent and independent variables

Slide fifty-six

Sometimes we would like to be able to estimate a mathematical relationship between two or more

variables, such that we could use one or several variables to predict the value for a variable of interest

to us. We call the variable we are trying to predict the dependent variable, and the variables that we're

using to predict it independent variables. Let's look at a regression model and then I'll tell you about a

real application of regression I did some time ago.

57



Slide fifty-seven

In this example, knowing only the sex of the person, we are trying to estimate their height with the

regression equation that's shown. Notice that if the person is a male, then the value of the sex variable

is zero and we predict that the height will be 71.15 inches. This is the average height for males that we

computed earlier. If you go back and average the height for women, you will see that it's 4.27 inches

shorter than the men. So this regression equation makes some sense. There is some additional

information in this slide that the typical statistical software package provides that we need to

understand.

The value shown as R-Squared (0.376174) is the squared value of the correlation coefficient that

measures the correlation between the predicted values versus the actual values for height from the

equation. The value shown just below it as the Adjusted R-Squared corrects the R-Squared value for the

size of the sample. The interpretation of this adjusted value is that it is the proportion of the variability

in the data that is explained by our regression model. In other words, our model explains about 35.5% of

the variation in the data. That means about 65% is unexplained and so our model is not a very good

model. We probably need to find additional independent variables, such as the height of the parents of

each person in our data set, in order to try to improve our prediction. The next value shown is the

standard error of the estimate, and you can think of it as the standard deviation of the model for the



predicted values. Notice that it is slightly smaller than the 2.55 value for the standard deviation that we

computed for males.

This is because the variations in height for the women were included here, and they exhibit less

variability than the men, so they reduce the overall variability. The last value in the slide just tells us that

all 32 people from our data set were included in these computations.

I promised an application example of regression. A number of years ago a graduate student and I were

working on a project for a company called Astro Metallurgical in Wooster, Ohio, that was a subsidiary of

Harsco Corp. The company was a titanium fabrication shop that manufactured heat exchangers and

pressure vessels. To make a pressure vessel, the first operation was to create a rolled and welded

cylinder. This looked like a big tin can where the top and the bottom had been removed. There were

four steps in this process, forming, fitting, seam welding, and re-rolling. The forming process started

with a big sheet of titanium of the proper length and width to create the proper sized cylinder, and then

we folded the sheet until the two edges met to form the basic cylinder shape. The fitting process very

carefully lined the edges up and clamped them together in a few places to keep them aligned. They

were then welded together. Since the welding operation created some stress, the cylinder shape was

sometimes distorted when the welding was completed. So the final step of re-rolling was done to

restore the nice cylinder shape before proceeding to additional operations. The company was having a

difficult time accurately estimating the cost of creating these cylinders, particularly the labor costs

involved in these four processes. As a result, jobs that they bid on and were awarded often resulted in

losses rather than profits because they were underestimated. They were not sure if they lost jobs that

might have been profitable because they overestimated those.

Regression modeling to the rescue! There were only three independent variables available for the sheet

of titanium from which the cylinder would be made; the length, the width, and the thickness. We used

historical data for a lot of jobs that they had completed to build a regression model for each of the four

steps in the process. The models typically explained 95% or more of the variation in the data. I am going

to tell you how the models worked and it will appear obvious to you, but if you ask yourself for these

answers right now, they might not be so obvious.

The two variables that affected the forming process were the length and width of the sheet; the

thickness did not seem to matter, possibly because there was not a wide range of thicknesses. These

same two variables affected the fitting operation. For the welding operation, the thickness and the

length were the two independent variables in the regression equation. Clearly, the thicker the metal the

slower the welding and the longer the sheet the slower the welding. The reroll operation was once again

driven by the length and the width variables. I trained a shop floor employee to build these regressionmodels using the STORM software package. He built a bunch of models and then created a bunch of

tables so that his coworkers could simply use the length, width, and thickness values to enter these

tables and read the estimated times for each of the four operations. We did a number of other projects

as a part of our relationship with this company that further contributed to their success. But this

regression modeling was an important component of what we did. The result of the work we did

together with the people at the company resulted in this company making a profit for the first time in six



years. The nice thing was that it was a sizable profit. So I guess our equation in this case was regression

equals profit!

58

Six Sigma is about

Minimizing Variation

• Short-term variation

• Long-term variation

Slide fifty-eight

Now that you understand statistical variation, we can share with you that a major objective of the Six

Sigma process is to minimize variation. In fact, you could say that we are often obsessed with minimizing

variation in processes. It is important to distinguish between short-term and long-term variation, sinceshort-term variation is much more difficult to reduce than long-term variation.

59



Slide fifty-nine

In the graph in this slide, we have plotted the yield per hour from a process during calendar years 2004

and 2005. We implemented improvements to the process at the end of 2004 during the year end

shutdown. You can see that our yield per hour jumped from around 4000 pounds in 2004 to over 5000

pounds in 2005. If we were to compute the standard deviation of the yield for 2004 alone or for 2005alone, the values would be pretty similar. If we computed the value for both years combined, it would

be higher than either year alone.

60

Short- and Long-Term Variation

• Entitlement = Best observed SHORT-TERM variation

• Forces that cause long-term variation are often called “assignable causes” or “special causes”

• We normally try to reduce long-term variation first because it’s easier!

• Forces that cause short-term variation are often called “random causes” or “common causes”

• It is much harder to reduce this type of variation in a process; normally revolutionary discoveries are

needed

Slide sixty

We introduced the concept of entitlement during the define step of the Six Sigma process. We can use

the concepts of short-term and long-term variation to sharpen our understanding of entitlement. For

process variation, the entitlement value equals the best observed short-term variation in the process. If we accept the entitlement value as our objective for the process, then we would seek to maintain the

process at this value into the indefinite future. We will study more about assignable or special clauses

when we study statistical process control later in the course. For now, we will just say that it is easier to

reduce long-term variation created by assignable or special clauses than it is to reduce short-term

variation of the entitlement variety.

So we normally attack long-term variation first.

61

Short- and Long-Term Variation

• We use measures of variation to determine process capability for a process

– Short-term variation is used to estimate shortterm process capability

– Long-term variation is used to estimate longterm process capability



• Process capability indices are all based on some ratio of tolerance specifications divided by the

process width (variation)

Slide sixty-one

Six Sigma practitioners often talk about the concept of process capability. We use values of both short-

term and long-term variation to compute various process capability indices of interest. Again, we will

learn exactly how to compute those in the statistical process control module later in the course.

62

Outline


• Define

• Measure

• Analyze

• Improve

• Control

Slide sixty-two

We are now ready to consider the analyze phase of a Six Sigma project. We introduced quite a few

statistics in the measure phase because the statistics may be needed during that phase. We point out

however, that many of those same statistics will provide the foundation for the analyze phase. In that

sense, the measure and analyze phase may overlap at times.

63

Objective of Analyze Phase

• We seek to develop a deep understanding of the process behavior based on facts and data and their

analysis

• We want to understand how the x’s in the original Six Sigma function affect the y’s that are of interest

in our project

• At the end of this phase we should be able to suggest changes to the process that we expect to

improve its performance

Slide sixty-three



When I do applied projects for companies, I often talk about the first phase of the project as being the

saturation phase. The reason for that is that I am trying to saturate myself with the problem that the

company has so I understand it as well as the company personnel understand it.

The analyze phase of the Six Sigma project represents a similar saturation for the Six Sigma project

team. The team should understand the process as well as or better than anyone on the planet whenthey have finished the analyze phase. With a deep understanding of the process, they should be in a

great position to propose how to change it so as to improve it in a significant way.

64

What We Use to Analyze

• Team building process

• The 7 tools of quality

• Measurements from the process

• Statistical analysis of the measurements

• The team’s theory of the process

– For physical processes, this can be based on chemistry and/or physics, for example

– For business processes, flow charts may show this

Slide sixty-four

What tools, techniques, and concepts do we use during the analyze phase of a Six Sigma project? In

addition to the statistical analysis of any data available to us, we use the teambuilding process

constantly in managing our Six Sigma team and facilitating its work. We may use any of the seven basic

tools of quality, even though they are simpler than some of our sophisticated statistics. Even though

they’re simple, they can be very powerful. In addition to the data and its analysis, the team may have

developed its own theory of how the process works that fills in some blanks that the data did not

provide. We may have to test this theory later, but it may nonetheless be a very valuable output from

the analyze phase and the phases that preceded it.

65

Quality Processes We May

Use to Analyze

• Cost of poor quality

• Methods engineering and reengineering



• Benchmarking

• Quality auditing

• Vendor relationships

• Quality function deployment

Slide sixty-five

There are additional quality processes that may be used as a part of the analyze phase, and in fact may

be integrated into earlier steps of the Six Sigma process as well. We have listed several of those in this

slide but will not elaborate on them here. We will introduce all of them but quality auditing in later

modules. If anyone is interested in quality auditing, I can point you to a very good reference for that

subject.

66

Outline


• Define

• Measure

• Analyze

• Improve

• Control

Slide sixty-six

We are gaining on it; the improve step is the next to the last step in the process.

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Experimentation and Improvement

• Up to now, no tangible benefit has accrued to the company, even though a lot of new knowledge may

have been gained

• In this phase, the theory of the process that has been developed by the team and the ideas for

improving the process are put to work

• This could also be called “implementation”



At this point, we said that the team should have ideas about how to improve the process. Notice that

the company does not enjoy any benefit of any kind until the implementation takes place and starts to

produce results. Planning and decision-making are fun parts about being a professional in a company,

but never forget that the only thing the company takes to the bank is implementation. At this point in

the Six Sigma process, we want to start experimenting with our ideas for improvement to determine if

we can put them in the bank!

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• The only way to find out if the suggested changes will work is to try them in some fashion

• Simulation

• Incremental

• Wholistic

Slide sixty-eight

There are three broad categories of ways to test our theories about the process and our ideas for

improving it. We will discuss simulation, incremental approaches, and the wholistic approach of design

of experiments.

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• In simulation, we try to imitate the behavior of the real world system with a computer model so that

we can test changes in the computer before we risk them in the real world process

• We still may try to experiment with the changes via a simulation model in either an incremental or a

wholistic manner

Slide sixty-nine

Computer simulation modeling involves building a computer model to imitate the behavior of a real

world system over some extended period of time. For example, we could simulate the flow of orders

through a factory before we ever built the factory. It is much easier to correct mistakes in the factory

design in a computer simulation model than it is after we have put bricks and mortar together in a

building. Dr. Kamlesh Mathur, the Department Chair for Operations, two graduate students from my

Department, and I are currently building such a manufacturing simulator for a fuel-cell company that is

planning to build a factory in Ohio in the near future.

To the extent that the computer simulation model captures the essence of the real world system, the

simulated behavior should be a good estimate of the real world system behavior if we were to make the



same changes to the real world system that we made in the simulation model. Simulation models would

typically be used for fairly large-scale projects where it would be very expensive to run physical

experiments on the system. In addition to computer simulation, we should also recognize physical

simulations here. You may be familiar with flight simulators that all are used for training pilots. We have

a company in Cleveland in the medical area that builds simulators to train surgeons for specific types of

surgery.

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• Incremental Approaches

– Trial and error – if the process is at all complex, this will likely be a disaster and the company will be

experimenting permanently

– One-factor-at-a-time – this may be useful if there are a limited number of factors and the team feels

they have a very strong knowledge of the relationships among the factors and the outcome; otherwise,

this can take a long time and lead to erroneous conclusions

Slide seventy

Simple incremental approaches for experimentation and improvement are used more often in industry

than any other approach. Whenever the problems being addressed are manageable enough, this can

work out to be acceptable. We sometimes set up a pilot operation to test our solution with a limited

test, and then if the pilot is successful we scale up for the full implementation. This is similar to test

marketing a new product in a limited geographic area. However, if the problem being studied is of

significant complexity, incremental approaches may simply not be up to the task. We are going tointroduce an example below that I think you will agree seems like a fairly simple problem, but you may

be surprised at its complexity, and by the fact that a formal design of experiments might be needed to

address this problem.

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• Wholistic Approaches

– Design of Experiments (DOE) – in this approach, a carefully designed set of experiments are run on the

process that help prove conclusively how it behaves as a result of different factors that may be

controlled, and the different levels at which they are set

Slide seventy-one

Some Ph.D. programs in statistics offer a two semester sequence in design of experiments. So let me

caution you that the two to three weeks we will spend this semester on design of experiments will not



make you an expert. What we hope it will do is introduce you to the language of design of experiments

and help you develop an ability to recognize a situation that demands a design of experiments approach,

and to be able to participate with a team to carry it out.

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Design of Experiments

• Select the factors (x’s) from the team’s knowledge of the process

• Select the factor levels

• Randomize the experiments to protect against unknown nuisance factors

• Block to safeguard against known nuisance factors

• Run the experiments and gather the data

Slide seventy-two

To introduce the concept of design of experiments, let's consider a simple case in which we would like to

develop a recipe and baking procedures to bake the best cake ever. We will measure best by having a

panel of expert tasters whose ratings will be averaged. If we can solve this problem, we can open a

bakery that just bakes this one product, but does it so well that we make a lot of money! What are some

of the factors to be considered in baking a cake? The amount of each ingredient provides a fairly obvious

set of factors. They might include items such as flour, sugar, eggs, milk, and butter. Assuming that we

are using an electric mixer, another factor could be how long do we mix the ingredients? Even before we

mix them, a factor could be the order in which we put them in a mixing bowl. Do we put the moist

ingredients in first, so it is easier to blend the dry ingredients with them? Once the batter is mixed, what

type of baking container do we use? Do we use a round pan, a square pan, or a rectangular pan? Should

the container be made out of metal, or glass? Are you starting to get a headache? Don't, because we're

not done yet. We still have to consider at what temperature to bake the cake, for how long, and

whether to bake it on the top rack or the bottom rack of the oven. If we took a particular value for each

of the factors listed above, then we would typically bake maybe 10 cakes using that set of factors in

order to make sure we were getting some uniformity in the results. Let’s suppose that we took three

levels for each factor listed above (we could easily try more levels for several of the factors, but let’s

keep it simple). The spreadsheet below shows how many cakes we’d have to bake and taste in order to

decide on the best plan if we try every combination, ten times each!



If I was asked to do all this before I can open my

bakery and start selling anything, I would very

likely be broke and overweight before I ever

started my business! Later in the semester, we will

learn that through a careful design of experiments

that we can get most of the information we would

get from running all these experiments by running

only a small fraction of them. That is the power of

design of experiments. If we were to run the

177,147 experiments listed above, and the three

levels for eggs were one egg, two eggs, and three

eggs, we would not run the experiments in an

orderly fashion by cycling from one to two to three

and back to one egg. Instead, we would randomize

the experiments so as to protect against unknown

nuisance factors. One such factor might be the

humidity in the kitchen. This might vary from day

to day, and even from hour to hour within a day.

By randomizing the experiments, we hope to

neutralize the impact of any nuisance factors on

the results.

We may know some nuisance factors and we may

take steps to prevent them from impacting the results. For example, if Dale Flowers is the baker, we

should not schedule any of the baking experiments whenever the Cleveland Indians, Cleveland Browns,

or Cleveland Cavaliers are on TV.

Assuming that we have carefully completed the design of our experiments using the efficient techniques

we will study later in the semester, we would run the experiments and collect data on the results. For

our cake making experiments, we would collect the taste ratings from our panel of experts for all the

different trials that we made.

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• Analyze the data using appropriate statistical methods (ANOVA – analysis of variance is often useful)

• Analyze the MAIN effects to determine how much each factor impacts the results

• Analyze the INTERACTION effects to determine how much each of them impacts the results

Slide seventy-three



Once we have the results, we have to apply the appropriate statistical methods to analyze the results.

So you can see that even though we're in the improve step of the Six Sigma process, we are still doing

analysis as a part of our experiments. So the boundaries between the steps in Six Sigma projects are not

necessarily neat and tidy. The analysis of the results will help us determine the main effects and the

interaction effects of our different factors. If the three levels that we tried for butter were one half stick,

three fourths of a stick, and a full stick of butter, then we can perform a statistical analysis to estimate

the main effect of butter on the taste of the cake. Notice, however, that milk is another ingredient that

is also a dairy product. There may be an interaction effect between milk and butter. It is possible to

study such effects and to allow for their estimation.

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• From your analysis, estimate the optimal factor settings for the process and its resulting performance

• Run a confirming experiment to see if the optimal performance is achieved

• If yes, continue on; otherwise, it’s back to the drawing board for additional analysis and experiments!

Slide seventy-four

I mentioned above that an efficient design of experiments may cause us to run only a tiny fraction of all

possible trials. From the results of these experiments, we will be able to estimate the best combination

of factor levels to create the best tasting cake. Suppose that the best combination includes a full stick of

butter and 2 cups of flour. It is very possible that we did not bake a single cake in our experiments that

contained one full stick of butter and 2 cups of flour. So whatever our analysis told us was the best

combination, if we did not run that experiment in our original set of experiments, then we need to do soto confirm that our experts agree that this yields the best tasting cake. This experiment is called a

confirming experiment. If all goes well, then our experts will agree that this is the best cake we found. If

for some reason it is not judged as the best, then it probably means that there were some confounding

or nuisance factors that we did not control for that affected our results. This is bad news, since it means

we have to go back to the drawing board and figure out what to do. We hope this doesn't happen too

often.

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Outline


• Define

• Measure

• Analyze



• Improve

• Control

Slide seventy-five

We are in the home stretch. Once we have figured out how to improve the process, we want to make

sure that our organization implements our results in precisely the right manner so that benefits will

accrue for a long time into the future.

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Process Management Summary

• Basically summarizes everything the team has learned about what makes the process tick

• Identifies all the “critical-to-quality” factors including how they impact on the process

• Becomes the primary documentation of the process

Slide seventy-six

Our team should write a process management summary that contains all their important findings. The

summary identifies all the critical to quality (CTQ) factors and explains how they impact the process.

The minutes, charts, graphs, reports, and other documentation that the team prepared following our

team building guidelines will prove invaluable in writing this summary.

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Process Control Plan

• Focuses on the x’s and what we know about them

• Administrative section provides key information including the process owner

• Operational definition of the control plan

• What is being controlled

• Requirements and current performance levels

• Method of control, and actions to be taken if the process goes out of control

Slide seventy-seven

The simplest way to explain what the process control plan does is to say that it explains exactly what to

do to the x’s in the process in order to achieve our desired y. If you are familiar with computer

programming, it has lots of “if … then” statements. We may have a lot of those in our documentation.

The plan instructs the people implementing the process on what to do when different situations arise in



order to have the process perform at its best. It is critically important to develop a great process control

plan; remember, the benefit that the organization receives is going to come from implementing the

process control plan. There's that word again, implementation.

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Process Control Plan

• This step is heavily based on statistical process control that we included in the 7 tools of quality

• Additional concepts used in this step are Poka-Yoke or fool-proofing the process

Slide seventy-eight

In many instances, a statistical process control chart will be utilized by the process and the design of this

chart will be a part of the control plan. So SPC is often a component of a control plan. We will be

studying SPC a little later in the course. The team should spend some time trying to figure out how to

implement the process control plan in the most foolproof way they can. The Japanese call this Poka-

Yoke. For those of you who remember cassette tapes as a way to play music in your car, I can use

cassette players in cars as an example of this technique. When United States car manufacturers

introduced auto cassette players, they created one large rectangular opening into which you were to

place the cassette. If you look at a cassette, you will notice that the plastic container is only open on one

surface of the cassette and you can see the tape through that opening; let's call that surface the bottom.

The correct way to load the cassette into the United States vehicle was to put the bottom end into the

rectangular opening first and push the cassette on in. However, there was nothing to prevent those of

us who are technologically challenged from putting the top in first, in which case we got no music. The

Japanese had a better idea. In their vehicles with cassette players, they created a contoured opening

such that you put the end of the tape in first, and the side of the contoured opening that was larger is

where the bottom had to go. So there was only one way you could insert the tape into the opening. This

is what we mean by foolproofing.

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Repeat!


• Define

• Measure

• Analyze

• Improve

• Control



Slide seventy-nine

I bet you thought we'd never get here. You now have an introduction to the complete Six Sigma process.

Once you've successfully completed a Six Sigma project, there's always another one waiting so that you

can further improve your organization's operations. This is what we mean by continuous improvement,

and doing it relentlessly is a hallmark of many of our great companies today. I hope this module has de-mystified this thing that we call Six Sigma for you. I'll bet that you now realize that you already knew a

lot of the elements of it, and now you know how it all fits together.

Here’s an exercise that I would like for you to do. Think about some important work or school project

that you had to do as a part of a team or group. Think about how your group did it, and then think about

how you think they would have done it if they used a Six Sigma process. Describe aspects of the project

for which you think the team used Six Sigma concepts, even if the team didn’t call it that. Describe

aspects of the project that would have been different if you had followed the Six Sigma process. Then

tell us if you think the project performance would have improved, stayed the same, or gotten worse if

your team had used the Six Sigma approach. You should also include all the team building concepts from

that module into your analysis of your previous project.

the six sigma process

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