Practitioner's Guide to Statistics and Lean Six Sigma for Process Improvements
In today's business world, Six Sigma, or Lean Six Sigma, is a crucial tool utilized by companies to improve customer satisfaction, increase profitability, and enhance productivity. Practitioner's Guide to Statistics and Lean Six Sigma for Process Improvements provides a balanced approach to quantitative and qualitative statistics using Six Sigma and Lean Six Sigma methodologies.
Emphasizing applications and the implementation of data analyses as they relate to this strategy for business management, this book introduces readers to the concepts and techniques for solving problems and improving managerial processes using Six Sigma and Lean Six Sigma. Written by knowledgeable professionals working in the field today, the book offers thorough coverage of the statistical topics related to effective Six Sigma and Lean Six Sigma practices, including:
Discrete random variables and continuous random variables
Estimation and hypothesis tests
Analysis of variance
Linear and multiple regression
Survey methods and sampling techniques
The authors provide numerous opportunities for readers to test their understanding of the presented material, as the real data sets, which are incorporated into the treatment of each topic, can be easily worked with using Microsoft Office Excel, Minitab, MindPro, or Oracle's Crystal Ball software packages. Examples of successful, complete Six Sigma and Lean Six Sigma projects are supplied in many chapters along with extensive exercises that range in level of complexity. The book is accompanied by an extensive FTP site that features manuals for working with the discussed software packages along with additional exercises and data sets. In addition, numerous screenshots and figures guide readers through the functional and visual methods of learning Six Sigma and Lean Six Sigma.
Practitioner's Guide to Statistics and Lean Six Sigma for Process Improvements is an excellent book for courses on Six Sigma and statistical quality control at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in the fields of engineering, business, physics, management, and finance.
1 Principles of Six Sigma.
1.2 Six Sigma Essentials.
1.2.1 Driving Need.
1.2.2 Customer Focus.
1.2.3 Core Beliefs.
1.2.4 Deterministic Reasoning.
1.2.5 Leverage Principle.
1.3 Quality Definition.
1.4 Value Creation.
1.5 Business, Operations, Process and Individual (BOPI) Goals.
1.5.1 Differences between Product and Process Capability from a Six Sigma Perspective.
1.6 Underpinning Economics.
1.6.1 Sigma Benchmarking.
1.6.2 Breakthrough Goals.
1.6.3 Performance Benchmark.
1.7 Performance Metrics.
1.8.1 Process Models.
1.9 Design Complexity.
1.10 Nature and Purpose of Six Sigma.
1.10.1 Not Just Defect Reduction.
1.11 Needs That Underlie Six Sigma.
1.11.1 Looking Across the Organization.
1.11.2 Processing for Six Sigma.
1.11.3 Designing for Six Sigma.
1.11.4 Managing for Six Sigma.
1.11.5 Risk Orientation.
1.12 Why Focusing on The Customer is Essential to Six Sigma.
1.13 Success Factors.
1.14 Software Applications.
2 Six Sigma Installation.
2.2 Six Sigma Leadership-The Fuel of Six Sigma.
2.3 Deployment Planning.
2.3.1 Executive Management.
2.3.2 Six Sigma Champion.
2.3.3 Line Management.
2.3.4 Master Black Belts.
2.3.5 Black Belts.
2.3.6 Green Belts.
2.3.7 White Belts.
2.3.8 Six Sigma Roadmap.
2.3.9 Characteristics of Effective Metrics.
2.3.10 The Role of Metrics.
2.3.11 Six Sigma Performance Metrics.
2.3.12 Profit and Measurement
2.3.13 Twelve Criteria for Performance Metrics.
2.4 Application Projects.
2.5 Deployment Timeline.
2.6 Design for Six Sigma [DFSS] Principles.
2.7 Processing for Six Sigma [PFSS] Principles.
2.8 Managing for Six Sigma [MPSS] Principles.
2.9 Project Review.
2.9.1 Tollgate Criteria.
2.9.2 Project Closure.
2.9.3 Project Documentation.
2.9.4 Personal Recognition.
2.9.5 Authenticating Agent.
References and Notes.
3 Lean Sigma Projects.
3.3 Project Description.
3.4 Project Guidelines.
3.5 Project Selection.
3.5.1 Project Selection Guidelines.
3.6 Project Scope.
3.7 Project Leadership.
3.8 Project Teams.
3.9 Project Financials.
3.10 Project Management.
3.11 Project Payback.
3.12 Project Milestones.
3.13 Project Roadmap.
3.14 Project Charters (General).
3.15 Six Sigma Projects.
3.16 Project Summary.
4 Lean Practices.
4.3 The Idea of Lean Thinking.
4.4 Theory of Constraints [TOC].
4.5 Lean Concept.
4.6 Value-Added Versus Non-Value-Added Activities.
4.7 Why Companies Think Lean.
4.8 Visual Controls-Visual Factory.
4.9 The Idea of Pull (Kanban).
4.10 5S-6S Approach.
4.11 The Idea of Perfection (Kaizen).
4.13 Poka-Yoke System-Mistakeproofing.
4.14 SMED System.
4.15 7W + 1 Approach-Seven Plus One Deadly Waste(s).
4.16 6M Approach.
5 Value Stream Mapping.
5.3 Value Stream Mapping.
5.3.1 Waste Review.
5.3.2 Value-Added and Non-Value-Added Activities.
5.3.3 Elements of a Value Stream Map.
5.4 Focused Brainstorming.
5.5 Graphical representation of a Process in a Value Stream Map.
5.6 Effective Working Time.
5.7 Customer Demand.
5.8 Takt Time.
5.9 Pitch Time.
5.10 Queuing Time.
5.11 Cycle Time.
5.12 Total Cycle Time.
5.13 Calculation of Total Lead Time(s).
5.14 Value-Added Percentage and Six Sigma Level.
5.15 Drawing the Current-Value-Stream Map.
5.15.1 Drawing Tips.
5.15.2 Common Failure Modes.
5.15.3 Common Definitions.
5.16 Drawing the Value Stream Map.
5.17 What Makes a Value Stream Lean.
5.18 The Future Value Stream Map.
References and Notes.
6 Introductory Statistics and Data.
6.3 Genetic Code of Statistics.
6.4 Population and Samples.
6.5 The Idea of Data.
6.6 Nature of Data.
6.6.1 Quantitative Variables and Data.
6.6.2 Qualitative/Categorical Variables and Data.
6.7 Data Collection.
6.8 The Importance of Data Collection.
6.8.1 Control Cards.
6.8.2 Data Collection Sheet.
6.9 Sampling in Six Sigma.
6.9.1 Random Sampling.
6.9.2 Sequential Sampling.
6.9.3 Stratified Sampling.
6.10 Sources of Data.
7 Quality Tools.
7.3 Nature of Six Sigma Variables.
7.3.1 CT Concept.
7.3.2 CTQ and CTP Characteristics.
7.3.3 CTX Tree (Process Tree).
7.3.4 CTY Tree (Process Tree).
7.3.5 The Focus of Six Sigma.
7.3.6 The Leverage Principle.
7.4 Quality Function Deployment (QFD).
7.5 Scales of Measurement.
7.5.1 Likert Scale.
7.5.2 Logarithm Scale.
7.6 Diagnostic Tools.
7.6.1 Elements for Problem Solving-Diagnostic Tools and Methods.
7.6.2 Problem Definition-Defining Project Objective.
7.7 Analytical Methods.
7.7.1 Cause-Effect (CE) Analysis.
7.7.2 Failure Mode-Effects Analysis (FMEA)
7.7.3 XY Matrix.
7.8 Graphical Tools.
7.8.1 Graphical Summary.
7.8.2 Boxplot or Box-and-Whisker Plot.
7.8.3 Normal Probability Plot.
7.8.4 Main-Effects Plot.
7.8.5 Pareto Chart.
7.8.6 Run Chart.
7.8.7 Time-Series Plot.
7.8.8 Multi-Vari Charts.
7.9 Graphical Representation of a Process.
7.9.1 Process Flowcharts.
7.9.2 Process Mapping.
7.9.3 Cross-Functional Mapping.
7.9.4 Process Mapping-Deployment Diagram.
7.10 SIPOC Diagram.
7.11 IPO Diagram-General Model of a Process System.
7.12 Force-Field Analysis.
7.13 Matrix Analysis-The Importance of Statistical Thinking.
7.16 Affinity Diagram.
7.17 Concept Integration.
8 Making Sense of Data in Six Sigma and Lean.
8.2 Summarizing Quantitative Data: Graphical Methods.
8.2.1 Analytical Charts.
8.2.3 Stem-and-Leaf Plots.
8.2.4 Frequency Tables.
8.2.5 Histograms and Performance Histograms.
8.2.6 Run Charts.
8.2.7 Time-Series Plots.
8.3 Summarizing Quantitative Data: Numerical Methods.
8.3.1 Measures of Center.
8.3.2 Measures of Variation.
8.3.3 Identifying Potential Outliers.
8.3.4 Measures of Position and the Idea of z Scores in Six Sigma.
8.3.5 Measure of Spread and Lean Sigma.
8.4 Organizing and Graphing Qualitative Data.
8.4.1 Organizing Qualitative Data.
8.4.2 Graphing Qualitative Data.
8.4.3 Pareto Analysis with Lorenz Curve.
8.5 Summarizing Bivariate Data.
8.5.2 Correlation Coefficient.
8.6 Multi-Vari Charts.
9 Fundamentals of Capability and Rolled Throughput Yield.
9.3 Why Capability.
9.3.1 Performance Specifications.
9.3.2 Fundamental Concepts of Defect-Based Measurement.
9.4 Six Sigma Capability Metric.
9.4.1 Criteria for Performance Metrics.
9.4.2 Computing the Sigma Level from Discrete Data.
9.4.3 Defective Proportions.
9.4.4 Six-Sigma-Level Calculations (DPU, DPO, DPMO, PPM)-Examples.
9.5 Discrete Capability.
9.6 Continuous Capability-Example.
9.6.1 Data Collection for Capability Studies.
9.7 Fundamentals of Capability.
9.8 Short- Versus Long-Term Capability.
9.8.1 Short-Term Capability.
9.8.2 Long-Term Capability
9.8.3 Introduction to Calibrating the Shift.
9.9 Capability and Performance.
9.10 Indices of Capability.
9.10.1 Cp Index.
9.10.2 Cpk Index.
9.10.3 Pp Index.
9.10.4 Ppk Index.
9.11 Calibrating the Shift.
9.12 Applying the 1.5σ Shift Concept.
9.13.1 Final Test Yield (FTY).
9.13.2 Yield Related to Defects.
9.13.3 Rolled Throughput Yield (RTY).
9.13.4 In-Process Yield (IPY).
9.13.5 In-Process Yield (IPY) and Rolled Throughput Yield (RTY).
9.14 Hidden Factory.
9.14.1 Hidden Factory Composition.
10.2 Experiments, Outcomes, and Sample Space.
10.3 Calculating Probability.
10.3.1 Equally Likely Events.
10.3.2 Probability as Relative Frequency.
10.3.3 Subjective Probability.
10.4 Combinatorial Probability.
10.5 Marginal and Conditional Probabilities.
10.6 Union of Events.
10.6.1 Addition Role.
10.6.2 Mutually Exclusive Events.
10.6.3 Complementary Events.
10.7 Intersection of Events.
10.7.1 Independent Versus Dependent Events.
10.7.2 Multiplication Rule.
11 Discrete Random Variables and Their Probability Distributions.
11.2 Six Sigma Performance Variables.
11.3 Six Sigma Leverage Variables.
11.4 Random Variables.
11.4.1 Discrete Random Variables.
11.4.2 Continuous Random Variables.
11.5 Probability Distributions of a Discrete Random Variable.
11.6 Mean of a Random Variable.
11.7 Standard Deviation of a Discrete Random Variable.
11.8 The Binomial Distribution.
11.8.1 Factorials and Combinations.
11.8.2 The Binomial Experiment.
11.8.3 The Binomial Probability Distribution and Binomial Formula.
11.8.4 Probability of Success and Shape of the Binomial Distribution.
11.8.5 Mean and Standard Deviation of the Binomial Distribution.
11.9 The Poisson Probability Distribution.
11.9.1 Mean and Standard Deviation of the Poisson Probability Distribution.
11.10 The Geometric Distribution.
11.11 The Hypergeometric Probability Distribution.
12 Continuous Random Variables and Their Distributions.
12.2 Continuous Probability Distributions.
12.3 The Normal Distribution.
12.3.1 The Empirical Rule.
12.3.2 The Standard Normal Distribution.
12.3.3 Applications of the Normal Distribution.
12.4 The Exponential Distribution.
13 Sampling Distributions.
13.2 Sampling Distribution of a Sample Mean.
13.2.1 Sampling and Nonsampling Errors.
13.3 Sampling Distribution of a Sample Proportion.
13.4 The Central-Limit Theorem (CLT).
13.4.1 The CLT and Sampling Distribution of the Sample Mean.
13.4.2 The CLT and Sampling Distribution of the Sample Proportion.
14 Single-Population Estimation.
14.2 Meaning of a Confidence Level.
14.3 Estimating a Population Mean.
14.3.1 Confidence Interval for a Population Mean Using the Normal Distribution.
14.3.2 Confidence Interval for a Population Mean Using the t Distribution.
14.4 Estimating a Population Proportion.
14.4.1 Traditional Large-Sample Method.
14.4.2 Wilson Estimator.
14.5 Estimating a Population Variance.
15 Control Methods.
15.3 Control Logic.
15.4 Statistical Control Systems.
15.5 Statistical Control.
15.6 Prevention Versus Detection.
15.7 A Process Control System Definition.
15.8.1 Common Causes.
15.8.2 Special Causes.
15.9 Process Out-of-Control.
15.10 Fundamentals of Process Control.
15.11 Continuous Statistical Process Control (SPC) Tools.
15.12 Interpreting Process Control.
15.13 Statistical Process Control and Statistical Process Monitoring.
15.14 The Foundation of SPC.
15.15 Tools for Process Controls - Control Charts.
15.16 Control Limits.
15.17 Process Out-of-Control Condition.
15.18 Western Electric Rules.
15.19 Control Charts and How They Are Used.
15.20 Precontrol Method.
15.20.1 The Foundations of Precontrol.
15.20.2 Precontrol Charts.
15.21 Control Charts for Variables.
15.21.1 X Chart.
15.21.2 R Chart (Range Chart).
15.21.3 X-R Chart.
15.21.4 Moving Range (MR) Chart.
15.21.5 Standard Deviation Chart.
15.22 Control Chart for Attributes.
15.22.1 p Chart.
15.22.2 Control Chart-np Chart.
15.22.3 c Chart.
15.22.4 u Chart.
References and Notes.
16 Single-Population Hypothesis Tests.
16.2 Introduction to Hypothesis Testing.
16.3 Testing a Claim About a Population Mean.
16.3.1 Hypothesis Test Using the Normal Distribution.
16.3.2 Hypothesis Test Using the t Distribution.
16.3.3 Hypothesis Test About the Median.
16.4 Hypothesis Test About a Population Proportion.
17 Estimation and Hypothesis Tests: Two Populations.
17.2 Inferences About the Differences Between Two Population Means for Independent Samples.
17.2.1 Two-Sample t Test.
17.2.2 Mann-Whitney Test
17.3 Inferences About the Differences Between Two Population Means for Paired Samples.
17.3.1 Paired t Test.
17.3.2 Wilcoxon Signed-Rank Test.
17.4 Inferences About the Differences Between Two Population Proportions.
17.4.1 Large-Sample Procedure.
18 Chi-Square Tests.
18.2 A Goodness-of-Fit Test.
18.3 Contingency Tables.
18.4 Tests of Independence and Homogeneity.
18.4.1 Test of Independence.
18.4.2 Test of Homogeneity.
19 Analysis of Variance.
19.2 The F Distribution.
19.3 One-Way Analysis of Variance.
19.3.1 Variance Between Groups.
19.3.2 Variance Within Groups.
19.3.3 Total Sum of Squares (SST).
19.3.4 Relationships within Sums of Squares and Degrees of Freedom.
19.3.5 Equal Sample Sizes.
19.3.6 Calculating the Value of the Test Statistic.
19.3.7 The One-Way ANOVA Table.
19.4 Pairwise Comparisons.
19.5 Multi-Factor Analysis of Variance.
19.5.1 Two-Way ANOVA
19.5.2 N-Way ANOVA.
19.6 What to Do When the Assumptions Are Unreasonable.
20 Linear and Multiple Regression.
20.2 Simple Regression Model.
20.3 Linear Regression.
20.3.1 Simple Linear Regression.
20.3.3 Assumptions of the Regression Model.
20.3.4 Standard Deviation of Random Errors.
20.4 Coefficient of Determination and Correlation.
20.5 Multiple Regression.
20.5.1 Assumptions of the Multiple Regression Model.
20.5.2 Standard Deviation of Random Errors.
20.5.3 Coefficient of Multiple Determination.
20.6 Regression Analysis.
20.6.1 Testing for Overall Significance of Multiple Regression Model.
20.6.2 Inferences about a Single Regression Coefficient, Bi.
20.7 Using the Regression Model.
20.8 Residual Analysis.
20.9 Cautions in Using Regression.
20.9.1 Determining whether a Model is Good or Bad.
20.9.2 Outliers and Influential Observations.
21 Measurement Analysis.
21.4 Measurement Error.
21.5 Accuracy and Precision.
21.6 Measurement System as a Process.
21.7 Categories of Measurement Error that Affect Location.
21.8 Categories of Measurement that Affect Spread.
21.9 Gage Accuracy and Precision.
21.10 Exploring Linearity Error.
21.11 Gage Repeatability and Reproducibility (R&R).
21.11.1 Variable Gage R&R.
21.11.2 Crossed Gage R&R.
21.11.3 Attribute Gage R&R.
21.12 ANOVA Method Versus X-R Method.
21.13 ANOVA/Variance Component Analysis.
21.14 Rules of Thumb.
21.15 Acceptability Criteria.
21.16 Chapter Review.
22 Design of Experiments.
22.3 Design of Experiments (DOE)Definition.
22.4 Role of Experimental Design in Process Improvement.
22.5 Experiment Design Tools.
22.6 Principles of an Experimental Design.
22.7 Different Types of Experiments.
22.7.1 Main Effects.
22.8 Introduction to Factorial Designs.
22.9 Features of Factorial Designs-Orthogonality.
22.10 Full Factorial Designs.
22.11 Residual Analysis (22).
22.12 Modeling (22).
22.13 Multi-Factor Experiment.
22.14 Fractional Factorial Designs.
22.15 The ANOVA Table.
22.16 Normal Probability Plot of the Effects.
22.17 Main-Effects Plot.
22.18 Blocking Variable.
22.19 Statistical Significance.
22.20 Practical Significance.
22.21 Fundamentals of Residual Analysis.
22.23 Noise Factors.
22.24 Strategy of Good Experimentation.
22.25 Selecting the Variable Levels.
22.26 Selecting the Experimental Design.
22.28 Analyzing the data (ANOVA).
22.30 Achieving the Objective.
22.31 Chapter Summary.
22.32 Chapter Examples.
23 Design for Six Sigma (DFSS), Simulation, and Optimization.
23.3 Six Sigma as Stretch Target.
23.5 Statistical Tolerances.
23.6 Design Application.
23.7 Design Margin.
23.8 Design Qualification.
23.9 Design for Six Sigma (DFSS) Principles.
23.9.1 DFSS Leverage in Product Design.
23.9.2 Importance of DFSS for Product Design.
23.10 Decision Power.
23.12 Experiment Design.
23.13 Response Surface Designs.
23.14 Factorial Producibility.
23.15 Toolbox Overview.
23.16 Monte Carlo Simulations.
23.16.1 Monte Carlo Simulation Defined.
23.16.2 When Simulation is an Appropriate Tool.
23.16.3 Defining Distributions and Outputs in Crystal Ball.
23.17 Design for Six Sigma Project Selection Example.
23.18 Defining Simulation Inputs.
23.19 Defining Outputs and Running a Simulation.
23.19.1 Analyzing a Simulation.
23.20 Stochastic Optimization: Discovering the Best Portfolio with the Least Risk.
24 Survey Methods and Sampling Techniques.
24.3 The Sample Survey.
24.4 The Survey System.
24.5 Clear Goals.
24.6 Target Population and Sample Size.
24.7 Interviewing Method.
24.8 Response Rate, Respondents and Nonrespondents.
24.9 Survey Methods.
24.10 Sources of Information and Data.
24.11 Order of the Questions.
24.12 Pilot Testing the Questionnaire.
24.13 Biased Sample or Response Error.
24.14 Sampling-Random and Nonrandom Samples.
24.15 Population Distribution.
24.16 Sampling Distribution.
24.17 Sampling and Nonsampling Errors.
Appendix A Statistical Tables.
Table I Table of Binomial Probabilities.
Table II Standard Normal Distribution Table.
Table III The t Distribution Table.
Table IV Chi-Square Distribution Table.
Table V The F Distribution Table.
Table VI Critical Values for the Mann-Whitney Test.
Table VII Critical Values for the Wilcoxon Signed-Rank Test.
Table VIII Sigma Conversion Table.
Appendix B Answers to Selected Odd-Numbered Exercises.
Prem S. Mann, PhD, is Professor and Chair of the Department of Economics at Eastern Connecticut State University. Dr. Mann has published numerous articles in the areas of labor economics, microeconomics, and statistics. He is the author of Introductory Statistics, Seventh Edition (Wiley).
Ofelia C. De Hodgins, MS, is a Six Sigma Global Master Black Belt. She has over twenty-five years of consulting experience in manufacturing and finance and has published more than thirty journal articles in the areas of physics, industrial engineering, statistics, and Statistical Process Control (SPC).
Richard L. Hulbert, MBA, is Vice President of Systems and Technology for the Bank of New York Mellon. He has more than thirty-five years of industry experience in the areas of network engineering, installation, implementation, network operations of technology infrastructure, distributed systems, market data, and government telecommunications.
Christopher J. Lacke, PhD, is Associate Professor of Mathematics at Rowan University. He has published numerous journal articles in his areas of research interest, which include decision analysis, Bayesian analysis, and operations research.
- The goal of the book is to show the reader how to solve problems and to improve processes.
- Successful Six Sigma projects from a variety of decades and disciplines are showcased throughout the book.
- Problem sets are graded in an effort to appeal to wide and varied audiences.
- Extensive data sets are available on a related Web site and several computer programming languages and systems (such as Excel, Minitab, MindPro®, among others) are employed throughout the book. Supplements with additional information and projects are also available.
- Other pedagogical tools include incorporation of case studies, “Uses and Misuses of Statistics,” decision-making sections, and Value Stream Mapping icons.
- Plentiful illustrations are displayed to attract the interest level of the reader through the functional and visual method of learning.