LEAN Six Sigma Green Belt

LEAN Six Sigma Green Belt First Edition Manual Featuring SigmaXL Statistical Software v.7 A LSV Group A/S Publication LSV Group A/S www.lsvgroup.com LSV Group is accredited and certified by the IASSC. IASSC is a professional Association dedicated to growing and enhancing the standards within the LEAN Six Sigma Community LSV Group A/S LEAN Six Sigma Green Belt Manual Copyright, 2015 LSV Group A/S. All rights reserved. Individual Copy. No portion of these materials may be reproduced, transmitted, stored in a retrieval or translated into any language in any form or by any means without the prior written permission from LSV Group A/S

Introduction... 5 1. Define Phase... 10 1.1 Six Sigma Overview... 11 1.1.1 What is Six Sigma?... 11 1.1.2 Six Sigma History... 14 1.1.3 Six Sigma Approach... 15 1.1.4 Six Sigma Methodology... 16 1.1.5 Roles and Responsibilities... 21 1.2 Six Sigma Fundamentals... 27 1.2.1 Defining a Process... 27 1.2.3 Quality Function Deployment... 45 1.2.4 Cost of Poor Quality... 52 1.2.5 Pareto Charts and Analysis... 55 1.3 Six Sigma Projects... 60 1.3.1 Six Sigma Metrics... 60 1.3.2 Business Case and Charter... 63 1.3.3 Project Team Selection... 67 1.3.4 Project Risk Management... 71 1.3.5 Project Planning... 75 1.4 Lean Fundamentals... 85 1.4.1 Lean and Six Sigma... 85 1.4.2 History of Lean... 86 1.4.3 Seven Deadly Muda... 87 1.4.4 Five-S (5S)... 89 2. Measure Phase... 92 2.1 Process Definition... 93 2.1.1 Cause and Effect Diagram... 93 2.1.2 Cause and Effects Matrix... 96 2.1.3 Failure Modes and Effects Analysis (FMEA)... 98 2.1.4 Theory of Constraints... 104 2.2 Six Sigma Statistics... 109 LSV Group A/S 1

2.2.1 Basic Statistics... 109 2.2.2 Descriptive Statistics... 110 2.2.3 Normal Distribution and Normality... 114 2.2.4 Graphical Analysis... 118 2.3 Measurement System Analysis... 129 2.3.1 Precision and Accuracy... 129 2.3.2 Bias, Linearity, and Stability... 132 2.3.3 Gage Repeatability and Reproducibility... 137 2.3.4 Variable and Attribute MSA... 139 2.4 Process Capability... 150 2.4.1 Capability Analysis... 150 2.4.2 Concept of Stability... 156 2.4.3 Attribute and Discrete Capability... 158 2.4.4 Monitoring Techniques... 158 3. Analyze Phase... 160 3.1 Inferential Statistics... 161 3.1.1 Understanding Inference... 161 3.1.2 Sampling Techniques... 163 3.1.3 Sample Size... 168 3.1.4 Central Limit Theorem... 171 3.2 Hypothesis Testing... 177 3.2.1 Goals of Hypothesis Testing... 177 3.2.2 Statistical Significance... 180 3.2.3 Risk; Alpha and Beta... 181 3.2.4 Types of Hypothesis Tests... 182 3.3 Hypothesis Tests: Normal Data... 186 3.3.1 One and Two Sample T-Tests... 186 3.3.2 One Sample Variance... 205 3.3.3 One-Way ANOVA... 210 3.4 Hypothesis Testing Non-Normal Data... 220 3.4.1 Mann Whitney... 220 LSV Group A/S 2

3.4.2 Kruskal Wallis... 224 3.4.3 Mood s Median... 228 3.4.4 Friedman... 231 3.4.5 One Sample Sign... 233 3.4.6 One Sample Wilcoxon... 236 3.4.7 One and Two Sample Proportion... 239 3.4.8 Chi-Squared (Contingency Tables)... 244 3.4.9 Tests of Equal Variance... 249 4. Improve Phase... 259 4.1 Simple Linear Regression... 260 4.1.1 Correlation... 260 4.1.2 X-Y Diagram... 264 4.1.3 Regression Equations... 268 4.1.4 Residuals Analysis... 277 4.2 Multiple Regression Analysis... 284 4.2.1 Non-Linear Regression... 284 4.2.2 Multiple Linear Regression... 286 4.2.3 Confidence and Prediction Intervals... 292 4.2.4 Residuals Analysis... 293 5. Control Phase... 300 5.1 Lean Controls... 301 5.1.1 Control Methods for 5S... 301 5.1.2 Kanban... 304 5.1.3 Poka-Yoke... 305 5.2 Statistical Process Control... 307 5.2.1 Data Collection for SPC... 307 5.2.2 I-MR Chart... 310 5.2.3 Xbar-R Chart... 314 5.2.4 U Chart... 318 5.2.5 P Chart... 321 5.2.6 NP Chart... 324 LSV Group A/S 3

5.2.7 X-S Chart... 326 5.2.8 CumSum Chart... 330 5.2.9 EWMA Chart... 332 5.2.10 Control Methods... 333 5.2.11 Control Chart Anatomy... 334 5.2.12 Subgroups and Sampling... 340 5.3 Six Sigma Control Plans... 341 5.3.1 Cost Benefit Analysis... 341 5.3.2 Elements of Control Plans... 343 5.3.3 Response Plan Elements... 351 Index... 354 LSV Group A/S 4

I NTRODUCTION LEAN Six Sigma has become our generation s most outspoken process optimization concept, and used right and to their fullest, it can turnaround or empower a business beyond imagination. Being a world class provider in today s market field depends on your ability to meet your customers expectations and demands. Most people know that the customer has the power to make your company either a success or a failure. You need to be better than your competitors and create a trustworthy relationship with your customer in order to be successful. LEAN Six Sigma is a methodology based on gaining customer satisfaction by reducing defects in the process. LEAN Six Sigma is all about becoming faster better and cheaper than your competitor. LEAN Six Sigma is a powerful toolkit for maximizing productivity, profitability and growth. With this LEAN Six Sigma education you will learn how to listen to your customers and meet their expectations. You will be able to conduct your process around the expectations of customers. Furthermore, you will learn how to lower cost and eliminate waste from your processes and reduce variation and defects, which have a negative impact on your customers. We believe that this book contains all of the aspects needed to become a great LEAN Six Sigma practitioner. We are sure that this book will help you become a successful Green Belt. During this course you will learn the terminology within LEAN Six Sigma and be able to structurally work with process improvement projects on your own. This course is giving you the ability to have a leading role in future improvement projects. How to use this book? This book has been written to explain the topics of Lean Six Sigma and provide step by step instructions on how to perform key statistical analysis techniques using SigmaXL. As expected from an international provider of LEAN Six Sigma educations, this book is built around the DMAIC approach, and is a step by step roadmap to improving existing processes. During the course we will use this book as our main guideline. Every step in this book will be needed during your first process improving project (your learning project), and you will have to understand and apply every single step before moving on to the next step in the DMAIC approach. After you have finished this course, the book will serve as a reference guide every time you are working with process optimization or just need to read up on a specific tool. Always remember to go through the steps of DMAIC chronologically when working with an optimization project. LSV Group A/S 5

1.1 SIX SIGMA OVERVIEW 1.1.1 WHAT IS SIX SIGMA? In statistics, sigma (σ) refers to standard deviation, which is a measure of variation. You will come to learn that variation is the enemy of any quality process; it makes it much more difficult to meet a customer s expectation for a product or service. We need to understand, manage, and minimize process variation. Six Sigma is an aspiration or goal of process performance. A Six Sigma goal is for a process average to operate approximately 6σ away from customer s high and low specification limits. A process whose average is about 6σ away from the customer s high and low specification limits has abundant room to float before approaching the customer s specification limits. Most people think of Six Sigma as a disciplined, data-driven approach to eliminating defects and solving business problems. If you break down the term, Six Sigma, the two words describe a measure of quality that strives for near perfection. A Six Sigma process only yields 3.4 defects for every 1 million opportunities! In other words, 99.9997% of the products are defect-free, but some processes require more quality and some require less. Fig. 1.1 Six Sigma Process with mean 6 standard deviations away from either specification limit. The more variation that can be reduced in the process (by narrowing the distribution), the more easily the customer s expectations can be met. LSV Group A/S 11

Figure 1.28 depicts a full House of Quality with each room labeled. In summary the rooms are: Customer Requirements Technical Specifications Relationship Matrix Prioritized Customer Requirements Competitive Assessment Correlation Matrix Prioritized Design Requirements Fig. 1.28 House of Quality Pros of QFD Focuses the design of the product or process on satisfying customer s needs and wants. Improves the contact channels between customers, advertising, research and improvement, quality and production departments, which sustains better decision making. Reduces the new product development project period and cost. LSV Group A/S 51

1.4 LEAN FUNDAMENTALS 1.4.1 LEAN AND SIX SIGMA What is Lean? A Lean enterprise is one which intends to eliminate waste and allow only value to be pulled through its system. A Lean enterprise can be achieved by identifying and effectively eliminating all waste (which will result in a flowing, cost-effective system). A Lean manufacturing system drives value, flows smoothly, maximizes production, and minimizes waste. Lean manufacturing is characterized by: Identifying and driving value Establishing flow and pull systems Creating production availability and flexibility Zero waste Waste elimination Waste identification and elimination is critical to any successful Lean enterprise Elimination of waste enables flow, drives value, cuts cost, and provides flexible and available production The Five Lean Principles The following five principles of Lean are taken from the book Lean Thinking (1996) by James P. Womack and Daniel T. Jones. 1. Specify value desired by customers. 2. Identify the value stream. 3. Make the product flow continuous. 4. Introduce pull systems where continuous flow is possible. 5. Manage toward perfection so that the number of steps and the amount of time and information needed to serve the customer continually falls. Principle 1: Specify Value Defined by Customers Only a small fraction of the total time and effort spent in an organization actually adds value for the end customer. With a clear definition of value (from the customer s perspective), it is much easier to identify where the waste is. Principle 2: Identify the Value Stream The value stream is the entire set of activities across all parts of the organization involved in jointly delivering the product or service. It is the end-to-end process that delivers the value to the customer. As stated above, once you understand what determines value to the customer, it is easier to determine where the waste is. LSV Group A/S 85

3.1 INFERENTIAL STATISTICS 3.1.1 UNDERSTANDING INFERENCE What is Statistical Inference? Statistical inference is the process of making inferences regarding the characteristics of an unobservable population based on the characteristics of an observed sample. Statistical inference is widely used since it is difficult or sometimes impossible to collect the entire population data. It is rare that we ever know the characteristics of a population, so we need to take limited data and infer what the population looks like. Outcome of Statistical Inference The outcome or conclusion of statistical inference is a statistical proposition about the population, such as an estimate of the population mean or standard deviation. Examples of statistical propositions: Estimating a population parameter Identifying an interval or a region where the true population parameter would fall with some certainty Deciding whether to reject a hypothesis made on characteristics of the population of interest Making predictions Clustering or partitioning data into different groups Population and Sample A statistical population is an entire set of objects or observations about which statistical inferences are to be drawn based on its sample. It is usually impractical or impossible to obtain the data for the entire population. For example, if we are interested in analyzing the population of all the trees, it is extremely difficult to collect the data for all the trees that existed in the past, exist now, and will exist in the future. A sample is a subset of the population (like a piece of the pie above). It is necessary for samples to be representative of the population. The process of selecting a subset of observations within a population is referred to as sampling. Fig 3.1 Sampling a statistical population LSV Group A/S 161

Hypothesis Testing Conclusion There are two possible conclusions of hypothesis testing: 1. Reject the null 2. Fail to reject the null When there is enough evidence based on the sample information to prove the alternative hypothesis, we reject the null. When there is not enough evidence or the sample information is not sufficiently persuasive, we fail to reject the null. Decision Rules in Hypothesis Testing Fig 3.14 Rules in Hypothesis Testing As we get into the technicalities of hypothesis testing, it is important to understand some terms as they pertain to a distribution. Consider in this picture a normal distribution, and what we know about the distribution. Remember 68 95 99.7? The amount of data that falls within +/ 1, 2, and 3 standard deviations of the mean. The test statistic in hypothesis testing is a value calculated using a function of the sample. Test statistics are considered the sample data s numerical summary that can be used in hypothesis testing. Different hypothesis tests have different formulas to calculate the test statistic. The critical value in hypothesis testing is a threshold value to which the test statistic is compared in order to determine whether the null hypothesis is rejected. The critical value is obtained from statistical tables. Different hypothesis tests need different statistical tables for critical values. Hypothesis testing is made easy with our fancy software packages, but it is important that you understand how the theory and rules work behind the software. LSV Group A/S 179

I-MR Charts Diagnosis Fig 5.8 I-MR Charts Diagnosis I Chart (Individuals Chart): Since the MR chart is out of control, the I chart is invalid. MR Chart (Moving Range Chart): Two data points fall beyond the upper control limit. This indicates the MR chart is out of control (i.e., the variations between every two contiguous individual samples are not stable over time). We need to further investigate the process, identify the root causes that trigger the outliers, and correct them to bring the process back in control. 5.2.3 XBAR-R CHART Xbar-R Chart The Xbar-R chart is a control chart for continuous data with a constant subgroup size between two and ten. The Xbar chart plots the average of a subgroup as a data point. The R chart plots the difference between the highest and lowest values within a subgroup as a data point. The Xbar chart monitors the process mean and the R chart monitors the variation within subgroups. The Xbar is valid only if the R chart is in control. The underlying distribution of the Xbar-R chart is normal distribution. Xbar Chart Equations Xbar chart LSV Group A/S 314

Test 2: Nine points in a row on the same side of the center line. Fig 5.44 Western Electric Test 2 Test 2 identifies situations where the process mean has temporarily shifts in the process. Test 3: Six points in a row steadily increasing or steadily decreasing. Test 3 identifies significant trends in performance. Fig 5.45 Western Electric Test 3 Test 4: Fourteen points in a row alternating up and down. Test 4 indicates a cycle. Fig 5.45 Western Electric Test 4 LSV Group A/S 337