WELCOME SIX SIGMA BLACK BELT CLASS Week 2 Virtual Class The 'live' session will start at the top of the hour In the meantime you can try out your microphone and speakers, select 'Meeting' then 'Audio Setup Wizard' Topics Project Charter Villanova Project Requirements 1. Define - Project Charter 2. Define - Customer Needs and Requirements 3. Define - Process Map 4. Measure - Data Collection Plan 5. Measure - Baseline Sigma 6. Analyze - Data Analysis 7. Analyze - Process Analysis 8. Analyze - Root Cause Analysis 9. Improve - Generate Solutions 10. Improve - Select Solutions 11. Improve - Implement Solutions 12. Control - Control Plan 13. Control - Response Plan The Project Charter The Objective: a Project Charter is to commission a project that has a clear scope and ties to financial and strategic objectives. The Project Charter It is important to view the Project Charter as a contract between all the people associated with the project. It represents a two-way commitment: Management will commit a certain level of resources (time, people, capital...) In return the team will deliver results in a certain time frame. (4-6 months) The Project Charter Clearly defines the teams mission. Does not solve the problem. It is a living document. DMAIC Project Charter Worksheet Project Title: Business Case: Provide a broad definition of the issue assigned to the team, as well as the rationale for why this particular project should be a key business priority. The Project Charter consists of: Business Case Problem Statement Goal Statement Project Scope Project Plan Team members and Stakeholders Problem/Opportunity Statement: One or two sentence description of the symptoms arising from the problem to be addressed. It will often parallel the Business Case, but will be more specific and focused. Answer; What's wrong? Where is the problem appearing? How big is the problem? What is the impact of the problem on the business? Goal Statement: Goal Statement and Problem Statements are a matched pair. Includes a description of what is to be accomplished (reduce, increase, eliminate), a measurable target for desired results, and a projected completion date to reach the goal (SMART) Simple Measurable Accurate Realistic Timely Project Scope: Outline the project scope in process terms (where does it start and stop), and identify constraints and assumptions. How long can the project take? Is there a deadline? How much of our work time can be devoted to project per week? Do we have any authority to spend money? Who (what) are our internal/external resources? Sponsor: Project Leader: Project Black Belt: Team Members: Preliminary Plan Start Date: Stakeholders: The people who can influence or are affected by your project, both internal and external to your organization. Target Date Actual Date Estimated Cost Savings: Identify potential cost savings then realized cost savings after completion of the project. DEFINE MEASURE ANALYZE Notes: Capture lessons learned IMPROVE CONTROL Completion Date: A template can be found under 'Resources' on the Villanova website DMAIC Project Charter Worksheet Project Title: Business Case: Provide a broad overview of the issue assigned to the team, as well as the rationale for why this particular project should be a key business priority. Problem/Opportunity Statement: One or two sentence description of the symptoms arising from the problem to be addressed. It will often parallel the Business Case, but will be more specific and focused. Answer; What's wrong? Where is the problem appearing? How big is the problem? What is the impact of the problem on the business? Goal Statement: Goal Statement and Problem Statements are a matched pair. Includes a description of what is to be accomplished (reduce, increase, eliminate), a measurable target for desired results, and a projected completion date to reach the goal (SMART) Simple Measurable Accurate Realistic Timely Project Scope: Outline the project scope in process terms (where does it start and stop), and identify constraints and assumptions. How long can the project take? Is there a deadline? How much of our work time can be devoted to project per week? Do we have any authority to spend money? Who (what) are our internal/external resources? Sponsor: Project Leader: Project Black Belt: Team Members: Preliminary Plan Start Date: Stakeholders: The people who can influence or are affected by your project, both internal and external to your organization. Target Date Actual Date Estimated Cost Savings: Identify potential cost savings then realized cost savings after completion of the project. DEFINE MEASURE ANALYZE IMPROVE CONTROL Completion Date: Notes: Capture lessons learned Try to limit the Project Charter to one page (keep it clear & concise!) Project Charter Project Title: Insert title here Business Case: Provide a broad overview of the issue assigned to the team, as well as the rationale for why this particular project should be a key business priority. What is the value of closing the gap between 'current' and 'future' states? Example: Customer satisfaction has fallen from last years levels for three quarters in a row, resulting in lost $$ revenue $$ and reducing cash flow to record lows. Project Charter Why is the Business Case usually found on the top of the page? DMAIC Project Charter Worksheet Project Title: Business Case: Provide a broad overview of the issue assigned to the team, as well as the rationale for why this particular project should be a key business priority. Problem/Opportunity Statement: One or two sentence description of the symptoms arising from the problem to be addressed. It will often parallel the Business Case, but will be more specific and focused. Answer; What's wrong? Where is the problem appearing? How big is the problem? What is the impact of the problem on the business? Goal Statement: Goal Statement and Problem Statements are a matched pair. Includes a description of what is to be accomplished (reduce, increase, eliminate), a measurable target for desired results, and a projected completion date to reach the goal (SMART) Simple Measurable Accurate Realistic Timely Project Charter Problem/Opportunity Statement: One or two sentence description of the symptoms arising from the problem to be addressed What is the 'current' state? What's wrong? Where is the problem appearing? How big is the problem? What is the impact of the problem on the business? Example: In the past six months, IMF Company has generated (198) customer complaints due to shipping errors, which has resulted in reduced customer satisfaction and invoicing concerns, resulting in delayed payments. Project Charter Goal Statement: Goal Statement and Problem Statements are a matched pair. Includes a description of what is to be accomplished (reduce, increase, eliminate), a measurable target for desired results, and a projected completion date to reach the goal. What is the 'future' state? (SMART) Simple, Measurable, Accurate, Realistic, Timely Example: By January 20, 2016, we will have a process in place to reduce shipping errors identified in our analysis by 90% Problem Statement + Goal Statement = Team Focus Project Charter Project Scope: Outline the project scope in process terms (where does it start and stop - refer to the SIPOC), and identify constraints and assumptions. SUPPLIER INPUT PROCESS OUTPUT CUSTOMER SIPOC When working with a process it is important to understand the following: What are inputs into the process? Who are the suppliers to the process? Suppliers Input Process Output Customer What are the outputs from the process? Who are the customers of the process? SIPOC Diagram SUPPLIER INPUTS Providers of the inputs Inputs into the process PROCESS Top-level process description *Provide a description of the process * Define the start and end point of the process that the project is focused on (project scope) OUTPUTS CUSTOMER Outputs of the process Receivers of the process outputs *Special care should be taken to determine how these outputs relate to customer expectations A template can be found under 'Resources' on the Villanova website SUPPLIER INPUTS PROCESS OUTPUTS Villanova News/AOL Newspaper/ Internet Select Dealer Dealership Dealership Car Test Drive Enabler Dealership/ Manufact. Brochure Select Option Package Right car Customer Information /Offer Negotiate Price $$ Customer/ Loan Co. Credit info Finance Contract Dealership Prepped Car Drive Off Car CUSTOMER Me/Family Project Charter Project Scope: Outline the project scope in process terms (where does it start and stop - refer to the SIPOC), and identify constraints and assumptions. How long can the project take? Is there a deadline? How much of our work time can be devoted to project per week? Do we have any authority to spend money? Who (what) are our internal/external resources? Example: The process boundaries are incoming material assembly. Team members are expected to spend 2 hrs /week working on the project. No money is available for buying new equipment or assigning new people to the operation. Team can implement any decisions based on good data after discussion with Champion. Project Charter Project Scope: Outline the project scope in process terms (where does it start and stop - refer to the SIPOC), and identify constraints and assumptions. How long can the project take? Is there a deadline? How much of our work time can be devoted to project per week? Do we have any authority to spend money? Who (what) are our internal/external resources? Keep in mind that the project benefits are proportional to scope! Project Charter Project Project Project Project Sponsor: Manager Leader: Green Belt Black Belt: Black Belt Team Members: Balanced Team Stakeholders: The people who can influence or are affected by your project, both internal and external to your organization. Project Charter Plan Target Date Actual Date Estimated Cost Savings: Identify potential cost savings then realized cost Start 10/01/2015 10/01/2015 savings after completion of the project. Define Measure Analyze Improve Control Completion 01/20/2016 Notes: Capture lessons learned: Things Gone Right (TGR) Things Gone Wrong (TGW) Project Charter Summary Use the Project Charter to set direction and gain agreement on the project expectations. Keep the Project Charter clear and concise! Be careful not to over 'wordsmith' the Project Charter. Villanova Projects - REQUIRED! Case Study Includes Some Tools, not others Feel for Project w/o Overall Length Four (4) Case Studies (select one) Health Care 2 Popularity Finance Industry 4 Manufacturing 1 Information Technology 3 23 ** No statistical software is required to complete the projects! Villanova Projects - REQUIRED! Posted on the Discussion Board Manufacturing Finance Healthcare IT Excel File **Read the Welcome! tab first to learn about the project format Helpful Hints! Select the project based on the tools that you would like to learn about, not necessarily the current industry you are in! Robert Lidtke Please do not send as an attachment! Paste response here Assignment Tabs Color coded by phase Tool Read 'The Project' tab for background information, it contains information for the Project Charter and establishing the Baseline Sigma Be sure to use ALL of the helpful hints provided! For example for next week (3) the Project Charter assignment is due Project Case Studies The Projects are posted on the Discussion Board You MUST successfully complete one of the posted Villanova projects by January 13, 2016 to successfully complete the course! Work related projects will NOT be accepted! Project Case Studies E-mail the project assignments to me, do not post on the discussion board You will receive the following feedback for the assignments: 'full credit' - no further action required 'partial credit' - I will provide feedback and hints so you can make the corrections and resubmit Project Case Studies You MUST receive FULL credit for all of the assignments to successfully complete the course! Please do not procrastinate, if you are struggling please let me know! Project Case Studies You MUST submit your own work! No 'team' projects are allowed. Project Case Studies No 'team' projects are allowed. Be sure to use the helpful hints and self checks provided in the assignments I will also be providing additional helpful hints for the project assignments in the virtual classes. Week Topic 1 Introduction to the Technology 2 Project Charter, and Villanova Project Introduction 3 Data Collection Plan 4 Measures of central tendency, dispersion, and Normal 5 Hypothesis Testing and the t-distribution 6 Types of VA,NVA and Lean 5-step 7 Lean Sigma and 5S 8 Chi-Sqr distribution and Scatter Diagrams 9 F distribution and ANOVA 10 Design of Experiments - Full Factorial 11 Design of Experiments - Fractional Factorial 12 Design of Experiments - Taguchi 13 Control Charts 14 Process Capability 15 Certification Exam Prep 16 Culture, Stages of Learning, Key takeaways Remember! The last day of class (and access) is January 20, 2016! The Nation's Leading Universities Online Lean Six Sigma Black Belt Online Textbook www.VillanovaU.com 800-571-4953 | Intl. +1 813-612-4296 Villanova Student Use Only 2012 Bisk Education, Inc. - All rights reserved, and/or 2012 Transformation Technologies, Inc. - All rights reserved. Permission to print this document is limited to one copy per student. Villanova University Six Sigma Black Belt Online Textbook |2 Villanova Student Use Only Table of Contents Index of Topics................................................................................................9 . Week 1 Project Tracking: Gantt Chart. ..........................................................................15 Project Tracking: Tracking Reporting and Corrective Action System (TRaCAS)........16 Project Tracking: Project Priority Matrix. ...........................................................17 . Project Charter: Description. ...........................................................................18 . Project Cost/Benefit Analysis (CBA)..................................................................19 Project Charter: Blank Worksheet. ...................................................................20 . Project Charter Highlights...............................................................................21 Project Charter: Example................................................................................26 . Critical-to-Quality Tree....................................................................................28 House of Quality............................................................................................29 Flow Chart....................................................................................................31 Input-Output (IPO) Model...............................................................................34 Swim Lane Flow Chart...................................................................................35 Week 2 Target Values: Illustration 1.............................................................................37 Target Values: Illustration 2.............................................................................38 Target Values: Illustration 3.............................................................................39 Check Sheet..................................................................................................40 Check Sheets: Defect Location Check Sheet......................................................41 Check Sheets: Two-Way Check Sheet...............................................................42 Check Sheets: Five Basic Types.......................................................................43 DPU, DPMO, PPM, and RTY...........................................................................46 Rolled Thoughput Yield. .................................................................................48 . DPMO to Sigma Level Relationship..................................................................49 Week 3 Histograms, Part 1.........................................................................................50 Histograms, Part 2.........................................................................................51 Cell Intervals: Impact on Shape.......................................................................53 Cell Intervals: Rules of Thumb.........................................................................54 Stem-and-Leaf Plots.......................................................................................56 Week 4 Standard Deviation: Six Steps to Calculation.....................................................58 Villanova University Six Sigma Black Belt Online Textbook |3 Villanova Student Use Only Standard Deviation: Description and Example...................................................60 . Basic Statistics Using the Texas Instruments TI-30 Calculator.............................61 Normal Probability Plots: Minitab Example.......................................................66 . Normal Probability Plots: Paper and Manual Example........................................67 F Distribution: Basic Illustration.......................................................................71 Hypergeometric Distribution, Part 1.................................................................73 . Hypergeometric Distribution, Part 2.................................................................74 . Binomial Probability Distribution. ....................................................................75 . Analyzing Bivariate Data: Income Example. ......................................................80 . Analyzing Bivariate Data: Cost vs. Billed Hours Example....................................83 . Exponential Distribution: Coffee Example..........................................................84 Exponential Distribution: Reliability Example.....................................................85 Lognormal Distribution, Part 1. .......................................................................86 . Lognormal Distribution, Part 2. .......................................................................88 . Poisson Distribution: Basic Model....................................................................90 Cumulative Poisson Distribution Table............................................................100 Tables of the Poisson Cumulative Distribution..................................................103 Paired t-Test: Description..............................................................................105 Paired t-Test: Student's t Distribution Table. ....................................................108 . Student's t Distribution.................................................................................109 Student's t Distribution: Example...................................................................110 Student's t Distribution Table.........................................................................111 Week 5 Cost of Poor Quality. ....................................................................................113 . Week 6 Classic Wastes. ...........................................................................................115 . Spaghetti Diagram.......................................................................................117 Pull System.................................................................................................118 Kanban in Assembly. ...................................................................................120 . Kanban in a Hospital. ..................................................................................121 . Kanban in a Law Office................................................................................122 . Pull System Using Kanban Cards...................................................................123 Pull System Without Kanban Cards................................................................124 Cellular Manufacturing. ................................................................................126 . 5S. ............................................................................................................128 . 5S in Manufacturing. ...................................................................................129 . 5S in an Office Environment..........................................................................134 Kaizen Event...............................................................................................141 Visual Workplace.........................................................................................144 Takt Time Ebb and Flow...............................................................................150 Villanova University Six Sigma Black Belt Online Textbook |4 Villanova Student Use Only Value Stream Mapping: Illustration. ...............................................................152 . Poka-Yoke, Part 1. .......................................................................................157 . Poka-Yoke, Part 2. .......................................................................................158 . Poka-Yoke, Part 3. .......................................................................................159 . Quick Changeover........................................................................................160 Week 7 Brainstorming..............................................................................................162 Lean Accounting..........................................................................................164 Cause-and-Effect Diagram. ...........................................................................165 . Fault Tree Diagram.......................................................................................168 Interrelationship Diagram..............................................................................169 Box and Whiskers Plot. ................................................................................170 . Radar Chart................................................................................................172 . Cause-and-Effect Diagram. ...........................................................................174 . Week 8 Hypothesis Testing: Decision Tree..................................................................175 Type I and Type II Errors in Hypothesis Testing................................................176 P-Values: Example 1. ...................................................................................177 . P-Values: Example 2. ...................................................................................178 . P-Values: Example 3. ...................................................................................179 . Chi-Square: Table........................................................................................180 . Chi-Square: Example....................................................................................181 Chi-Square Distribution: = 1......................................................................182 Chi-Square Distribution: = 5......................................................................183 Chi-Square Distribution: = 10....................................................................184 Chi-Square Distribution: = 15....................................................................185 F Distribution: Illustration with v1 = 10 and v2 = 1.......................................186 . F Distribution: Illustration with v1 = 15 and v2 = 15.....................................187 . F Distribution: Illustration with v1 = 1 and v2 = 10.......................................188 . F Distribution: Illustration with v1 = 1 and v2 = 1.........................................189 . F Table: 1% Alpha Risk................................................................................190 F Table: 2.5% Alpha Risk.............................................................................191 F Table: 5% Alpha Risk................................................................................192 F Table: 10% Alpha Risk..............................................................................193 F Distribution..............................................................................................194 F Test for Variance: Example.........................................................................195 . ANOVA: One-Way........................................................................................196 Analysis of Variance (ANOVA): One-Way Manufacturing Example. .....................197 . Analysis of Variance (ANOVA): One-Way Service Example.................................200 Analysis of Variance (ANOVA): One-Way Productivity Example. .........................203 . Villanova University Six Sigma Black Belt Online Textbook |5 Villanova Student Use Only Analysis of Variance (ANOVA): Two-Way Example............................................206 Analysis of Variance (ANOVA): Two-Way Illustration, Part 1..............................209 . Analysis of Variance (ANOVA): Two-Way Illustration, Part 2..............................211 . ANOVA: Two-Way........................................................................................213 Week 9 Simple Linear Regression..............................................................................214 Affinity Diagram. .........................................................................................216 . Matrix Diagram: L-Shaped............................................................................219 . Matrix Diagram: X-Shaped............................................................................220 Matrix Diagram: Y-Shaped............................................................................221 Process Decision Program Charts (PDPC).......................................................222 . Tree Diagram...............................................................................................223 Activity Network Diagram.............................................................................224 . Prioritization Matrix......................................................................................228 Effort/Impact Matrix.....................................................................................229 Finding a Z Score: Example 1........................................................................230 Finding a Z Score: Example 2........................................................................231 Finding a Z Score: Example 3........................................................................232 Z Table: Form 1...........................................................................................234 Z Table: Form 2...........................................................................................237 Central Limit Theorem..................................................................................239 Z Table: Form 3...........................................................................................241 Weibull Analysis: Example 1.........................................................................243 Weibull Analysis: Example 2.........................................................................245 Design for Six Sigma (DFSS): DMADV............................................................247 Design for Six Sigma (DFSS): Design for X......................................................248 Week 10 Design of Experiments (DOE) Terminology: Designed Experiment.......................249 Design of Experiments (DOE) Terminology: Response Variable...........................252 Design of Experiments (DOE) Terminology: Factors and Levels...........................253 Design of Experiments (DOE) Terminology: Design Matrix.................................254 . Design of Experiments (DOE) Terminology: Effect.............................................256 Design of Experiments (DOE) Terminology: Interaction......................................257 Design of Experiments (DOE) Terminology: Randomization and Replication.........258 DOE: Main Effects Plot.................................................................................259 DOE: Interaction Plot. ..................................................................................261 . Design of Experiments (DOE) Terminology: Factorial Designs.............................264 DOE Strategy for Experimentation: Full Factorial Illustration..............................266 DOE: Full Factorial Example..........................................................................269 DOE: Determining Statistical Significance.......................................................272 Villanova University Six Sigma Black Belt Online Textbook |6 Villanova Student Use Only Week 11 Design of Experiments (DOE) Terminology: Fractional Factorial Designs..............274 DOE: Fractional Factorial Example.................................................................276 DOE Strategy for Experimentation: Screening Designs Illustration. .....................279 . Design of Experiments (DOE) Terminology: Blocking. .......................................282 . DOE: Design Resolution................................................................................283 DOE: Standard Order of Design Matrix. ..........................................................284 . DOE: Illustration of F Ratio Test (Example 1 of 3)............................................285 DOE: Illustration of F Ratio Test (Example 2 of 3)............................................287 DOE: Illustration of F Ratio Test (Example 3 of 3)............................................289 DOE: Taguchi Loss Function..........................................................................291 Week 12 DOE: Evolutionary Operations (EVOP)............................................................292 DOE: Graeco-Latin Square Design..................................................................294 DOE: Hyper-Graeco-Latin Square...................................................................296 DOE: Latin Square.......................................................................................298 Failure Mode and Effects Analysis (FMEA), Part 1............................................300 Failure Mode and Effects Analysis (FMEA), Part 2............................................301 Standard Operating Procedures. ....................................................................303 . Control Plan................................................................................................305 Week 13 Run Chart: Basic Construction.......................................................................306 Run Chart: Shifts.........................................................................................307 Run Chart: Trends........................................................................................308 Control Chart Construction: Formulas for Centerlines........................................309 Measurement Discrimination.........................................................................310 Control Chart Construction: Formulas for Control Limits....................................315 Control Chart Tests: Shewhart's Test for a Natural/Normal Pattern #1................316 Control Chart Tests: Shewhart's Test for a Natural/Normal Pattern #2................317 Control Chart Tests: Shewhart's Test for Outliers..............................................318 Control Chart Tests: Shewhart's Test for Runs #1............................................319 . Control Chart Tests: Shewhart's Test for Runs #2............................................320 . Control Chart Tests: Shewhart's Test for Runs #3............................................321 . Control Chart Tests: Shewhart's Test for a Sudden and Drastic Shift in Level.......322 Control Chart Tests: Shewhart's Test for a Stable Mixture..................................323 Control Chart Tests: Shewhart's Test for an Unstable Mixture. ...........................324 . Control Chart Tests: Shewhart's Test for a Repeating Pattern/Cycle.....................325 Control Chart Tests: Shewhart's Test for a Trend/Gradual Change in Level...........326 x-bar and R Control Chart Construction Rules..................................................327 x-bar and R Chart: Example..........................................................................328 Villanova University Six Sigma Black Belt Online Textbook |7 Villanova Student Use Only Moving Average Chart: Construction...............................................................329 Moving Average Chart: Interpretation. ............................................................330 . Rational Subgroup.......................................................................................331 . X-MR Control Chart Constants.......................................................................332 X-MR Control Chart Construction Rules..........................................................333 . X-MR (I-MR) Control Chart: Example. ............................................................335 . S Chart: Basic Idea......................................................................................336 S Chart: Identifying Out-of-Control - Exceeding Control Limits, Part 1................339 S Chart: Identifying Out-of-Control - Exceeding Control Limits, Part 2................341 S Chart: Identifying Out-of-Control - Runs......................................................343 . S Chart: Identifying Out-of-Control - Trends....................................................345 S Chart: Identifying Out-of-Control - Cycling...................................................347 . S Chart: Identifying Out-of-Control - Zone Analysis..........................................349 Formulas and Factors for X-Bar: Sigma Control Charts......................................351 Exponentially Weighted Moving Average (EWMA) Chart: Construction................352 Exponentially Weighted Moving Average (EWMA) Chart: Interpretation...............354 Week 14 Attribute Control Charts................................................................................357 Cumulative Sum (CUSUM) Charts: Construction..............................................358 Cumulative Sum (CUSUM) Charts: Interpretation. ...........................................361 . Cp and Pp Process Potential Indices. .............................................................363 . Cpk and Ppk Process Capability Indices. ........................................................365 . 1.5 Sigma Shift...........................................................................................368 Cp and Cpk: Example...................................................................................369 Cp and Cpk: Formulas..................................................................................370 Cpk to DPMO Conversion Chart.....................................................................371 Pp and Ppk: Example...................................................................................372 Pp and Ppk: Formulas..................................................................................373 Sigma to Ppk Conversion Chart. ....................................................................374 . Ppk to PPM/DPMO Conversion Chart.............................................................376 Villanova University Six Sigma Black Belt Online Textbook |8 Villanova Student Use Only Index Of Topics 1.5 Sigma Shift.......................................................................................................368 5S. ........................................................................................................................128 . 5S in an Office Environment. ....................................................................................134 . 5S in Manufacturing. ...............................................................................................129 . Activity Network Diagram.........................................................................................224 . Affinity Diagram. .....................................................................................................216 . Analysis of Variance (ANOVA): One-Way Manufacturing Example. .................................197 . Analysis of Variance (ANOVA): One-Way Productivity Example......................................203 . Analysis of Variance (ANOVA): One-Way Service Example.............................................200 Analysis of Variance (ANOVA): Two-Way Example........................................................206 Analysis of Variance (ANOVA): Two-Way Illustration, Part 1..........................................209 . Analysis of Variance (ANOVA): Two-Way Illustration, Part 2..........................................211 . Analyzing Bivariate Data: Cost vs. Billed Hours Example................................................83 . Analyzing Bivariate Data: Income Example. ..................................................................80 . ANOVA: One-Way....................................................................................................196 ANOVA: Two-Way....................................................................................................213 Attribute Control Charts............................................................................................357 Basic Statistics Using the Texas Instruments TI-30 Calculator.........................................61 Binomial Probability Distribution. ................................................................................75 . Box and Whiskers Plot. ............................................................................................170 . Brainstorming. ........................................................................................................162 . Cause-and-Effect Diagram. .......................................................................................165 . Cause-and-Effect Diagram. .......................................................................................174 . Cell Intervals: Impact on Shape...................................................................................53 Cell Intervals: Rules of Thumb.....................................................................................54 Cellular Manufacturing.............................................................................................126 . Central Limit Theorem..............................................................................................239 Check Sheet..............................................................................................................40 Check Sheets: Defect Location Check Sheet..................................................................41 Check Sheets: Five Basic Types...................................................................................43 Check Sheets: Two-Way Check Sheet...........................................................................42 Chi-Square Distribution: = 1..................................................................................182 Chi-Square Distribution: = 5..................................................................................183 Chi-Square Distribution: = 10................................................................................184 Chi-Square Distribution: = 15................................................................................185 Chi-Square: Example................................................................................................181 Chi-Square: Table....................................................................................................180 . Villanova University Six Sigma Black Belt Online Textbook |9 Villanova Student Use Only Classic Wastes. .......................................................................................................115 . Control Chart Construction: Formulas for Centerlines....................................................309 Control Chart Construction: Formulas for Control Limits................................................315 Control Chart Tests: Shewhart's Test for a Natural/Normal Pattern #1............................316 Control Chart Tests: Shewhart's Test for a Natural/Normal Pattern #2............................317 Control Chart Tests: Shewhart's Test for an Unstable Mixture. .......................................324 . Control Chart Tests: Shewhart's Test for a Repeating Pattern/Cycle.................................325 Control Chart Tests: Shewhart's Test for a Stable Mixture..............................................323 Control Chart Tests: Shewhart's Test for a Sudden and Drastic Shift in Level...................322 Control Chart Tests: Shewhart's Test for a Trend/Gradual Change in Level.......................326 Control Chart Tests: Shewhart's Test for Outliers..........................................................318 Control Chart Tests: Shewhart's Test for Runs #1........................................................319 . Control Chart Tests: Shewhart's Test for Runs #2........................................................320 . Control Chart Tests: Shewhart's Test for Runs #3........................................................321 . Control Plan............................................................................................................305 Cost of Poor Quality. ................................................................................................113 . Cp and Cpk: Example...............................................................................................369 Cp and Cpk: Formulas..............................................................................................370 Cp and Pp Process Potential Indices. .........................................................................363 . Cpk and Ppk Process Capability Indices. ....................................................................365 . Cpk to DPMO Conversion Chart.................................................................................371 Critical-to-Quality Tree................................................................................................28 Cumulative Poisson Distribution Table........................................................................100 Cumulative Sum (CUSUM) Charts: Construction..........................................................358 Cumulative Sum (CUSUM) Charts: Interpretation. .......................................................361 . Design for Six Sigma (DFSS): Design for X..................................................................248 Design for Six Sigma (DFSS): DMADV........................................................................247 Design of Experiments (DOE) Terminology: Blocking. ...................................................282 . Design of Experiments (DOE) Terminology: Designed Experiment...................................249 Design of Experiments (DOE) Terminology: Design Matrix.............................................254 Design of Experiments (DOE) Terminology: Effect.........................................................256 Design of Experiments (DOE) Terminology: Factorial Designs.........................................264 Design of Experiments (DOE) Terminology: Factors and Levels. .....................................253 . Design of Experiments (DOE) Terminology: Fractional Factorial Designs..........................274 Design of Experiments (DOE) Terminology: Interaction..................................................257 Design of Experiments (DOE) Terminology: Randomization and Replication.....................258 Design of Experiments (DOE) Terminology: Response Variable.......................................252 DOE: Design Resolution............................................................................................283 DOE: Determining Statistical Significance...................................................................272 DOE: Evolutionary Operations (EVOP)........................................................................292 Villanova University Six Sigma Black Belt Online Textbook |10 Villanova Student Use Only DOE: Fractional Factorial Example.............................................................................276 DOE: Full Factorial Example......................................................................................269 DOE: Graeco-Latin Square Design. ............................................................................294 . DOE: Hyper-Graeco-Latin Square...............................................................................296 DOE: Illustration of F Ratio Test (Example 1 of 3)........................................................285 DOE: Illustration of F Ratio Test (Example 2 of 3)........................................................287 DOE: Illustration of F Ratio Test (Example 3 of 3)........................................................289 DOE: Interaction Plot. ..............................................................................................261 . DOE: Latin Square...................................................................................................298 DOE: Main Effects Plot.............................................................................................259 DOE: Standard Order of Design Matrix. ......................................................................284 . DOE Strategy for Experimentation: Full Factorial Illustration..........................................266 DOE Strategy for Experimentation: Screening Designs Illustration. .................................279 . DOE: Taguchi Loss Function......................................................................................291 DPMO to Sigma Level Relationship..............................................................................49 DPU, DPMO, PPM, and RTY.......................................................................................46 Effort/Impact Matrix.................................................................................................229 Exponential Distribution: Coffee Example......................................................................84 Exponential Distribution: Reliability Example.................................................................85 Exponentially Weighted Moving Average (EWMA) Chart: Construction............................352 Exponentially Weighted Moving Average (EWMA) Chart: Interpretation...........................354 Failure Mode and Effects Analysis (FMEA), Part 1. ......................................................300 . Failure Mode and Effects Analysis (FMEA), Part 2. ......................................................301 . Fault Tree Diagram...................................................................................................168 F Distribution..........................................................................................................194 F Distribution: Basic Illustration. ..................................................................................71 F Distribution: Illustration with v1 = 1 and v2 = 1.......................................................189 F Distribution: Illustration with v1 = 1 and v2 = 10.....................................................188 F Distribution: Illustration with v1 = 10 and v2 = 1.....................................................186 F Distribution: Illustration with v1 = 15 and v2 = 15...................................................187 Finding a Z Score: Example 1....................................................................................230 Finding a Z Score: Example 2....................................................................................231 Finding a Z Score: Example 3....................................................................................232 Flow Chart................................................................................................................31 Formulas and Factors for X-Bar: Sigma Control Charts..................................................351 F Table: 1% Alpha Risk............................................................................................190 F Table: 2.5% Alpha Risk.........................................................................................191 F Table: 5% Alpha Risk............................................................................................192 F Table: 10% Alpha Risk..........................................................................................193 F Test for Variance: Example.....................................................................................195 Villanova University Six Sigma Black Belt Online Textbook | 11 Villanova Student Use Only Histograms, Part 1.....................................................................................................50 Histograms, Part 2.....................................................................................................51 House of Quality........................................................................................................29 Hypergeometric Distribution, Part 1.............................................................................73 Hypergeometric Distribution, Part 2.............................................................................74 Hypothesis Testing: Decision Tree..............................................................................175 Input-Output (IPO) Model...........................................................................................34 Interrelationship Diagram. ........................................................................................169 . Kaizen Event...........................................................................................................141 Kanban in a Hospital. ..............................................................................................121 . Kanban in a Law Office............................................................................................122 . Kanban in Assembly. ...............................................................................................120 . Lean Accounting......................................................................................................164 Lognormal Distribution, Part 1. ...................................................................................86 . Lognormal Distribution, Part 2. ...................................................................................88 . Matrix Diagram: L-Shaped........................................................................................219 Matrix Diagram: X-Shaped........................................................................................220 Matrix Diagram: Y-Shaped........................................................................................221 Measurement Discrimination.....................................................................................310 Moving Average Chart: Construction...........................................................................329 Moving Average Chart: Interpretation. ........................................................................330 . Normal Probability Plots: Minitab Example...................................................................66 . Normal Probability Plots: Paper and Manual Example....................................................67 Paired t-Test: Description..........................................................................................105 Paired t-Test: Student's t Distribution Table. ................................................................108 . Poisson Distribution: Basic Model................................................................................90 Poka-Yoke, Part 1....................................................................................................157 . Poka-Yoke, Part 2....................................................................................................158 . Poka-Yoke, Part 3....................................................................................................159 . Pp and Ppk: Example...............................................................................................372 Pp and Ppk: Formulas..............................................................................................373 Ppk to PPM/DPMO Conversion Chart.........................................................................376 Prioritization Matrix..................................................................................................228 Process Decision Program Charts (PDPC)...................................................................222 . Project Charter: Blank Worksheet. ...............................................................................20 . Project Charter: Description. .......................................................................................18 . Project Charter: Example............................................................................................26 . Project Charter Highlights...........................................................................................21 Project Cost/Benefit Analysis (CBA)..............................................................................19 Project Tracking: Gantt Chart. .....................................................................................15 . Villanova University Six Sigma Black Belt Online Textbook |12 Villanova Student Use Only Project Tracking: Project Priority Matrix. .......................................................................17 . Project Tracking: Tracking Reporting and Corrective Action System (TRaCAS)....................16 Pull System.............................................................................................................118 Pull System Using Kanban Cards...............................................................................123 Pull System Without Kanban Cards............................................................................124 P-Values: Example 1. ...............................................................................................177 . P-Values: Example 2. ...............................................................................................178 . P-Values: Example 3. ...............................................................................................179 . Quick Changeover....................................................................................................160 Radar Chart............................................................................................................172 Rational Subgroup...................................................................................................331 . Rolled Thoughput Yield. .............................................................................................48 . Run Chart: Basic Construction...................................................................................306 Run Chart: Shifts.....................................................................................................307 Run Chart: Trends....................................................................................................308 S Chart: Basic Idea..................................................................................................336 S Chart: Identifying Out-of-Control - Cycling...............................................................347 S Chart: Identifying Out-of-Control - Exceeding Control Limits, Part 1............................339 S Chart: Identifying Out-of-Control - Exceeding Control Limits, Part 2............................341 S Chart: Identifying Out-of-Control - Runs..................................................................343 S Chart: Identifying Out-of-Control - Trends................................................................345 S Chart: Identifying Out-of-Control - Zone Analysis......................................................349 Sigma to Ppk Conversion Chart.................................................................................374 . Simple Linear Regression..........................................................................................214 Spaghetti Diagram...................................................................................................117 Standard Deviation: Description and Example...............................................................60 . Standard Deviation: Six Steps to Calculation.................................................................58 Standard Operating Procedures. ................................................................................303 . Stem-and-Leaf Plots...................................................................................................56 Student's t Distribution.............................................................................................109 Student's t Distribution: Example...............................................................................110 Student's t Distribution Table.....................................................................................111 Swim Lane Flow Chart...............................................................................................35 Tables of the Poisson Cumulative Distribution. ............................................................103 . Takt Time Ebb and Flow...........................................................................................150 Target Values: Illustration 1.........................................................................................37 Target Values: Illustration 2.........................................................................................38 Target Values: Illustration 3.........................................................................................39 Tree Diagram...........................................................................................................223 Type I and Type II Errors in Hypothesis Testing............................................................176 Villanova University Six Sigma Black Belt Online Textbook | 13 Villanova Student Use Only Value Stream Mapping: Illustration. ...........................................................................152 . Visual Workplace.....................................................................................................144 Weibull Analysis: Example 1.....................................................................................243 Weibull Analysis: Example 2.....................................................................................245 x-bar and R Chart: Example......................................................................................328 x-bar and R Control Chart Construction Rules..............................................................327 X-MR Control Chart Constants...................................................................................332 X-MR Control Chart Construction Rules......................................................................333 X-MR (I-MR) Control Chart: Example. ........................................................................335 . Z Table: Form 1.......................................................................................................234 Z Table: Form 2.......................................................................................................237 Z Table: Form 3.......................................................................................................241 Villanova University Six Sigma Black Belt Online Textbook |14 Villanova Student Use Only Project Tracking: Gantt Chart Project Tracking: Gantt Chart Whether you realize it or not, as a Black Belt you will spend a considerable amount of your time tracking projects. Six Sigma is a project-driven approach to improvement; the success of the Six Sigma effort rises and falls with the success of the projects that are undertaken. Black Belts should find the following fact sobering: one of the major reasons for Six Sigma project failure is the lack of effective project management and one of the most often listed project management failures is the inability to recognize that a project is falling behind and, therefore, implement effective corrective actions in a timely fashion. A simple tool that will assist the project manager in tracking and monitoring a project is the Gantt chart. A Gantt chart is a simple graphical tool that illustrates the time completion profiles of each task. The Gantt chart below is for a Six Sigma project team that is at work on a relatively simple project. The project has five major tasks that must be completed. The Gantt chart shows, for example, that Activity B cannot begin until Activity A has been completed. The project manager will need to track the time completion of activities carefully in order to be sure the project duration doesn't begin to slide. Take Activity C for example. If there is a delay to the completion of Activity C, then Activity E cannot start on time and cannot be completed on time, thereby causing the project to miss its completion date. The Gantt chart should be combined with a Project Responsibility Matrix which identifies each task and the level of responsibility of each team member for each task (see below). Team Member Susan Bill C Ron Debbie R C R A A R C A B R C R R D E Responsible C Contributes A R A C Legend C Advises F Tasks Villanova University Six Sigma Black Belt Online Textbook | 15 Villanova Student Use Only Project Tracking: Tracking Reporting and Corrective Action System (TRaCAS) Project Tracking: Tracking Reporting and Corrective Action System (TRaCAS) Whether you realize it or not, as a Black Belt you will spend a considerable amount of your time tracking projects. Six Sigma is a project-driven approach to improvement; the success of the Six Sigma effort rises and falls with the success of the projects that are undertaken. Black Belts should find the following fact sobering: one of the major reasons for Six Sigma project failure is the lack of effective project management and one of the most often listed project management failures is the inability to recognize that a project is falling behind and, therefore, implement effective corrective actions in a timely fashion. A Six Sigma project should be treated like any other project by the project manager and that means that in order to effectively track the project, the project manager must develop and utilize a Tracking Reporting and Corrective Action System (TRaCAS). The TRaCAS is designed to provide the project management with timely feedback and information about the project. Most project management software contains some variation of this system, but at the very least, the project manager needs the following. Task Description Complete by Major Responsibility Backup Slack Corrective Action Impact on Project A B C D Some of the information in the TRaCAS spreadsheet is obvious, but some may not be. For example, every project task should have a back-up who is tasked with staying up-to-date on a project activity that is not their direct responsibility. Things do go wrong, even with personnel! The project manager cannot afford to lose valuable time transitioning someone into a project task assignment in the middle of the project. The project manager needs to be able to quickly assess if a specific project task has any \"slack time\" (something that is found from the critical path analysis of the project). Any corrective action that has been taken needs to be quickly documented and its impact on the project must be quickly assessed. That is, did the corrective action return the project to its projected time completion path or not? Did the corrective action consume resources that weren't budgeted? The leader or manager of a Six Sigma project needs to have this kind of information \"at his or her fingertips\" and it must be up-to-date. Tracking a Six Sigma project is one of the major duties of a Black Belt. The Black Belt will be held responsible for the success of the project; the project will be successful only if effective tracking and corrective action is in place. Villanova University Six Sigma Black Belt Online Textbook | 16 Villanova Student Use Only Project Tracking: Project Priority Matrix Project Tracking: Project Priority Matrix Whether you realize it or not, as a Black Belt you will spend a considerable amount of your time tracking projects. Six Sigma is a project-driven approach to improvement; the success of the Six Sigma effort rises and falls with the success of the projects that are undertaken. Black Belts should find the following fact sobering: one of the major reasons for Six Sigma project failure is the lack of effective project management and one of the most often listed project management failures is the inability to recognize