Six Sigma Workbook for Dummies

Chapter 1 - Defining Six Sigma - Introductory Section



    Getting Ready for Six Sigma: The Effects of Variation Introduction

    This chapter deals with realizing that variation is everywhere, mastering the Six Sigma breakthrough equation and exploring the effect of variation on business performance


    The characterization, measurement, analysis, and control of variation is the central theme of Six Sigma.  The key goals of Six Sigma are to fix undesirable variation, ignore variation that doesn’t matter, and allow for variation that can’t be fixed.


  1. Evaluating Variation and Business Performance with Y = f(X) + ε (breakthrough equation)

    All outcomes (Ys) are the result of some number of inputs (Xs) that interact in some way — f, or the function — to produce that outcome, and that there are always some other factors, either known or unknown — ε, or epsilon — that will impact the outcome.



  3. Outcome (Y) — properly cooked eggs
  4. Inputs (Xs) — eggs, oil, heat, pan, timer
  5. Function (f) — shells are removed, oil is added to pan, eggs are placed in pan, heat is applied for a specific time, eggs are removed
  6. Epsilon (f) — size of eggs, age of eggs, temperature of eggs, thickness of pan, amount of heat, timer accuracy, type of oil, altitude

    Note: Some of these factors can be quantified and controlled, but others can’t. The trick is to determine which, if any, of these inputs have a significant impact on the outcome and can be controlled. One of the basic tenets of Six Sigma is focusing efforts only on those inputs that have a substantial impact and that are practical to address.


  8. Assessing the impact of Variation on Business Performance

    After you realize that variation is prevalent in all processes, you have to determine the effect variation has on your process, and then you have to assess if it’s really a problem at all. After all, some variation is inevitable, and you can live with it, right? Well, maybe, or maybe not.


  10. Rolled Throughput Yield (RTY)
  11. Defects Per Unit (DPU)

    Chapter 2 - Forming a Six Sigma Initiative


    Forming a Six Sigma Initiative

    This chapter deals with with key business objectives (KBOs), determining a training program, choosing your Six Sigma trainers and selecting your implementation partners.


  1. Planning Your Key Business Objectives (KBOs)
  2. There's the risk of turning your team loose with the Six Sigma arsenal: They can charge off and solve the wrong problems. Pursuing paths that aren’t important is wasteful for any business. For example, your team would be wrong to invest in improving the production quality of a product that the market doesn’t want or to improve the sales efficiency for a product with negative margins.


    Functional sub-optimization - improving areas that don’t contribute to what’s most important. Obviously, improvement is improvement, but in the Six Sigma world, the improvement has to really mean something in the big picture, or it doesn’t count.


  3. Establishing a KBO checklist

    • Overall Corporate Goals  - are identified in annual reports, corporate tag lines, missions, and vision and values statements. They’re also articulated in speeches and position papers by key executives. Often, these goals are not identified in measurable, objective terms. You may need to translate amorphous goal statements into quantifiable metrics.
    • Voice of the Business objectives (VOB) -  These objectives are defined in operating plans, budgets, sales or other productivity targets, quotas, and other operating parameters that reflect the goals of the organization. They’re in both the core business product and service line areas as well as the support process areas, such as IT, HR, Facilities, and Finance.
    • Voice of the Customer objectives (VOC) - These objectives, which are critical to the success of your initiative, are typically expressed through the marketing and research efforts that reflect the wishes of the market and of your customers. Certain exercises in Design for Six Sigma (DFSS), which is the practice of applying Six Sigma to designing products, services, or business processes, strictly define quantifiable VOC measures.
    • Make sure objectives are consistent - Check to verify that your objectives are internally consistent and prioritized and that they tie together logically. Make sure that any inconsistencies have been addressed and rectified.
    • Make sure objectives are quantifiable. Be sure your objectives are in quantified, measurable terms. They should be expressed numerically and in such a way that the results of the projects can be measured and compared to the original values.
    • Make sure objectives are current. KBOs change and in some organizations they change often! Put an update mechanism in place to ensure that you have the current set in front of you


  5. Determining the proper training program

    The first step in your deployment initiative is training. You must get your staff up to speed on how to apply the methods and tools of Six Sigma. The training program needs to be precise, and the various training courses need to be delivered in a specific manner and order.


    Who will manage the training program?

    Each option in this decision has consequences in terms of the orientation, consistency, and buy-in from your staff.  Options include: the leaders of your profit and loss (P&L) areas and major functional organizations, the Six Sigma Deployment Leader (typically reports directly to the CEO), the training department (larger organizations).


    Finding the expertise within your organization

    Before you go any further in your deployment initiative, take the time to assess the level of Six Sigma deployment initiative expertise in your organization.


    Scoping the training program

    You must determine the scope of your training program, which means you have to know the number of staff members who will be trained, the level of proficiency they’ll be trained to, and in which functions of the organization they’ll be trained in.


    Recognizing cultural predisposition

    The degree of cultural predisposition toward or against a change initiative like Six Sigma is a key factor in rolling out the training program. If you misjudge the culture and implement the program the wrong way, your initiative may backfire.


    Defining the training plan

    After determining who will manage the education program, identified your organization’s internal capabilities, scoped the program, and assessed the cultural predispositions, it's time to define the training program plan. Topics to consider include training schedule, facilities to use, resources,


    Deciding Who Will Conduct the Training

    There are four general options as to who will conduct the training: contract a Six Sigma systems shop, contract several boutique Six Sigma trainers (Belt Training, Design for Six Sigma, Executive Coaching, Project Management, focus on vertical markets, such as health care, financial services, or manufacturing), hire on Six Sigma training expertise and buy materials, hire on Six Sigma training expertise and develop materials.


    Teaming for Success: Shopping for Your Implementation Partners

    Like in any other established market, the Six Sigma training marketplace has a healthy selection. You’ll find a few great providers, many good ones, many not-so-good ones, and a few really awful ones. It’s no trick to find the right partner, but you need to know what to look for.

    Chapter 3 - Pinpointing The Essentials of Six Sigma - Introductory section, Project Strategy, DMAIC (*REQ)


    Leading and Managing a Six Sigma Initiative

    This Chapter deals with choosing a team to lead your Six Sigma initiative, understanding the importance of communication and working with a Six Sigma Management Plan.


  1. Selecting Your Leadership Team
  2. The Leadership Team should have both the authority and responsibility to ensure that everyone across the organization is properly empowered and supported throughout the life of your Six Sigma initiative. This team is directly accountable for producing the results — the measurable, quantifiable, and significant improvements in key metrics and benchmarks — through facilitation of the initiative process. The makeup of the Leadership Team defines your success.  The Leadership Team is more of a SWAT team that fans out

    across your organization — as well as across your various constituencies — to ensure that your initiative deploys successfully.


    Approaching the Selection Process


    1. Identify central organizational roles - all leaders accountable for financial performance (financial performance areas are the most important target areas for Six Sigma process improvement), all leaders of the major enabling process areas (Finance, Accounting, Legal, Procurement, Human Resources,

    Information Technology, Facilities, and other similar processes that enable core business processes

    1. Identify central Six Sigma initiative roles:
      1. Communications Leader - communication is vitally important to a Six Sigma initiative, and because the initiative will have a communications plan, you may consider naming a specific individual to lead the communications activities.
      2. Deployment Leader - this leader is the individual charged with ensuring that the initiative is deployed across the organization per the deployment plan. Even though this role is traditionally titled as a leadership role, it’s more related to management than leadership.
      3. Champion -  the true Six Sigma leadership role. The Champion is the senior evangelist who must understand what Six Sigma can and can’t do. This person must champion, or support, the initiative’s adoption.
    1. Identify other key participants - In addition to the organizational and Six Sigma initiative leaders, you may have other key individuals who belong on your Leadership Team. Identifying these other key individuals is critically important to your success, particularly where change management is concerned. Additional stakeholders may include the following:
      1. An outside board member - Six Sigma is going to shake things up in your company: Business will be done differently from now on, which results in changes to the way you communicate the status and performance of your company. If you need an advocate who can effectively “carry the water” for you to key shareholders, analysts, sponsors, donors, or other external constituents, you want to include an outside board member on your Leadership Team.
      2. An outside advisor - Your business will be different after Six Sigma. You may modify organization structures, reporting alignments, and other internal institutions. These changes impact the company culture. Throughout the Six Sigma process, you may want to have an external advisor — someone who’s been through this process before. This outside advisor is someone whom members of the Leadership Team can confide in and seek advice and solace from. You should consider seeking an advisor who isn’t part of your training team.
      3. Key suppliers - Your initiative will reach into your supply chain. Suppliers will be directly affected by your initiative, so you may want to include them.
      4. Key customers - the direct beneficiaries of your efforts certainly have a keen interest in how your initiative is accomplished, so keep them informed.
      5. Social network leaders. Remember that all organizations have leaders who don’t appear at the top of an organization chart. The cultural changes from the initiative will affect areas of the organization that may be invisible to the official leadership channels — so much so that you would be remiss if you didn’t recognize and include individuals who represent the social organization.
      6. A training team leader. If you have selected an outside implementation partner (see Chapter 2 for details), you may want to include a senior member on your Leadership Team


  3. Implementing a Communication Plan

    Communications are the tugboats of change. In fact, many organizations have discovered through their Six Sigma communications initiatives how to better communicate in general. Without consistent messages, active listening, and strong reinforcements, no regimen of training or army of consultants can align everyone in the same new way.


    Understanding the two communications plans


    You actually have two communications plans to choose from for your Six Sigma initiative. Together, these two communications plans serve as the basis for applying the many tools of Six Sigma management to build momentum and sustain progress. By working with these plans, you can keep everyone aligned, confirm key tenets of the initiative, fight project scope creep, head off rumors, and consistently improve business performance.


    Communication Plan


    Deployment Initiative

    Identifies and directs how everyone in the organization knows what is occurring during the life cycle of the program. Communications are occurring in all directions: from the top-down and bottom-up, internally and externally, laterally, and informally and formally. With this plan, you ensure that all these channels and forms of communication are enabled and active.

    Project Communications Plan

    Because projects are the critical implementation tools of a Six Sigma initiative (see Chapter 4 for more on project tools), they warrant a communications plan all their own. Each project team adheres to the protocol as called for in its Project Communications Plan to ensure that the activities, resources, and focus of the project team are reaching the intended results.


     Elements of your communications plan

    1. Why: The purpose for the communication, which is to formally establish and enforce the commitment to communicate certain information.
    2. What: The item of communication. Refer to Figure 3-2 for a summary of the many items of communication in a Six Sigma initiative.
    3. By Whom: The individual responsible for ensuring that the communication occurs (see Figure 3-5).
    4. To Whom: The audience or recipients of the communication. Chapter 3: Leading and Managing a Six Sigma Initiative 31
    5. When: The time and frequency at which you deliver the communication.
    6. How: The tool or delivery mechanism that you use to communicate. Refer to Figure 3-6 for a list of the many ways you can communicate.
    7. Where: The location — physical or virtual — where the recipients find the communicated information.


    Before the initiative can proceed beyond the Leadership Team, one critical item of communication must be prepared — the Six Sigma elevator pitch - a common way of defining and describing your initiative in a smooth, brief, passionate, and consistent manner, is a cornerstone of the initiative’s communications plan.



    Who does the communicating?


    Everyone communicates in Six Sigma. They are the top-down , bottom-up, from anyone in the organization who sees a problem that needs fixing or a way to do something better, lateral — which means that

    methods and tools are shared and results are verified across and between projects and departments, and they’re both outside-in, with inputs from customers, suppliers, and stakeholders, and inside-out, with inputs going from the organization to these constituents. Finally, communications are also very much bidirectional, with everyone listening as much as he or she is being listened to.


    Six Sigma FAQS


    Basic Information -  What is Six Sigma all about?, Isn't Six Sigma just for manufacturing?, We've seen all these various "quality" initiatives come and go. What makes this one different?, What's with all the goofy belts?, Isn't this really just a job-reduction initiative?, Does this mean more consultants?

    How it affects me - How will this affect my job?, How will this affect my department or team?, How does this affect my career opportunities?, We're so busy now; how can we possibly take on a new initiative?,

    Do we all have to become math geeks?

    How it affects the company - How does this make us a better company?, Does this mean another reorganization?, Will the managers understand and support this?, How's it going to roll out? Where do we start?, How does this affect our customers?, How does this affect our suppliers?

    How it works -  Where did the term – and the movement – come from?, What has this meant for other businesses like ours?, Is there a great book that describes it?, Do we really have to achieve Six Sigma?

    How will this affect our company culture?


    Timing is everything


    Writing your communications plans



    Six Sigma Deployment Initiative Communications Plan





    Title, Date, Release Version. Author, Approval(s)

    Role and Purpose

    State the role this plan will play within the organization


    Identify the way your organization values and uses communications. Indicate the communications responsibilities for executives. Managers, practitioners, and staff.

    Items of Communication

    Identify the scope of the communications plan.

    Indicate key items to be communicated.

     Key Personnel

    List the I)principal author and responsible 1)arties for this l)lan.

    Confirm participation and approval from the tolp organization executive(s).

    Indicate who will be responsible for issuing and responding to the communication items.


    Indicate communications items by milestone.

    Indicate communication items by fixed frequency


    List the different tools to be used and by whom.

    Indicate where certain tools are inappropriate as well.


    Identify where published reports, presentations, letters, and other pertinent communications will be archived and accessible for reference. Indicate other facilities, environments, information technologies, and channels to l)e used.

    Measurement & Analysis

    Identify key measures of successful communications and how the analyses of these measures will lead to improvements.


    Six Sigma Project Communications Plan


    Selecting Software Products and Integrating Information Technology Architectures


    The software tools for Six Sigma sort into two major categories: practitioner tools and management tools.


    Practitioner Tools




    Process Modeling

    Process Definitions, Material Flow, Value Stream Identification, Resources Cycle Times, Functional Alignments (Swimlanes)


    Process Timing, Resource Consumption, Patterns, Bottlenecks


    Measurement Systems Analysis, Graphical Analysis, C&E Matrix,

    Time-Series, Descriptive Statistics, ANOVA, Advanced Statistics,

    Process Capability and Capability-Complexity Analysis, Tolerance

    Analysis, Regression, Exploratory Analysis, Mutivariate Analysis

    Design of Experiments

    Robust Experiments, Multi-Factorial Designs, Response Surface

    Designs, Taguchi Designs


    Axiomatic Design, QFD, Kano Modeling, Robust Design, TRIZ,

    Pugh Concept Selection


    Management Tools


    Management tools enable and assist project management, facilitate communications, aid learning and retention, and provide a repository for future reference.





    Leadership, Motivation, Statusing, Informing, Explaining, Listening, Direction, Correction, Rewarding, Celebration

    Program and Portfolio


    Initiative-level tracking and management of program performance; Ideation; Project Selection; Alignment; Prioritization

    Project Management

    Project-level budgeting, schedules, resources, milestones, methodology, benefits, risks, controls


    Statusing, Actions, Results, Recommendations, Achievements, Failures, Challenges, Lessons-Learned, Best Practices, Dashboards, Balanced Scorecard



    Methods and Tools repositories, Best Practices Reference Databases, Collaboration, Plans, History and Archives

    Learning Tools

    Lectures; e-Learning; Handbooks; Guides


    Enterprise Integration, SOA, and BPM


    In addition to the practitioner and management software tools specific to Six Sigma program execution, there are other information technology contributions to a Six Sigma initiative.  They include "Enterprise Application Integration and Service-Oriented Architectures" and "Business Process Management".


    Defining and Implementing Your Management Plan


    A Six Sigma initiative has a life cycle with four distinct phases:





    The process of preparing and developing the infrastructure and support systems needed to begin the initiative.


    In this phase, the many elements of the infrastructure are  deployed. Training and project work begin, and the first results come in.


     After the initial deployment phase is completed, you expand the program to encompass the entire organization, including key suppliers and customers.


    This is the most challenging phase of all because you have to sustain the gains — and these aren’t the gains in bottom-line performance. They’re the gains in cultural agility. This is the phase of transitioning from “the new initiative” to “the way we work.”


    To accomplish a successful Six Sigma initiative, you need to create and work with an Initiative Management Plan.



    Management Task


    Business Objectives


    Scope of Initiative


    Leadership Team Selection / Assignments


    Communications Plan Definition


    Human Resources


    Definition of Training Regimen


    Critical Success Factors


    Timeline of Major Milestones


    Risk Factors and Contingency Plans


    Revision and Update Management




    Leadership Team Initiation Workshop


    Infrastructure Readiness


    Communications Elements


    Information Technology


    Human Resources Alignment


    Initial Training Waves


    First Projects / Process Improvement Areas


    Results, Reports, Communications


    Lessons Learned – System / Plan Updates


    Scope Adjustments


    Training Waves


    Additional Projects / Process Improvements


    Results, Reports, Communications




    Lessons Learned – System / Plan Updates


    Infrastructure Adjustments


    Cultural Incentive Realignments


    Institutionalization Elements


    Additional Projects / Process Improvements


    Chapter 4


    Putting the Right Foot Forward: Defining a Six Sigma Project

    This Chapter deals with Identifying problem areas with a business case, Creating scorecards to prioritize projects, Defining projects with problem statements, using objective statements for project definition and Following a launch checklist


    Getting Project Ideas by Using the Business Case Writing Tool

    The first step is to identify the problem areas of the business. By using a tool called a business case, you can identify where in the business problems are occurring, provide a summary description of the situation, and estimate the potential value of improvement efforts. The intent here isn’t to define a Six Sigma project, but to clearly illuminate where projects are needed the most.


    In order to stimulate you to find problem areas in your business, following is a checklist of red flag items, any one of which could indicate a business problem area to address:

    Product returns

    Low quality

    Capacity restraints

    Receivable collection issues

    Low yield

    Long cycle times

    Stressful work


    Excessive inventory

    Chaotic or complicated workflow


    Customer complaints


    Prioritizing and Aligning Projects with Business-Customer-Process Scorecards

    To obtain the maximum benefit from your initiative, you must link your Six Sigma project selection with the strategic needs of the business.

    At this critical point in the selection process, you probably have a number of “Voices” shouting at you and demanding attention: the Voice of the Customer (VOC), Voice of the Process (VOP), and Voice of the Business (VOB). Often you find these Voices competing with each other for your attention. For example, the VOC wants lower prices, better pizza, and faster delivery, the VOP wants the best possible ingredients regardless of the cost, and the VOB wants to make more money.


    Take the Three Sigma Pizza Emporium for example. This business has a number of problems, and the Six Sigma team didn’t know where to start on improvement efforts. So, the team completed a business-customer-process scorecard.


    Project Definition I: Writing a Problem Statement

    Before mounting your white horse and leaping right into solving your business problems, you need to define and describe the problem by using a problem statement. This tool clarifies the issue by specifically identifying what has to improve to meet your goal, the magnitude of the problem, where the problem occurs, and the financial impact. The problem statement can then be used to communicate the problem to the people whose support you need. Following is a checklist that shows all the critical elements of a successful problem statement:

    A description of the problem and the metric used to describe it.

    The process name and location of the problem.

    The time frame over which the problem has been occurring.

    The size or magnitude of the problem.


    Project Definition II: Writing an Objective Statement

    One more tool is important for you to make sure that your improvement project launches properly. This tool is called an objective statement, which directly addresses the problem statement. In order to be effective, the objective statement must contain all of the following elements: it must improve some metric from some baseline to some goal, in some amount of time with some positive impact on some corporate goal or

    objective. Simply put, the objective statement must indicate the level of improvement expected from improvement efforts, including specific, quantifiable amounts and the time required to complete


    Six Sigma practitioners often use a memory jogger, called SMART, to help write effective objective statements. Each letter reminds you of a goal to achieve in your statement:


     Make sure that the specific deliverables and outcomes are stated and that you answer the question, “What’s the specific purpose of this project?”


    Be sure that your objective is both quantifiable and verifiable and that it includes such things as quality, quantity, cost, and timeliness.

    Aggressive , but Attainable

    A challenging objective makes the project interesting and fulfilling, while also providing worthwhile returns. However, don’t try to solve world hunger.


    The objective must be relevant to business goals.

    Time bound

    You must state a definitive time frame for reaching your objective.


    Launching a Project

    To make sure the launch process is orderly, follow this checklist

    Identify everyone who has to approve the project.

    Obtain written approval.

    Identify the people impacted by your project.

    Notify the impacted people of what’s to come.

    Get final approval from the project team leader.

    Identify Six Sigma skill levels (Belts) that are needed.

    Identify the process members who will participate.

    Identify the entire project team by name.



    Chapter 5 - Graphical Representation of a Process



    Brainstorming the Inputs to Your Process

    This Chapter deals with creating diagrams to identify inputs, developing process flow maps and sorting inputs with CT trees


    Every process, every product, every event is comprised of, or caused by, some number of inputs, known in Six Sigma parlance as Xs, which take their place in the equation, Y= f(X). Before you can start improving your outcome,or Y, you have to first identify all of the inputs that created this outcome. Without tools and a rigorous process, identifying inputs is a daunting task.


    Brainstorming with Your Team to Create Affinity Diagrams

    Brainstorming works because the ideas and knowledge generated by two or more people acting as a group are always greater than those of the sum of the people acting individually.  Brainstorming best practices



    Agree on a subject. The group must first agree on the category or condition to be the subject of the session.


    Encourage participation. Each team member should be encouraged to participate.


    Discourage criticism. Ensure that everyone understands that debates and criticism aren’t allowed.


    Decide on a contribution method. Members can contribute in rotation or in free flow. Just make sure everyone is heard.


    Promote equality. Ensure that every member has an equal opportunity to be heard.


     Listen. Hear and respect the ideas of others — there are no stupid ideas.


    Record ideas. Make sure all ideas are written down.


    Continue as long as necessary. Stop only after no more new ideas are offered.


    Edit. Review the list for clarity and duplicates.


    Repeat. Repeat the process for all identified categories


    After you’ve generated lots of ideas, you can start your affinity diagram. The process of creating an affinity diagram stimulates an effective gathering and organization of the ideas into natural groupings — groupings that start to pinpoint the essence of a problem and provide the raw material for a breakthrough solution.  Likely more than one person in the brainstorming group already knows what’s causing the problem — they just don’t know that they know. After the ideas are generated and organized, the light will come on and the entire group will say, “Ahhh, so that’s the problem!”


    Here’s a checklist for generating an affinity diagram.




    Write down the problem or issue

    Be sure that the topic is clear and concise enough to address in one session. “How do we boil the ocean?” is too broad. However, “Why is our server computer crashing?” is a more suitable topic to delve into.

    Conduct a brainstorming session for the problem

    Follow the brainstorming steps that we outlined earlier in this section. Spend a minimum of 15 minutes, and as long as necessary, discussing this issue.

    During the discussion, have the participants write each of their ideas on a separate sticky note, with only one idea per note.

    Avoid using ideas that are single words. Instead, use phrases or sentences. For instance, unacceptable ideas for the topic “Why is our server computer crashing?” would be: “stupidity,” “junk,” “evil spirits,” or “who knows?” Acceptable ideas would be: “Users are poorly trained,” “Computer

    hardware is obsolete,” and “Software is incompatible.” Continue as long as necessary. It’s not unusual to generate more than 100 notes.

    Post all of the sticky notes on a smooth surface, such as a wall or whiteboard.

    Without discussion, have the participants sort the notes into a few logical categories — usually around five, but in no case more than ten. Encourage participants to move notes from category to category to where they fit best.

    Sorting in silence helps participants focus on meaning and not on the emotion or baggage that arises in most discussions.

    After all the sorting is done, instruct the participants to create titles for the categories

    A category title should fit the notes bundled under it. Don’t force titles or notes into places they don’t fit. When the sorting process is done, create an affinity diagram.


    The affinity diagram classifies the inputs into different categories.



    Dem Bones: Creating Fishbone Diagrams

    The next step is to drill down a bit into the inputs to find the causes of variation by using a very useful tool called the cause-and effect, Ishikawa (creator) or, the fishbone diagram. This diagram , is used to explore all the potential causes (inputs) that result in a single output. Even though an affinity diagram helps you group inputs into general categories, the fishbone diagram goes a step further and links inputs together to help you dig for the true root causes of variation. Many of the ideas produced in an affinity diagram exercise may not be causes at all, or they may turn out to be symptoms of the root cause. In a fishbone diagram exercise, each input is explored in depth, linked to associated inputs, and classified as either a root or secondary cause.



    In constructing the fishbone diagram, the problem or condition (the output, or Y) is entered at the “head” of the fish. Each of the major intersecting “bones” is a primary category of input. These categories may be the same ones identified in the affinity diagram process, or they can be the often-used generic categories - Measurement, Man (or People), Method (or Process), Materials, Machine (or Equipment), Environment. The important thing to remember is that categories need to fit your identified output and the inputs generated.


    The smaller, horizontal “bones” are the individual inputs previously generated. Each input is examined carefully to make sure it’s not only in the right category, but also to determine whether it’s a direct input at all. If an input turns out to be only indirectly contributing to the outcome, and primarily affects another input, these indirect inputs are placed as “sub-bones” connected to another input. Of course, if, upon examination, a generated idea has no impact at all on the outcome, this idea is discarded and not entered on the fishbone diagram.



    Examining Your Processes with Process Flow Maps

    After you’ve generated a number of potential inputs into your selected outcome and have begun to categorize and analyze these inputs, it’s time for you to take a look at the whole system, or process, of which your outcome is the end result. Before you can make improvements to your process, which will give you

    the outcome that you want, you have to know what the process really is. One way to examine a process is to use a graphical representation of a process called a process flow map. But beware of a process flow map if you haven’t verified that it represents what’s really occurring.



    Finding Critical Fruit in the CT Tree

    A CT tree is another diagrammatic way of sorting and displaying inputs, but with a different wrinkle. Affinity and fishbone diagrams sort inputs by type, but a CT tree sorts inputs by what is Critical To the major contributors to the success of your desired outcome. What makes the CT tree particularly useful is that it relates inputs to specific outputs that you’re interested in. This is the only such tool that starts with the outcome of interest and backs into the causes.






    Chapter 6


    Prioritizing Which Inputs to Address

    This Chapter deals with narrowing down your inputs by creating Pareto diagrams, finding critical inputs with SIPOC diagrams, discovering root causes with a cause-and-effect matrix and using a Failure Modes Effects Analysis (FMEA) to determine the inputs with the greatest impact.









    Cementing the Foundation: Creating SIPOC Diagrams

    SIPOC — which stands for Suppliers-Inputs-Process-Outputs-Controls — is a tool for building high-level process maps that consider the impact of suppliers and the requirements of customers. In this context, both suppliers and customers may be external or they may be people, systems, or processes within the same organization.   A SIPOC diagram is based on simple process flow maps, but it delves much further —

    providing immediate feedback as to which inputs are critical to the process output. A SIPOC diagram focuses on inputs, outputs, customers, and suppliers, and provides the foundation for significant DMAIC (Define-Measure-Analyze-Improve-Control, the basic Six Sigma process) improvement.






    Untangling Webs: Creating a Cause-and-Effect Matrix


    The Cause and Effect Matrix, or C&E Matrix, helps Six Sigma practitioners make a link between multiple inputs and the resulting outcomes. By identifying and prioritizing these relationships, you can explore and graphically display the possible causes of a problem or condition, which allows you to then search for the root cause.



    Performing a Failure Modes Effects Analysis (FMEA)

    An FMEA is a structured approach to identifying the potential ways a product or process can fail and to identifying how you can detect the failure and its effects so you can reduce the risk of either occurrence or

    impact, or both. Keep these points in mind for the next problem.


Chapter 7


Categorizing Data and Calculating Measures of Variation

This Chapter deals with determining what kind of data you have (discrete vs continuous), calculating "means, modes, and medians", calculating how much variation is in a set of data, separating variation into its short-term and long-term components


Differentiating Data Types


Your data values will either be able to be placed into named categories (this data is called attribute or categorical data) or will follow a continuous scale (this data is called continuous or variable data).


Calculating Measures of Variation Location

To begin to understand variation in your data, you have to be able to describe it with numbers. The most basic numerical measures are those that quantify the location of the central tendency of your variation — or, in other words, the values that are most likely to occur.


Variation Calculation



The mode of a set of data is the single value that is most frequently observed and is associated with the highest peak of a distribution.


The median of a set of data is the single value where half the data is below and half is above. The median is the preferred measure of variation location when your collected data contains outliers, or extreme data points well outside the range of other data. You determine the median by ordering your collected data from least to greatest and counting the total number of points. If you find an odd number of data points, the median is the middle value, or the one exactly halfway through the list. If you find an even number of data points, the median is the average of the two points in the middle of the list.


    The mean — or average — of a set of data, is represented mathematically by the symbol x:



    • x (pronounced “ex bar”) is the symbol representing the calculated mean.

    • xi represents each of the individual measurement values.

    Σ, the Greek capital letter sigma, tells you to sum up (add) all the individual


    • n is the number of individual measurements in your data set.



Measuring Variation Spread

The central location of the variation in your data is only the first of two critical parameters you need to quantify. The second parameter is the measure of how much variation spread you find in your data around its central location.


Measure of







Simple. Preferred metric for sets of data with only a few (2 to 9) members. Drawback: Greatly

influenced by outliers.



Useful for more advanced experimentation and analyses.

Standard Deviation

Most commonly used for data sets with 10 or more members. More accurate than the range

metric for larger data sets.


Time Warp: Separating Short-Term and Long-Term Variation


Quantifying variation spread can be tricky because it changes over time. Over a short period of time, the variation you observe is smaller than it will be over a longer period of time. One of the first tasks of the Six Sigma practitioner is to separate observed variation into these two buckets — short-term and long-term.


    Chapter 8


    A Picture’s Worth 1,000 Words: Measuring with Charts and Graphs

    This chapter deals with determining the shape of variation with dot plots and histograms, comparing variation distributions with box and whisker plots, setting up scatter plots to explore relationships between characteristics and creating process behavior and time series charts to see how a characteristic changes over time


    Putting Dot Plots or Histograms to Use

    The purpose of dot plots and histograms is to graphically show you where variation occurs within a critical characteristicwhether it’s all lumped together within a narrow interval or evenly spread out over a wide range of values. A dot plot or histogram will immediately tell you how frequently various values occur in your data and will provide clues to the sources of the variation.





    Create a horizontal line representing the scale of measure for the characteristic you’re charting.


    Divide the length of the horizontal scale into ten to twenty equal “buckets” between the smallest and largest observed values.


    For each measurement in your data set, place a dot in the corresponding bucket along the horizontal axis


    Repeat Step 3 until you’ve placed a dot on the chart for each measurement.


    Interpret your dot plot or histogram by looking for the following basic patterns.


    1. What shape does the data form?  Do the dots (or bars) on the graph form a single bell-shaped curve or hump? Or is there a uniform distribution across a range of values? Are the dots clumped together with one side trailing out more than the other?
    2. Where is the mode, or tallest peak of the distribution, located? Is there one peak or are there multiple peaks?
    3. At what point along the horizontal axis of your dot plot or histogram do the stacked dots or bars seem to balance out like a teeter-totter? This point is the approximate location of the variation mean, or average.
    4. What is the range? The distance along the horizontal axis between the largest dot (xMAX) and the smallest dot (xMIN) is the range (R = xMAX – xMIN).
    5. Are there outliers (specific points that don’t seem to fit the grouping of the rest) in your data? Are they either too far to the right or too far to the left of the rest of the data to be concluded as coming from the same set of circumstances that created all the other points?


    Setting Up Box and Whisker Plots

    Sometimes you need to quickly compare two or more variation distributions of the same characteristic. It’s like standing two people back-to-back to see who’s taller. But, in this case, you’re asking questions such as “Which distribution is more spread out?” and “Which has the higher central location?” This is when box and whisker plots come in handy.





    Rank order each of the sets of data, from smallest value to largest value, that

    you’ll be including in your box plot


    Separately for each set of data, divide your rank-ordered data into fourths, or quartiles , as statisticians like to say

    • From xMIN, the smallest observed point, to a point called Q1 is the lower quartile of the points in your data set.
    • From Q1 to the median of your data set is the second quartile of the points.
    • From the median to a point called Q3 is the third quartile.
    • From Q3 to xMAX, the largest point in your data set, is the fourth quartile.


    Draw a horizontal or vertical axis to place the box plot on.  Create a numerical scale along this axis that spans from just below the smallest value of all the data sets to just above the largest value.


    For the first data set, locate along the axis the points for xMIN, Q1, the median, Q3, and xMAX.


    Draw a box between the Q1 and Q3 points


    Place a heavy line through the box at the point of the median.


    Draw whisker-like lines extending from the Q1 and Q3 points to xMIN and xMAX, respectively.


    Repeat these same steps for each successive subgroup distribution you’re including for comparison with your box plot




    From the completed side-by-side box plots, you can easily see the similarities and differences between the performances of the two manufacturing lines. The variation for Line B is much more spread out than Line A. Line B also has its central location lower than Line A, and Line B’s data isn’t symmetrical — it’s skewed to the lower production volume values. If you wanted to select the production line that consistently produces higher volumes, you’d definitely pick Line A, even though Line B had the highest single measurement.


    Seeing Spots: Using Scatter Plots

    Scatter plots help you explore the relationship between two characteristics. As the values for Characteristic A increase, for example, what happens to values for Characteristic B? Do they also increase? Or do they decrease? Or neither? Scatter plots can be created when one of the two characteristics is not measured on a

    continuous scale, but instead consists of attribute data (see Chapter 7). For example, the characteristic of “production volume” (measured on a continuous units-per-hour scale) can be plotted against the characteristic of “production line ID” (perhaps named Line A and Line B).





    Form data pairs that represent x-y points from the collected data.  For each observation, pair the simultaneously measured values for the two characteristics together to form an x-y point that can be plotted on a two-axis x-y graph.


    Create a two-axis plotting framework. To create your framework, draw two axes, one horizontal and the other vertical. Draw one axis for each of the two characteristics you’re exploring.

    The scale for each axis should be in the units that correspond to its assigned characteristic — millimeters for length, pounds for weight, minutes for time, number of defects found on an inspected part, or whatever the units may be that quantify the characteristics you’re exploring.


    Plot each x-y pair as a point on the two-axis framework.


    You interpret your scatter plot by looking for relationships or patterns between the two plotted characteristics. Look for:

    1. Graphical correlation between the two plotted characteristics or variables. If there’s no pattern in the plotted points — just a random scattering of points — then there’s no correlation or relationship between the characteristics. Clustering of the plotted points or patterns that follow the shape of a line or a curve reveal correlation between the two variables.
    2. Direction of correlation between the variables. When there are patterns, does an increase in one variable lead to an increase in the other? Or a decrease in one lead to a decrease in the other? If so, there is a positive relationship between the variables. But if a change in one variable leads to a change in the opposite direction for the other, there is a negative relationship between the variables.
    3. Strength of effect between the variables. How drastic or steep is the linear relationship between the variables? If a small change in one variable leads to a large change in the other, you’re observing a strong effect between them.



    The plotted points follow a trend that slopes downward as you move from left to right. This means you’ve discovered a relationship between the production speed setting and the compressed air pressure variable. As the production speed setting increases, the compressed air pressure goes down. And, as you decrease production speed, air pressure goes up. This is a negative relationship.


    Hindsight Is 20/20: Using Process Behavior or Time Series Charts

    Dot plots, histograms, box plots, and scatter plots all neglect an important variable - time. To see how a characteristic changes over time, you have to plot its measurements in the sequence or series in which they occurred. When variation behavior is linked to time, you’re then able to link process behavior and changes back to historical events or conditions — such as the changing of a work shift, the gradual dulling of a

    cutting tool, or the steady jitter of the status quo.




    Chapter 9


    Yield and Defects: Calculating the Good, the Bad, and the Ugly

    In This Chapter setting meaningful and appropriate performance specifications, calculating and interpreting Six Sigma yield metrics, and determining how many defects are being created and how often


    Get Real: Creating Realistic Specifications

    Specifications represent the specific limit values that separate good performance from poor performance — they define what’s acceptable and what’s not. Specifications form the basis to determine what process outputs or characteristics are either good or bad. The mind-jogging acronym, RUMBA, helps you check the appropriateness of any specification.


    Is the specification based on a realistic assessment of the customer’s actual needs? Does the specification relate directly to the performance of the characteristic?


    Is the specification clearly stated and defined so that there is no argument about its interpretation?


    Can you measure the characteristic’s performance against the specification? If not, there will be a lot of debate between you and your customer as to whether the specification has been met or not.


    Have you bought into the specification setting? Can you and your coworkers strive to meet the specification?

    Attainable or Achievable

    Can you reach the level and range of the specification?


    Getting It Right the First Time: Calculating First Time Yield (FTY)


    FTY is the basic measure of a process’s real capability, or ability to produce good items the first time.


    where in is the number of items started into the process, scrap is the number of items that end up unusable, and rework is the number of items requiring additional effort to meet the specification.



    Rolling Many into One: Calculating Rolled Throughput Yield (RTY)


    RTY tells you how well the entire system works together.

    where FTYi is the first time yield of each of the n product or process components for i = 1 to n.


    RTY = FTY1 × FTY2 × FTY3 × FTY4 × FTY5

    RTY = 0.75 × 0.95 × 0.85 × 0.95 × 0.90

    RTY = 0.518


    An RTY of 0.518 means that the chance of a purchase order going through the entire process correctly the first time, with no rework or scrap, is only 51.8 percent.


    “How Bad Is It, Doc?” Calculating Defect Rates



    defects per unit


    defects per opportunity


    When you need to compare the defect rate of different products or processes you first have to put the rates for each into comparable units.


    defects per million



    What’s Missing? Linking Yield to Defects


    When you have an overall process with a relatively low defect rate — say, a process that produces units with a DPU less than 0.10 (or 10 percent) — you can mathematically link the process defect rate to the overall process yield:




    Chapter 10 - Locking in the gains covering basis of Process Control and Control Charts (*REQ)


    Mastering Measurement System Analysis (MSA)

    This Chapter deals with completing a basic measurement system audit, performing attribute measurement system analysis and interpreting the results of your continuous variable measurement systems analysis


    Measurement is the foundation of knowledge and subsequent improvement. Measurement is the tool you use to verify that you have come to the right answer, have corrected the problem, or have improved the situation.


    Your Basic Sanity Check: Auditing Measurement Systems


    An audit is when you compare your measurements to a known, correct standard. 



    Important note #1: Experience has shown that human inspection systems detect only about 80 percent of actual defects. Remember that eyewitness accounts often are incomplete or wrong. If you want to use human inspection, you need to take precautions to try to make them accurate enough for your needs.

    Important note #2: If your measurement system is one that classifies problems or defects into categories,

    a Pareto chart (or bar chart) of the number of problems or defects placed into each category shouldn’t be flat or even across the charted categories. Instead, about 80 percent of the total defects should come from a smaller subset of the possible defect categories. If the Pareto chart of your defects is flat, that means your measurement system probably isn’t accurately reflecting reality. Also, if a Pareto chart of classified defects looks extremely peaked, with almost all defects in a single category, your measurement system doesn’t have enough discriminating power and needs to be addressed. (Refer to Six Sigma for Dummies for background on creating and interpreting Pareto diagrams.)


    Do We Agree? Performing an Attribute Measurement System Analysis


    The purpose of some measurement systems is to categorize items by their attributes — to separate “good” items from “bad” ones, sort samples into “blue,” “green,” and “cyan” groups, and assign invoices to “engineering,” “production,” or “sales” departments. These types of measurement systems are called attribute measurement systems because they determine or measure one or more attributes of the item being inspected. The question is, how repeatably and reliably can one of these systems determine the specific attribute you’re looking for? For example, how repeatably and reliably does your attribute measurement system detect “bad” disk drives from among all the “good” ones being completed in production? To quantify how well an attribute measurement system is working, you perform an attribute measurement system analysis.


    Gauging Gages: Analyzing Continuous Variable Measurement Systems

    Many measurement systems operate in the realm of continuous variable data (thermometers, rulers, and stopwatches). All these are used to measure variables that vary continuously rather than just fall into attribute

    buckets such as “small,” “medium,” or “large.”


    Important note: When dealing with continuous variable measurement systems, the total variation you observe is a combination of the actual variation of the parts or process you’re investigating and the variation from the measurement system itself.


    When studying the accuracy of a continuous variable measurement system, you do experiments and calculations to quantify the observed variation, the actual variation, and the measurement system variation. These studies usually involve two to three inspectors and five to ten process outputs or characteristics to measure. Each inspector also measures each process output or characteristic two to three times.


    At this stage, statistical analysis software, such as Minitab or JMP, is used to automatically calculate the observed, actual, and measurement system variations.


    Calculated Variance Ratio




    This is an effective measurement system. Contribution of the measurement system itself to the overall observed variation is small enough to enable good decisions from the measurements.

    Use the measurement

    system as it is now. Look for opportunities to simplify or make the measurement system less expensive or more efficient.


    This is a marginal measurement system. Contribution of the measurement system itself to the overall observed variation is beginning to  cloud results. You risk making a wrong decision due to

    the extra variation of the measurement system.

    Use this system with caution and only if no better measurement alternative exists. Begin to improve the measurement system by training operators, standardizing measurement procedures, and investigating new  measurement equipment.


    This is an unacceptable measurement system. Guessing is probably just as precise. Don't base important decisions on information compiled from a measurement system that’s in this condition.

    This measurement system needs to be corrected before any valid information can be derived from the system. Investigate causes of gross inconsistency.


    Chapter 11


    Capability: Matching Performance to Need

    This Chapter deals with discovering how to calculate sigma (Z) scores, understanding the shift between short- and long-term performance and using capability indices (CP, CPK, PP, PPK) to apply an improvement plan.


    Capability is a measure of how well a product or process is able to meet a specific requirement. 

    In this chapter, you practice how to calculate the precise capability of a process or characteristic. With a proper capability metric in hand, you can compare the performance of one process to another, you can determine how many items will end up outside the required performance limits, and you’ll have a basis for measuring performance improvement.


    Calculating and Interpreting Sigma (Z) Scores


    The sigma (Z) score is one of the most basic ways to describe the capability of a process or characteristic. For example, if you know the Z score, you can quickly look up the corresponding level of defect rate performance. Calculating a sigma score is straightforward. A small Z is the number of short-term standard deviations you can fit between the mean value of the process’s or characteristic’s performance and its nearest specification limit (SL).

    Shift Happens: Transforming Between Short- and Long-Term Performance

    Why all the mixing of short- and long-term values? The reason is that early Six Sigma practitioners found it easier and more practical to gather a short-term sample and calculate a short-term standard deviation and Z score, but at the same time they wanted to convey the loss of capability that always occurs over the long-term. To accomplish this, the early practitioners contrived the now-famous 1.5-sigma shift and built it right

    into all of their sigma (Z) score tables.


    Calculating and Interpreting Capability Indices

    Six Sigma practitioners use indices to communicate the capability of a process or characteristic. These indices, CP, CPK, PP, PPK, each compare the width of the process’s or characteristic’s specification requirement to its short- or long-term variation width. Knowing these index values, you can quickly figure out how the process or characteristic is performing and you can compare the capabilities of different processes to each other.


    Index Name




    capability index (Cp)



    Compares the width of the specification to the short-term width of the process

    Adjusted short-term capability index (Cpk)



    Compares the width of the specification to the short-term width of the process AND accounts for off-centering of the process from the specification

    Long-term capability index (Pp)



    Compares the width of the specification to the long-term width of the process

    Adjusted long-term capability index (Ppk)



    Compares the width of the specification to the long-term width

    of the process AND accounts for off-centering of the process from

    the specification


    Prescribing an Improvement Plan

    Having calculated each of the four capability indices for a process or characteristic, you can use these values to determine a plan for improvement.





    CP ≠ CPK ≠ PP ≠ PPK

    Your process or characteristic isn’t centered and you find special causes are expanding the long-term variation.

    Begin by eliminating special causes. Later focus on centering the process.

    CP = CPK and  CP = CPK

    Overall, your process or characteristic is centered within its specifications.

    As needed, focus on reducing the long-term variation in your process or characteristic while maintaining on-center performance.

    CP = PP


    CPK = PPK

    Your process or characteristic suffers from a consistent offset in its center location.

    Focus on correcting the set point of your process or characteristic until it’s centered.

    CP = PPK

    Your process is operating at its entitlement level of variation.

    Continue to monitor the capability of your process. Redesign your


    Chapter 12


    Narrowing Your Inputs with Confidence

    This chapter deals with quantifying with confidence intervals for means, using confidence intervals for standard deviations, understanding how to use confidence intervals for proportions


    What the wheel is to transportation, sampling is to statistics. Statistical sampling allows you to understand an entire population that’s too large to measure individually by inspecting only a few, representative samples of the population.


    Statisticians have studied sampling to an almost sickening extreme. They use the Greek symbols, such as μ and σ, to represent the exact population parameters and the Roman symbols, such as x and s, to represent the calculated parameters of a sample. What they’ve found is that each time you take a different sample from the same population and calculate the sample’s mean or its standard deviation — or any other statistical measure — you end up with a slightly different calculation result. When you collect the repeated sample calculations together, they form what’s called a sampling distribution. And statisticians know exactly how

    wide this variation will be depending on how many data points are in your sample.


    A confidence interval quantifies the potential variation around your calculated metrics, such as the mean or the standard deviation. If, for example, you’re basing your mean calculation off of a sample rather than off of the entire population (which is almost always the case), a confidence interval allows you to say, “With 95 percent confidence, I know the average height of the European male population is between 1.75 and 1.78 meters.”


    Because in the real world you almost always work with calculated values from samples instead of entire populations, it’s important that you know how to quantify the potential error in your measurements and how this quantification affects your decisions. This chapter provides examples and practice problems that help you become an expert in creating confidence intervals around your calculations.


    Creating Confidence Intervals for Means

    Whenever you use the calculated average of a sample (x-bar) to infer what the average of the entire population (μ) is, you have a potential for error. Confidence intervals for means allow you to quantify how much your inference may be off based on the number of data points in your sample.


    When your sample has 30 or more data points, the confidence interval for the calculated mean is:


    Sample Size






    μ is the true population mean

    x-bar is the calculated sample mean

    Z is the sigma value corresponding to the desired level of confidence you want to have

    s is the sample standard deviation

    n is the number of data points in your sample





    Calculating Confidence Intervals for Standard Deviations

    Just as with the mean of a sample, the standard deviation of a sample (s) doesn’t exactly tell you what the true population standard deviation (σ) is. But, you can bind your calculation with a confidence interval surrounding the true value. And just as with confidence intervals for means, the more data points you have in your sample,

    the tighter your confidence interval for the population standard deviation will be.


    Confidence intervals for standard deviations are based on the χ2distribution


    The table below provides χ2 values for common sample sizes and confidence levels.


    Confidence intervals for the ratio of two variances are based on the F distribution:




    Four Out of Five Recommend: Using Confidence Intervals for Proportions

    Sometimes, the data you’ve collected creates a proportion, such as 8 “good” disk drives out of 10 disk drives inspected. The group of 10 disk drives inspected in this example is a sample of the larger population of total disk drive items produced. So, you can create a confidence interval. You can also create confidence intervals around the difference between two proportions.

    If y is the number of items identified out of the total number inspected (n), the proportion is written mathematically as y/n/.


    The confidence interval around the true population proportion (p) is written as


    To compute p, all you need to know is y (the number of items identified out of your sample), n (the actual number of items in your sample), and F (the sigma value corresponding to the level of confidence you want your interval to have). The confidence interval for the difference between two proportions is written as:


    Note:  In reality, proportions can never be less than zero or greater than one. So, if the calculated confidence interval for your proportion exceeds these natural limits, just adjust the confidence interval to the natural limit.

    Chapter 13


    Quantifying Variable Relationships

    This Chapter deals with calculating how much correlation there is between variables, determining equations with curve fitting and making sure fitted lines are valid.


    After you’ve defined your most important process or product outputs (Ys) and those process or product inputs most likely to affect them (Xs), you need to understand and quantify the relationship between them. The first step is to identify which Xs are correlated to Y. You can get hints about correlations by looking at scatter plots, discussed in Chapter 8. But to be sure, you need to quantify the correlation and test for statistical significance. You can also develop an actual line equation mathematically relating X to Y. This chapter covers these topics.


    Quantifying Correlation between Variables

    Correlation is all about quantifying the strength of the relationship between two variables. You want to know whether it’s a loose relationship or whether it’s so strong that by knowing one variable, you can predict the other confidently.


    To quantify the linear relationship between two variables (x and y), you use the following formula to calculate their correlation coefficient (r).



    1. where n is the number of data pair measurements,
    2. xi and yi are the individual x-variable and y-variable measurements, taken at the same time or within the same subject to create a data pair,
    3. x-bar and y-bar are the averages of the x- and y-variable measurements, respectively, σx and σy are the standard deviations of the x- and y-variable measurements, respectively, and


    The calculated r will always be between –1 and 1.

    • The sign of r tells you the direction of the relationship between the variables. If r is positive, then when one variable increases in value, the other variable will also increase. The opposite is also true: If one variable decreases, the other variable will also decrease. This is called a positive correlation. If r is negative, then when one variable increases in value, the other variable will decrease, and vice versa. This is called a negative correlation.
    • The absolute value of r tells you how strong the relationship between the variables is. The closer r gets to its theoretical limits of –1 or 1, the stronger the correlation is. An r equal to –1 or 1 indicates a perfect linear relationship, with all the x-y points lying exactly on a straight line. An r close to 0 indicates an absence of a linear fit, or correlation to the data.





    Assessing the Adequacy of a Fitted Line

    Fitting a line to your data isn’t always statistically valid. Sometimes no significant relationship exists, and sometimes a line isn’t the right type of curve to fit your data. So each time you fit a line to your data, you need to check to make sure that the result is statistically valid.


    Residuals are the errors between your actual data and the prediction of your fitted line model. Each point in your data set has a residual (ei), which can be written mathematically as:


    where yi are the actual, observed data values and y/i are the predicted values from your fitted line equation.


    To determine whether your fitted line equation is statistically valid, you need to plot the residuals in several different ways to make sure they appear normally distributed, which is the criteria for your line equation to be statistically valid.



    Chapter 14


    Planning and Conducting 2k Factorial Experiments

    This Chapter deals with setting up and implementing 2k factorial experiments, blocking and randomizing variables, calculating effect, eliminating insignificant effects and forming Y = f(X) equations


    Chapter 13 shows how Xs are related to the critical Ys. Now you have to determine what causes these effects. The questions you have to ask yourself are, “What can I adjust or change to improve my Ys?” and “What’s the ideal adjustment to make?” You have to experiment. Experimenting is at the heart of Six Sigma - Design of experiments (DOE).  This chapter gives you practice in planning, conducting, and analyzing the most common type of experiment used in Six Sigma — the 2k factorial. 2k factorial experiments can be adapted to provide screening, characterization, or optimization information.


    Planning Experiments

    Every experiment in Six Sigma targets a better understanding of the Y = f(X). Better understanding from experimentation includes:

    1. Knowing which input Xs have a significant effect on the output Y and knowing which Xs are insignificant
    2. Formulating and quantifying the mathematical relationship between the significant Xs and the output Y
    3. Discovering where to set the values of the significant Xs so that they combine to produce the optimal output value of Y


    When planning your 2k factorial experiment, take the following items into consideration:




    2K is best suited to studying two to five input variables

    So, first narrow your investigation down to this smaller subset of likely suspects. Typically, these are factors that have already been found to have a statistically significant impact on the output variable of interest. Your selected variables, or factors as they’re often called, can be either continuous or attribute variables. (In case you’re wondering, the “k” in 2k represents the number of factors in your experiment.)

    Select exactly two experimental levels for each input variable — one “high” and

    one “low”— which span the range you want to investigate for each variable.

    The “2” in 2k represents the number of levels for each factor in your experiment.

    Your factorial experiment will have 2k experimental runs

    For example, if you have three factors, you will have 23 = 2 × 2 × 2 = 8 experimental runs. Each run represents a unique setting of the factors at their high and low levels.

    Create a coded experiment design matrix that captures each of the 2k unique

    experiment settings by creating a column for each of the factors and a row for

    each of the 2k runs

    Using –1’s as codes for the “low” variable settings and +1’s

    as codes for the “high” settings, start with the left-most factor column. Fill in this column’s cells with alternating –1’s and +1’s. With the left-most column filled in, move on to the next column to the right and repeat the process — but this time fill the column in with alternating pairs of –1’s and +1’s. Fill in the next column to the right with alternating quadruplets of –1’s and +1’s, and so on, repeating this process from left to right until, in the right-most column, you have the first half of the runs marked as –1’s and the bottom half as +1’s. This table of patterned +1’s and –1’s is called the coded design matrix and represents the experimental settings for each of the 2k experimental runs.


    Managing Those Pesky Nuisance Variables

    In almost every experiment, you have variables that can affect the Y outputs that aren’t explicitly included in your experiment design plan. For example, an experiment studying the effect of depth of cut and cutting speed on a machined surface finish doesn’t include the variable of the machinist: Whether the machining operation is performed by Bob or Hank may affect the results of the surface finish. The experiment also doesn’t include cutting tool sharpness: Meaning that as the cutting tool dulls during the experiment runs, it may begin to have an impact on your results. In a well-designed experiment, these influential factors are addressed and managed so that the results of the experiment remain valid.


    A simple, catchy phrase can help you remember how to manage potential nuisance variables that aren’t included in your experiment: Block what you can and randomize against what you can’t block.



    When you know the source of a potential nuisance variable, you can purposely

    remove its influence completely or include its effect evenly through all of your

    experimental runs. By blocking, you guarantee that you won’t have an unfair bias on

    only a portion of your experimental settings.


    To inoculate your experiment against the detrimental effects of unknown nuisance variables, you need to randomize all the variables that aren’t directly part of your experiment. You randomize such things as the order of the experimental runs, the materials being used, the operators performing the work, the time of day the experiment runs are made, and so on. Randomizing spreads out the otherwise concentrated or confounding potential for unknown nuisance effects evenly and fairly over all of the experimental runs and preserves the accuracy of your results.


    Calculating Main Effects

    Main effects are the quantitative influences each single experiment factor (X) has individually on the output response (Y). Each factor in your experiment has a main effect. To explore and quantify the main effect of each factor in your experiment, follow these steps:




    Create a main effects plot for each factor.

    You create this plot by plotting the line between the point representing the average of the responses with the factor at its high level and the point representing the average of the responses with the factor at its low level.

    The steeper the line, the stronger the effect.

    Quantify the main effect for each factor Ei using this formula:



    Calculating Interaction Effects

    Sometimes a variable has an effect on an outcome when it combines and interacts with another variable.  A properly designed and conducted 2k factorial experiment allows you to identify and quantify all interaction effects among your experimental factors. You’ll have a potential interaction effect for each possible factor combination.


    Determining Which Effects Are Significant

    Unfortunately, just because you can calculate the main effects and the interaction effects for an experiment doesn’t mean that all of the values are statistically significant. The Pareto Principle (see Chapter 6) indicates that only a relatively small minority of all the possible effects will explain the majority of the changes in the response. After calculating all the possible main and interaction effects, you have to test them to see which few you should keep and which you should discard.


    To find out which calculated effects are significant, you plot the calculated effects against their normal Z scores. If the effects are insignificant, the plotted points will fall into the shape of a line. Any effect in which a corresponding point falls far off the line, however, is significant.


    The Ultimate Power Trip: Forming Y = f(X) Equations

    2k factorial experiments not only reveal which factors affect the output Y, but they also allow you to understand the form of the Y = f(X) equation for the system or process you’re improving. At the start, a 2k experiment investigates the possibility of all main and interaction effects being significant. Later, you whittle this list down to just the significant effects. What you do next is create a Y = f(X) equation for your system, which allows you to predict future outputs from known inputs.


    The equation has a constant term (β0) and also potential terms for each main and interaction effect (Xs). These terms each have a corresponding coefficient, labeled β. For a three-factor system, the general form of the equation with all its potential terms looks like this:



    For a two-factor system, the general form of the equation with all its potential terms looks like this:



    Chapter 15


    Constructing Control Plans and Charts

    This Chapter deals with avoiding mistakes with Poka-Yoke, maintaining your performance with control plans, selecting and interpreting control charts and creating (I-MR), (X -R), p, and u charts


    After you’ve finished defining, measuring, analyzing, and improving your process or product, you still have to do more: You have to figure out how to maintain your efforts. Hard-earned gains and improvements are

    quickly lost when things revert to “business as usual.” All of the improvements in the world will quickly evaporate without a plan to hold the achieved gains in place. This last step in the Six Sigma process is the control phase.


    Doing the Poka-Yoke: Mistake-Proofing Products or Processes

    Poka-Yoke is the transliteration of a Japanese phrase meaning “to make mistakes impossible.” Poka-Yoke’s purpose is to arrange and structure work so that mistakes can’t be made or, when they are made, to make them immediately obvious so they can be contained and fixed. Common Poka-Yoke implementations include:


    1. Physical features or geometry, such as guide pins or stops, that make incorrect assembly or work impossible
    2. Automated processing, assembly, or inspection systems
    3. Limiting controls that don’t allow the process to be operated at unacceptable levels


    The following are some changes that are NOT considered good Poka-Yoke implementations:

    1. Retraining of personnel or operators
    2. Threats of disciplinary actions on workers or operators who make mistakes
    3. Written work procedures or instructions
    4. Relying on increased attentiveness of workers


    Forming Control Plans to Maintain Your Improvements

    After your improvements are in place, you need to have an organized plan for controlling and maintaining your performance. Many acceptable ways exist to manage the control phase, but before you choose one, make sure that every plan you’re considering measures and tracks the following:


    • The output Ys that were found to be critical from your previous Define-Measure-Analyze-Improve work. Knowing that the critical outputs are performing to required levels and variation limits assures you that the important input Xs that determine process outputs are being controlled to their individual requirements. A process management summary is used to list and track critical output Ys.
    • The critical input Xs that were determined from your previous Define-Measure-Analyze-Improve work. The action lies in the critical X realm: When output Ys get off track, the input Xs must be addressed. And, by monitoring the input Xs, you can change people, equipment, materials, and production rates without losing the quality performance of the process. A process input control plan is used to list and track the critical input Xs.


    Selecting the Right Control Chart for Your Situation

    Your process control plan requires you to track and monitor your critical inputs and outputs. A primary tool you can use for tracking is a statistical process control chart (which is also known as a control chart).


    Control charts use statistics to monitor and control the variation in processes, and they display the results in easy-to-use graphical formats. Each chart is designed for a different type of data or situation. Using the wrong chart can be very costly!


    Use the decision tree in Figure 15-3 to determine which type of control chart to use for your specific situation.



    Interpreting Your Control Charts

    Selecting and creating the right control chart is only a start. After creating the chart, the real point is to correctly interpret it. What you’re looking for is the evidence of special causes, which are the out-of-the-ordinary events that throw performance off its normal level.


    To interpret a control chart, the plotted sequence of points on the chart is compared to the calculated control limits (more on calculating control limits later in this chapter). When the position or sequence of the points, in relation to each other or to the control limits, follows a non-normal pattern, you know that a special cause has occurred.




    Example 1

    Example 2


    Stable and predictable

    Chart points don’t form a particular pattern and they lie within the upper and lower control limits.



    The process is stable, not changing. Only common-cause variation is affecting the process.

    Beyond control limits

    0ne or more chart points lie beyond the upper and

    lower control limits.



    Alerts you that a special cause has affected the process. Investigate to

    determine the source of the special cause.


    Chart points are on one side of  the center line.

    The number of  consecutive points on one side is the “length” of the run.





    Suggests that the

    process has undergone a

    permanent change. May require you to compute new control limits for the shifted process.


    A continued rise or fall in a series of chart points.

    (Seven or more

    consecutive points in the same direction.)



    Indicates a special cause with a gradual, cumulative effect.  Investigate possible special cause  Sources.


    Chart points show the same pattern changes (for example, rise or fall over equal periods of time.



    Indicates a special cause with a cyclical, repetitive effect.

    Investigate possible special cause



    Chart points are close to the center line or to a control limit line.



    Suggests a possible error in data sub-grouping or selection. Verify validity of sampling plan and/or investigate possible special cause sources.


    To be more specific and clinical in finding evidence of special cause sources, you also divide the distance between the central line of the control chart and each calculated control limit into thirds.


    Constructing an Individuals and Moving Range (I-MR) Chart

    The individuals and moving range chart is probably the most widely used control chart because it requires only a sequence of individual numerical measurements. A daily recording of minimum temperature, a sequential accounting of sales figures, or an ordered history of length measurements — all of these measurements can be readily charted using an I-MR chart.





    Raising the Bar for Small Samples: Averages and Ranges (X-R) Charts

    When you have continuous data with each sample consisting of a small sample size of 2 to 10 measurements, pick the X -R chart. Like the I-MR chart, the X -R chart is a dual chart. In the top half, you plot the average, or X , for each sample. In the bottom half, you plot the range (R) for each sample subgroup.


    Making a p Chart for Your Attribute Data

    The “p” in p chart stands for “proportion defective.” When you’re tracking data that consists of a count of how many items in your sample are defective, you use a p chart. You create a p chart by plotting the sequence of values representing the proportion of each sample that’s defective (pi).


    Creating a u Chart for Your Attribute Data

    A u chart monitors defects per unit. A unit can be anything that provides a consistent opportunity for defects to occur — for example a physical assembly, a paper process, a transaction, a patient in a hospital, a day’s worth of sales, or a warehouse. As long as the concept of a unit is consistently defined and applied, a u chart works.




Chapter 16

Ten Implementation Myths of Six Sigma

This Chapter deals with dispelling the most common myths about implementing Six Sigma and avoiding mistakes and barriers to implementation.


As many times as Six Sigma has been implemented around the world, countless war stories, opinions, and myths have emerged, augmented by numerous urban legends, anecdotes, and hearsay. Misconceptions abound regarding what a Six Sigma implementation is really about.


This chapter addresses ten of the most common myths about a Six Sigma implementation. You’re likely to come across many more, but these are the biggies that you need to watch out for.




Six Sigma Is about Achieving “Six Sigma”

Six Sigma is NOT about achieving a Six Sigma level of performance. In other words, a Six Sigma implementation isn’t about achieving 3.4 DPMO in every key performance metric. Instead, it’s about achieving the proper, optimized level of performance of your organization — and it’s very likely not to be precisely 3.4 DPMO.  A Six Sigma initiative is about developing the capabilities to continuously improve the efficiency and effectiveness of your organization so that the performance and value of your work processes continuously increase. The precise sigma level at which any given process should operate is a matter of the process characteristics and the customer’s needs. In most cases, it’s below “six sigma.” In other words, it’s greater than 3.4 DPMO, and in some cases, it’s even more than Six Sigma!

Six Sigma Will Make Us Start All Over Again with Something Different

In fact, Six Sigma isn’t about stopping what you’re doing; it’s about changing how

you’re doing it. The Six Sigma initiative helps you do what you’re doing now, but more efficiently and effectively. Incremental change is self-perpetuating because project improvements result in measurable gains in performance, which feed more improvements, and so on.

Six Sigma Stifles Creativity

Six Sigma, which attacks the root cause of any problem, improves outcomes by improving processes. Any processes. Creative processes such as marketing and design are processes just as manufacturing and production are processes. And so are transaction processes, such as billing or procurement. And any such process — creative processes included — can be characterized, analyzed, and improved

Modeling Processes Is Too Complicated and Doesn’t Go Anywhere

The new era of tools, such as iGrafx, enables true process modeling and is a key enabler in a core activity in Six Sigma: the definition and analysis of processes.

Six Sigma Is Another “Program of the Month”

What makes a Six Sigma initiative so different is the prescriptive nature of the deployment. Unlike many initiatives in the past, which meant well, but had little deployment fidelity, a Six Sigma initiative has a thorough script, where everyone’s roles and actions in the deployment are defined and known. Not only does this help the initiative succeed on its own, but it also helps the senior managers understand what their role is and how to fuel the initiative going forward. This rigorous deployment definition is why Six Sigma initiatives in major corporations like GE and Honeywell not only began strong, but also have continued — well past the honeymoon phase and well beyond the tenure of the executives and managers who first announced them.

Six Sigma Is Just a Quick-hit, Cost-Reduction Initiative

Most companies today have committed leadership and are governed by principles and values that better balance short-term opportunities with long-term vision. As a result, most Six Sigma initiatives now create a culture of improvement that continues to produce gains and values for years. Companies like Motorola and Honeywell have Six Sigma initiatives that have lasted well over a decade and continue as strong as ever.

Six Sigma Is Too Onerous and Prescriptive

Does this sound familiar: “We’re different and we have our own way of doing things — and our unique style is what makes us special and competitive in our industry. We’re flexible and individualistic. Bringing in the Six Sigma standardized approach to doing things will wipe out our uniqueness. We’ll be just like everyone else and lose our edge.” Some people consider the Six Sigma training onerous because of the rigorous nature of the curricula and projects. And, yes, the deployment framework is clearly prescriptive, in that it formally defines the roles and activities in the leadership and knowledge transfer. But the Six Sigma formula is a toolbox and application knowledge set. It’s a language and communication framework.

You Can’t Implement Six Sigma Yourself

The perpetuated myth has been that Six Sigma is too heady, too difficult, too troublesome, and too dangerous to implement by yourself. The people who want you to believe that myth want you to think that without a group of consultants to assist you at every step, performing your training and overseeing your projects, you’re doomed to failure. Given the title of this workbook, you can probably guess that this myth is wrong: You can implement Six Sigma yourself! First of all, Six Sigma isn’t rocket science — yes, you will have to figure some statistics, to be sure, but nothing over the heads of your top staff. Second, the extensive body of experience across the industry has led to standardization and repeatability in the methods and approaches. Third, Six Sigma is now well-supported, with hundreds of books and guides, dozens of conferences and symposia, considerable online resources, standardized training curricula, and more.

The Six Sigma Approach Is Way Too Expensive and Disruptive

The training can be as inexpensive or as extensive as you want, and the implementations can be as rigorous or as informal as you like. And while these choices may be difficult, at least now you have them — Six Sigma teams never used to have the choices you do today.

On the cost front, the intellectual capital of Six Sigma can be bought and applied more inexpensively and seamlessly than ever. It need not be expensive. The training materials can be purchased from any number of providers — even on eBay! Most training can be conducted online, which eliminates the time and expense of classroom training.

Trainers are prevalent and you can contract with them or even hire them outright

to insource your training. Boutique mentors and facilitators can guide you through

the implementation.

If You’re Not Doing Black Belt Projects,

You’re Not Really Doing Six Sigma

This notion that you have to do Black Belt projects or none at all is absurd for many

reasons. Most directly, the majority of an organization’s challenges simply don’t

require a Black Belt level of analysis to solve. (For that matter, many don’t require any Belt level of analysis to solve!) Only a very small percentage of the problems are this serious. If you’re solving real business problems by using Six Sigma tools and techniques at a lower level than Black Belt, you’re still doing Six Sigma.




Chapter 17


Ten Tips for Finishing a Six Sigma Project Successfully

This Chapter deals with discovering the most important contributors to Six Sigma project success and avoiding pitfalls in completing your Six Sigma project




Properly Scoping Your Project

A project has to be worth completing, but it also has to be achievable. As a rule, you’re much better off if you define and solve a smaller problem instead of a larger one. Small projects are usually achievable, but larger ones are fraught with increased risk. So, be sure to scope your project tightly at the outset. Solve one problem at a time and don’t over-commit. As the expression goes, under-promise and over-deliver.

Anticipating Scope Creepy-Crawlies

Even if you scope the project perfectly from the beginning, the scope will naturally tend to grow and expand as the project progresses. This unruly phenomenon, known as scope creep, infects all projects. You must treat scope creep as the vicious and insidious monster that it is, and you must fight unwaveringly against it! If someone wants more, don’t fall prey to the seductive temptation to just take on more in an attempt to accomplish more and satisfy more people. Even if you get more time and resources to accomplish more, you risk failing in your primary objective. New or increased scope should be reserved for another project.

Charting the Entire Course

A Six Sigma project is a process too, so it deserves maps, analysis, and controls just

like any other process. You must chart the course and create a SIPOC diagram for your

project. You accomplish this manageability by building and maintaining the project

charter, which contains all the ingredients you must manage to ensure that your project is successful.

The project charter is your Magna Carta. It explicitly defines the scope and grants

authority to project activities. It’s the basis of communications and management. You

measure your accomplishments by its goals and milestones.

The project charter is a living document. Changes to the project in any form, including

scope (which is bad, but sometimes necessary), schedules, or resources, should be

reflected in a formal change to the project charter and should be properly communicated and authorized. In this way, your changes are explicitly managed and approved.

Making Sure the Right People Are Aboard

Having the right roles and skills is critical to the success of any project. For a Six Sigma

project, make sure that your skill set includes the appropriate degree of measurement, analytical, simulation, and experimental prowess needed to address the causes that affect your significant Y. The key word here is “appropriate” — not too little and not too much. If you have too little prowess, the problems overpower you, but if you have too much, you’re bound to overanalyze.

Remembering That Short Is Sweet

The milestone that matters most in your Six Sigma project is the endpoint — the point

where you have demonstrated the breakthrough improvement in the performance of

your key metric, or significant Y. Don’t waste one minute — get there as fast as you can. Swift project completion is paramount for two reasons:

  1. You lose interest and support if your project drags out. Team members with short attention spans will turn away, resources will dwindle, and people will lose confidence. Conversely, success attracts support and creates positive momentum.
  2. Slow project completion delays the creation of value in the organization. The cost of delay is significant — it cheats the organization out of money it would have if the project were completed.

Setting Achievable Goals

The solutions that affect your significant Y must be practically achievable. As you

complete your analyses and realize the critical few Xs that affect the outcomes, make

sure in the improvement phase that you can actually implement the changes. Keep

those changes simple, practical, understandable, and controllable.

Communicating for Success

In a Six Sigma project, communications failures most often include the failure to communicate with the groups whose processes, roles, obligations, workloads, empires, behaviors, and attitudes are redefined as you modify the critical Xs that create breakthrough performance in your significant Y. Not communicating with these groups can result in your failure to fully move a critical X, and therefore not achieve breakthrough.

Satisfying the Stakeholders

For every Six Sigma project, you find key stakeholders — the individuals who really

matter and whose personal or professional agendas are significantly enhanced by a

successful project outcome. At the end of the day, if you’re successful and the stakeholders realize it, you’ll likewise be rewarded.

Maintaining Active and Unwavering Support

Remember that Six Sigma projects often alienate those who have a vested interest in

maintaining the status quo of the critical Xs. The success of your project means that

you must marshal and maintain the armada of support required to displace all the

resistance. Keep your channels of support fully informed, enroll your supporters in the

process, and make them part of the success! Ask for help when you need it. And don’t

forget: You’re enabled on this mission to pursue breakthrough performance gains in

your significant Y and empowered to change the critical Xs.

Applying Formal Project Management

Just because Six Sigma projects are different from design or development projects

doesn’t mean that the formal rules of project management don’t apply, because in

reality they do. If you want your project to be successful, you need to treat the management of your project with the respect it deserves through the application of the methods and tools of formal project management.

Such formalities include the following:

  1. Official project documentation library
  2. Formal control, release, and configuration management of project information
  3. Official and prompt project status reporting and communications
  4. Strict budget, schedule, and milestone management
  5. Clearly defined and communicated participants, roles, and responsibilities