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SAE TECHNICALPAPER SERIES 2006-01-0794

Experimental Learning: Hands on Experimentsfor Six Sigma Green and Black Belt Training,

Part I – Manufacturing Environments

A. C. RamamurthyVisteon Automotive Systems

Arlette ReyesVisteon Philippines

2006 SAE World CongressDetroit, Michigan

April 3-6, 2006

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ABSRACT

Six Sigma methodologies in combination with Lean thinking have made considerable inroads as continuous improvement tools initially in manufacturing and more recently for service and transactional processes. There is considerable interest globally in training professionals on the use and application of these tools appropriate to either operational or transactional areas.

It has long been realized that adult learning is at its best when participants are involved in relevant “hands-on” experiments. Six Sigma training has seen the use of class room demonstrations ranging from the use of playing cards, simulations and to the use of sophisticated experiments to illustrate concepts of factorial designs.

This paper will focus on a series of simple but modular experiments that were developed over the past two years illustrating the application of all the Statistical tools that are taught as a part of Six Sigma Green and Black Belt body of knowledge. These experiments require the use of house hold items, are very simple to perform but yet the data can exhibit considerable complexity. We have been very successful in using these experiments at the Green Belt level and more recently at the BB level. In addition to these modular experiments, this paper also describes a simple but powerful illustration of the Central Limit Theorem.

INTRODUCTION Over the past six years the world has seen a significant increase in the use of continuous improvement tools in order to substantially improve quality, reduce lead time to bring products and services to market, to improve customer satisfaction and to be competitive in the ever changing global economy.

Among the multitude of continuous improvement tools available, Six Sigma and Lean have retained popularity in the manufacturing sector, and in past few years, in Healthcare, Finance and other service industries (transactional environments).

Deployment of these tools always starts with training a number of professionals at various skill levels typically termed as “belts”. Besides this there is also specific training that is directed towards management personnel also referred to as “Champions” or “Executives”.

Training professionals at various skill levels is now being offered by various methods, which include:

In-house instructor led training.

In-house web based training.

Training by numerous private organizations around the world

Instructor led training at Universities

Web based training from Universities

Self directed training offered by the American Society of Quality (ASQ)

Majority of training is also assisted by numerous books that are now available on these topics (A quick search at amazon.com for books on Six Sigma could list several thousand entries!!)

There are pro’s and cons’ in selecting a mode for training and a discussion on this topic is well beyond the scope of this paper (See reference 1).

A common feature among these training modes lies in its primary objective, which is to impart problem solving

2006-01-0794

Experimental Learning: Hands on Experiments for Six Sigma Green and Black Belt Training, Part I –

Manufacturing Environments

A. C. Ramamurthy Visteon Automotive Systems

Arlette Reyes Visteon Philippines

Copyright © 2006 SAE International

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skills to adults. Training is only intended to be a “means to an end”, where participants apply these learning’s in their day to day activities and bring about the desired change to the processes that have been chosen for improvement.

Given this motivation, the question comes down to, how can we best impart “advanced” problem solving skills to working adults? This brings us to the domain of “Andragogy” which stands for the science of helping adults learn (2-3).

There is considerable research that is available on, “How Adults learn”. This is a relevant topic in any discussion related to training, since the learning styles of adults are linked to:

• How one solves problems

• How one participates and works in teams

• How one manages conflict

• How one makes career choices and

• How one negotiates personal and professional relationships

The above attributes can be directly linked to success of Six Sigma Green and Black Belts (change agents) in their problem solving ability.

This paper will present a brief review on adult learning and the of Kolb’s LSI (Learning Style Inventory) (a widely accepted theory for adult learning (4)) as the basis for a set of simple but yet powerful set of experiments proposed for the Six Sigma training room.

Six Sigma training, particularly based on instructor led variety, usually involves a variety of hands-on activities which help adults learn and apply various statistical tools. These hands-on experiments can vary significantly between Green Belt and Black Belt training programs. Many of the distance based learning depend on simulations to illustrate key learning concepts.

Six Sigma training is now offered to learners whose backgrounds can range from being an Accountant, to a Health care professional, a HR professional, to a Chemist and degreed Engineers. Senior author of this paper has seen very little variation in terms of hands-on experiments (used in training) distinguishing the different professional backgrounds.

Education in Lean-Six Methodologies typically involves, familiarity, understanding and application of several tools. These tools can be classified into seven categories.

• Project Management and Financial Metrics tools (Team Dynamics, Change Agent, Gantt Charts, PERT, CPM, Benefit-Cost analysis)

• Mapping tools (SIPOC, Value Stream Mapping, Process Maps, Swimlane and Fishbone Diagrams)

• Data Collection tools (Check sheets)

• Management tools (Affinity Diagrams, Tree Diagrams…)

• VOC and Survey instruments (Surveys, Kano analysis, QFD)

• Lean Tools (5 S, Pull systems, Poka Yoke, Standardized work, Quality at source, Quick Change Over, …..)

• Statistical tools, which can be further categorized into:

o Tools used in Descriptive Statistics

o Tools used in Measurement System Analysis

o Tools used in Statistical inference, Regression and Correlation.

o Tools used in the Design of Experiments and

o Tools used in Statistical Process Control

This work described in this paper is a part of a larger effort to bring class room “hands on experiments” that are relevant to either manufacturing or transactional environments. In this paper we describe in detail, experiments that were developed to illustrate basic as well as advanced statistical concepts which can be used in either Green or Black Belt Training. These experiments cover most if not all the category of Statistical tools (as mentioned above) used in Green Belt and Black Belt project work.

This paper will focus on experiments which are suitable for training adult learners in Six Sigma problem solving akin to manufacturing environments. These experiments are based on house hold materials, hence inexpensive and to the delight of a trainer, add virtually no “baggage” to transport, when bringing training across continents. In a subsequent paper we propose to describe experiments appropriate to Six Sigma training focused on the transactional environment.

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Adult Learning and Six Sigma Training

The field of Andragogy has been researched across the developed world for over 40 years. Malcolm Knowles (2) first introduced this term to mean the art and sciences of helping adults learn. Knowles distinguishes education and knowledge. He defines educations as an activity undertaken or initiated by one or more agents, which is designed to effect changes in knowledge, skill and attitude of individuals. In contrast, “Learning” emphasizes the person in whom the change occurs or expected to occur. This leads to the definition of learning as, “a relatively permanent change in cognition, resulting from experience and directly influencing behavior”. Assumptions (2) of Andragogy (Learner centered and Facilitated) are:

1. Adult students are active learners 2. Adults bring work related experiences into the

training environment (teacher is a guide and facilitator)

3. Adults have the need to know why they are learning something: not motivated by gold stars or grades

4. They are self directed (a process by which adults take control of their own learning) and active participants in the learning process

5. They are motivated by both intrinsic and extrinsic motivation factors

In contrast to Andragogy is Pedagogy which is also referred to Teacher-centered or directed learning which is characterized by lecturing, drills, memorization and immediate feedback. Here the teacher is totally responsible for setting learning objectives and assessment of skills/knowledge. KOLB’S EXPERIMENTAL LEARNING AND SIX-SIGMA

“Tell me, and I will forget. Show me, and I may remember. Involve me, and I will understand”

Confucius circa 450 BC

Learners take in information as follows:

80 % if information is by sight

11 % if information is by hearing and

9 % if information is from other senses

Adult learners retain what they learn based on the type of instruction

10 % of what is read

20 % of what is heard

30 % of what is seen

50 % of what is seen and heard

70 % of what is seen and spoken

90 % of what is said while doing what is being talked about

95 % of what they teach someone else to do

In the mid 1980’s Professor Kolb (4-5) at the Case western Reserve University (Cleveland, OH, USA) proposed adult learning is more effective (implying processing of knowledge at deeper levels) when learners are more directly involved rather than passively receiving knowledge transmitted by their teachers or trainers. Kolb’s model is frequently referred to the theory of “Experimental Learning”. Kolb defines learning as, “a process whereby knowledge is created through the transformation of experience”. The three key elements in this definition are:

A. Emphasis is on the process as opposed to content or outcomes

B. Knowledge is a transformation process, being regenerative (creation and recreation), not some independent entity which is to be acquired or transmitted

C. Learning transforms in both its subjective and objective forms

Kolb proposed a learning model which he calls the “Experimental Learning Cycle” addresses the four ways we (adults) process information. They are

1. Concrete Experience (CE) which is synonymous to “Learning by Experiencing”

Characteristics of CE include

• Learning from specific experiences • Relating to people • Being sensitive to feelings and people

2. Reflective Observation (RO) which is

synonymous to “Learning by Reflecting”

Characteristics of RO include • Careful observations before making

judgments • Viewing issues from different

perspectives • Looking for the “meaning of things”

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3. Abstract Conceptualization (AC) which is synonymous to “Learning by Thinking”

AC is characterized by

• Logically analyzing ideas • Planning Systematically • Acting on an intellectual understanding

of a situation

4. Active Experimentation (AE) which is synonymous to “Learning by Doing”

AE is characterized by

• Demonstrating ability to get things done • Taking risks • Influencing people and events through

action CE and AC are the two ways by which adults take in experiences while AE and RO are the two ways used by adults to deal with experience. Ideally, using a well rounded process would involve cycling through all these four phases. Kolb discusses the pro and cons of favoring one phase over the other (4-5). Figure1 shows Kolb’s LSI (Learning Style Inventory)

Figure 1 Kolb’s contribution to adult learning goes well beyond proposing the Learning style cycle. Kolb points out that an adult learner adopts (based on hereditary equipment, past life experience and current environment) a specific learning style which could favor one phase over the other. Kolb’s contribution includes the development of a quantitative tool which starts by classifying the adult learner into four categories (see Figure 1). They are:

• The Converger whose dominant learning is via AC and AE. Here the strength is in practical application of ideas. Kolb’s extensive research points out that this learning style is characteristic of many Engineers (Nursing and Engineering majors adopt to this category)

• The Diverger who has exactly the opposite

strengths of a Converger which is in CE and RO. Here the strength is in imaginative ability. Typically personnel managers (HR) tend to be characterized by this learning style (History, Psychology and Political science majors adopt to this style)

The Assimilator’s dominant learning ability is via AC and RO. Here the strength is in the ability to construct theoretical models. Typically adults in research and planning departments adapt to this style (Mathematics, Economics, Chemistry and Physics majors are known to adapt to this learning style). The Accommodator has the opposite strengths of an assimilator where the focus is on CE and AE. Here the strength is in “doing things”, in carrying out plans and experiments, and being involved in new experiences. Typically personnel involved in marketing or sales adopt to this learning style (Business majors adopt to this style of learning) Based on these categories of adult learners Kolb developed a quantitative tool to measure an individuals learning style (5). Kolb extended his model to understand the relationship between an adult learning style and the ability to solve problems. Learning and problem solving share the same basic process, hence learning styles should have a profound influence on ones ability to solve problems which is the basic premise of Six Sigma training. Kolb overlaid his experimental learning cycle over the well know problem solving process as described by Pounds (6). This overlay is shown in Figure 2. In this figure one can observe that stages in problem solving sequence generally correspond to the learning styles strengths. Based on this overlay, we can expect an “accommodator’s” problem solving skill is in executing solutions and in initiating problem finding based on a goal or model. A "Diverger” on the other hand has problem solving skills akin to identifying the multitude of possible problems and comparing to reality. Similarly the strength of an “assimilator” is in abstract model building while the “converger” excels in evaluation of solution consequences and in the selection of the solution.

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Figure 2

Since we started with an objective of training adults to be problem solvers in the Lean-Six Sigma world, it would be worthwhile we compare the phases of Lean-Six Sigma (DMAIC or Lean) with Figure 2 which is Kolb’s overlay of learning styles and general problem solving cycle as suggested by Pounds (6). This overlay is shown in Figure 3. The CE-RO domain (first quadrant) can easily be identified as the role and responsibility of the Lean Value Stream manager or the Six Sigma Champion. Here we expect to choose the value stream or identify a scopped Six Sigma project for improvement. So this quadrant can be identified with the “Define” phase of Six Sigma. The Champion – GB or BB relation and the Six Sigma Charter statement is formulated in this phase. The RO-AC domain (second quadrant) is the early stages of a Lean-Six Sigma project. This domain can be identified with the Define- Measure-Analyze phase of Six Sigma. We include the “Define” phase again in this category since the GB and BB still needs to organize various pieces of project related information as a part of this phase. A good portion of Design for Six Sigma (DFSS) resides in this phase.

The AE-AC (third quadrant) can be identified with the IMPROVE phase of Six Sigma or the Kaizen’s associated (using the Lean tool box) with Future State Maps (Lean).

The Fourth quadrant (AE-AC) is the CONTROL phase of a Six Sigma project where the GB/BB with the help of the team and the Champion “gets things done” by being “adaptable and practical”.

Figure 3 Comparing the Kolb model and Six Sigma roadmap, it becomes clear, that one requires the strengths (learning styles) of a Diverger, Assimilator, Converger and Accommodator in order to successfully implement Lean-Six Sigma programs at the workplace. Given our understanding of the Kolb model and its implication to Lean-Six Sigma deployment, from a training perspective, one would have to recognize that:

• Trainees have different learning styles • Trainers have different learning styles • Set goals and pace by involving trainees • It is important to utilize the trainee’s own

experience (respect trainees world of experience) rather than just lecturing

• It is important to provide a learning environment that incorporates all the learning styles, Feeling (CE), Doing (AE), watching (RO) and Thinking (AC)

• Learning environment should clearly connect trainees goals with the objectives of the course (Body of Knowledge)

Another aspect of learning which has received attention is “Reflection”. Several authors (7-13) have gone beyond the Kolb model (where refection is the second stage) to explain the role of reflection in learning. Bound et.al. (9), define reflection as a “process of creating and clarifying the meaning of experience (past and present) in terms of self”. Schon (10) defines reflection as, “on the spot surfacing, criticizing, restructuring, and testing of intuitive understandings of experienced phenomenon”. Consequence of reflection is our ability to: change behavior, get new ideas, clarification of ideas, develop positive attitude towards learning, and create hypotheses, commitment to solutions, figure out solutions, change priorities, all essential ingredients to Lean-Six-Sigma Problem solving process

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Boud et.al. (9) visualize three major components to the process of reflection (also known as Praxis):

• Returning to experience • Attending to feelings • Re-evaluating the experience

Returning to experience entails the recollection of the salient events, the replaying of the initial experience in the mind of the trainee or recounting to others the features of the experience. Attending to feelings is composed of two components. The first one involves focusing on positive feelings about learning which is subject to reflection and the second one being the removal of obstructing feelings when recounting an event to others. Reevaluating experience can be a rehearsal in which the new learning is applied mentally to test its authenticity and the planning of subsequent activities where learning is applied in one’s work. In the context of Six-Sigma training, Reflective learning can be facilitated by:

• Providing a framework and environment where trainees can overlay their experiences

• Designing learning opportunities that enable/foster/force trainees to reflect and reevaluate events

• Providing consistent feedback about the value of this process and the expectation for enhancing reflective thinking skills

• Reviewing of trainees work and provide coaching comments that enable them to improve the quality of reflective thinking

The primary focus of this paper is to propose a series of hands on experiments to enhance the trainee’s ability to understand, apply and reflect on the use of Lean-Six Sigma tools. All this is accomplished within the framework Kolb’s “Experimental learning model”, augmented by the use of reflective thinking practices. An excellent resource to design workshops based on Experimental Learning Model (based on Kolb) can be found in Reference 14. Hands on experiments described in this paper are part of the traditional, instructor led lectures where at the end of each module small teams (typically five in number) of trainees discuss their mutual experiences of class room learning with their own work experiences and present their observations (including their own examples) to other teams. The trainer acts as a facilitator shares his/her experiences along with presenting alternate view points and presenting several what-if type of questions. At the end of this activity the facilitator emphasizes the value of this reflective thinking process within the context

the main objective (which is enhancing ones ability to solve complex problems in the workplace). In a later section we will describe our process of reflective thinking after completing several hands on experiments.

Teaching Statistical Tools and Six Sigma Training

In this section we will restrict our discussion solely to the learning and application associated with Six Sigma statistical tools.

Learning by Doing and Statistics Educators have paid considerable attention in the way Statistics is taught at the undergraduate and post graduate level. The Journal of Statistics Education (a publication of the American Statistical Association) has published numerous articles which address this topic. Hunter (15) was one the early teachers who wrote, “In most courses on experimental design, students get no practice designing experiments, although from home work assignments, they do get to practice analyzing data”.

Hunter visualizes two extremes to student exercises while studying design and analysis of experiments (DOE). At one extreme is the use of exercises with pre-existing, pre-run experiments. All the learners are assigned the same question and obtain the same results. At the other extreme are actual activities where students collect and analyze there own data. Here the students quickly learn that indeed data is variable and different students performing the identical experiment may receive different answers.

Vaughan (16) points out to some unintended consequences of this approach:

• Learners believe that there is one, unique answer to a scientific problem

• Learners do not see the extent that natural variation can change results when experiments are repeated

• Learners may believe that results are clear cut because everyone gets the same answers

Hogg (18) cites that “students frequently view statistics as the worst course taken in college”. The two schools of thought are, Statistics is about “data analysis” while the second view advocates changes to the pedagogy,

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replacing passively related lectures to hands-on activities (in line with Kolb’s adult learning model).

Several approaches have been practiced over the years to ensure learning statistics is a wholesome experience. These are:

• Hands-on activities (18-22, 33-37)

• Working on Case studies (22-25)

• Use of computer simulations (26-32)

• Working on Text-book problems (instructor led)

Objectives in the above approaches are (Learning by doing Statistics):

• The experience gained during the activity and ability to reflect upon it.

• To quantify some aspect of student’s knowledge (learning) about an everyday event thus providing a context within which the students can apply and develop an understanding of design and analysis.

• That collection of data is at the heart of statistical thinking. Data collection promotes learning by experience and connects the learning process to reality (38)

• To provide a firm basis in Statistical reasoning and not mearly understand the mechanics of data analysis via the use of user friendly software like MINITAB, SAS, SPSS and others.

Gary Smith (20) points out that design of hand-on activities needs to be realistic so that students (adult learners) are persuaded to use the critical learning skills that can be applied in the real world. He further points out that tools used to answer artificial questions will seem artificial to the student as well.

Learning based on Playing Cards Learning Statistics using a deck of cards is the subject of well presented book by Thomas Knapp (39). Using a deck of cards, it is possible to demonstrate:

• Properties of Populations and Distributions

• Central tendency

• Skewness and Kurtosis

• Probability and Sampling (with and without replacement)

• Properties Sampling distributions

• Hypothesis testing

• 2 × 2 Contingency tables

A unique advantage of using a deck of cards is that it offers a finite population from which one can draw samples either with or without replacement (not the same for illustrations with coins).

Learning based on case studies Several authors (23-25, 40-42) have adopted teaching statistics using real world “case studies” on topics that participants would be familiar with. This could include topics ranging from weather, elections, base ball data, popular clinical studies, well documented studies from the industry and also well known scientific studies. The teaching method involves discussing the case which includes presenting contextual information, methods used for data collection, formulating hypothesis, exploring data, analysis of data, interpretation of results along with reflections. These case studies are used to illustrate all the statistical tools that are learnt as part of class room lectures. Studies have shown that this approach to learning to be superior to traditional class room lecture and “working on problems” approach.

Learning based on simulations One of the most popular methods of teaching statistics in the past ten years has been the use of computer simulation methods (CSM’s). CSM’s are typically viewed as a teaching aid to instructor led class room learning. Simulations allow the learner to rapidly experiment (visualize) with random samples from a various populations (and distributions) with well defined set of parameters for the purpose of clarifying abstract statistical concepts. Hence simulators can be looked upon as “ready to go”, transfer functions which convert inputs into appropriate outputs. Learning with simulations is usually aided by the use of software such as MINITAB (with its various Graphical features) or Excel (43, 44). Simulations have the advantage of rapidly illustrating concepts and explore various “what-if” scenarios (example, in Power and Sample size estimations).

Mills (26) has conducted an extensive research on this topic and concluded that CSM’s enhanced the overall understanding of abstract statistical concepts.

Evans (45) brings out the unique advantages of teaching simulations using spreadsheets. Doane (28) has discussed the use of simulation methods to teach distributions and has coauthored a popular interactive learning tool, “Visual Statistics” which is used as a teaching aid in Statistics courses at universities (30).

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Kurji et al. (46) have described a simulation program for teaching statistics to students majoring in agricultural science. Real life examples are illustrated using a graphical interface. Schwarz (32) describes a web based simulation where the student has the ability to design his experiment in a virtual laboratory and carry out subsequent analysis. Anderson-cook et.al. (47) have described a simulation experiment to differentiate between a well designed and poorly designed experiment. Vaughan describes teaching statistical concepts with student specific data sets (16).

A key word search for “Statistics and Simulations” in the world wide web shows numerous Java based applets are available to illustrate various statistical concepts ranging from, Central Limit theorem, Confidence intervals to Regression concepts, Power and Sample Size selection and ANOVA methods. This paper will cite a few web resources (48-53) which are well maintained and contents ideally suited for class room or independent learning.

Finally, Vellman et.al. summarize the promises and pitfalls of Multimedia in teaching Statistics (54).

Learning based on “text book style problems” Learning statistics in class using text book problems has been the time honored approach to teaching statistics. Margaret (21) points out that text books over the years have made significant strides to provide more realistic data sets for analysis including some background information on the objective of the experiment. Mead (55) points out that these problems are sparse in the actual mechanics of data collection and frequently the cited references do not carry the details of the experimental method. Using “text book” problems for teaching statistics can be very powerful if the instructor can provide the background (motivation for the experiment) and insights into data collection methods. Discussion of statistical analysis can then be very rewarding. Working on these problems help illustrate the mechanics of using statistical tools and software such as MINITAB or Excel. Data sets found in two widely used text books, Box et.al. (56) and Montgomery (57) are very popular for in-class activity.

Learning based on Experiments (projects) “One must learn by doing the thing; for though you think you know it, you have no certainty until you try” Sophocles In the introduction to this section on learning Statistics, we have pointed out the role of conducting hands-on experiments while teaching the application of statistical

tools. Hogg (18) went on to write that, “relying on examples done by others is that students remain passive participants and do not experience firsthand the many issues that arise in data collection and analysis.

Planning, conducting, analyzing and reporting of well planned experiments map learning and reflection cycles, which are vital components for adult learning.

In the Six Sigma context, training aided by the use of hands on experiments offers a unique perspective, and to some advantages akin to hand on experiments are:

• Promote team work

• Initiate scientific query (can one predict how the system should behave?)

• Plan a data collection strategy

• Use of P- diagrams (17)

o Importance of minimizing uncontrolled variability

o Randomization of experiments

• Measurement System Analysis (power of observation)

• Data exploration (handling outliers)

• Data analysis

o Specifically randomization

o Clarity between factors or blocks

o Realization that not all errors are Gaussian (non-normal data)

o Dealing with factors outside the experimental design (add variables for exploration)

o What if the data collection plan does not work!

BH2 (56), point out that it would be rewarding to plan and perform a home made experiment, collect data and analyze the data, as part of learning. Experiments described in this paper using Alka Seltzer (antacid tablets) literally follows BH2’s suggestion. All the experiments originated in the home of the senior author and later brought to Green belt training classes.

Many authors have proposed ways to actively engaging students in hands-on data collection. Bradstreet (33) recommends a laboratory-based course while others endorse in-class activities. Dietz (34), Gnandesikan (19,

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34) and Hunter (15) recommend a single three-week project. Chance (35), Ledotler (36), Mackisack (21) and Fillebrown (37) recommend experiments to be a course long project.

We list here some sources describing hand on experiments which can be used as a part of teaching statistics during Six Sigma Training GB or BB training (58-62).

POPULAR EXPERIMENTS USED IN SIX SIGMA GREEN AND BLACK BELT TRAINING

Very little attempt has been made to tailor the learning process to participants background during Six Sigma training. Senior author of this paper was a part of an instructor led Black Belt training where participants backgrounds ranged from, degreed Engineers, Chemists and an HR professional. Examples used in class (text book style problems) were mostly “chemical” in origin. Hand on experiments had little in common with the participant’s backgrounds. Engineers understood the mechanics of using MINITAB for problem solving but had little to reflect on the outcome of the “text-book” style problems The HR professional simply did not see the relevance of either the “text book” problems or hand on experiments (based on the catapult).

Recently Lynch (63) presented an SAE paper where he outlines a Body of Knowledge (BOK) for training professionals involved in a transactional environment (service industries). Similar BOK is also being considered for those in the health care industry (65). It is of the opinion of the authors, that GB and BB training should be mainly divided into two categories. The first one serving need of process and design engineers, industrial chemists, manufacturing engineers while the second focused on the need for professionals in the transactional environment such as Human Resources, Finance and in the service sectors of the business. For example If training is targeted to Chemists and Chemical Engineers (example in a Chemical industry), it is possible to further customize the BOK by presenting case studies and hand on experiments pertinent to the craft.

A survey of various Six Sigma, Green and Black training methods shows, that instructor led lectures assisted by hand on experiments broadly fall into the following categories.

• Experiments based on the Catapult

• Working on “Text-Book” style Problems during training

• Simulations

• Case studies

• Other Experiments

Hands on experiments using the Catapult and its variants are very popular in Six Sigma Green Belt and BB training. Statistical tools such as variable Gage R & R determination, Multiple Regression and various DOE’s (including the Response surface analysis) can be illustrated using this device. Some use this device to include concepts of Lean (64) as a part of learning. This device is easy to setup and use. Some disadvantages of this devices cited are, that it is expensive, delicate and the mechanics is “intuitive” (system behavior is predictable) while training engineers.

Six Sigma training is also assisted by working on “text book” style problems in class. These problems help in terms of learning the mechanics of using software such as MINITAB or EXCEL and in the interpretation of results. An often cited criticism (in post training evaluations) of this approach is, the problems had no relevance to their real world experience. To address this concern, it is not uncommon to see training, particularly the in house variety, substitute most of these problems with examples that are from the real world (from previous or ongoing GB and BB projects) which is within the experience of the trainees. The advantage of this approach is that one can add details on the circumstances that lead to this experiment, how the data was collected, comments on the measurement system, experimental plan, data analysis, interpretation and lessons learnt.

The role of simulations in teaching concepts in statistics was discussed in an earlier section. In the context of Six Sigma training, this tool has not been used as widely as one would have expected. Web based training (offered by universities) have adopted this technique and simulations using an “animated” catapult is used to illustrate concepts in Regression and Design of experiments (65). A “Six Sigma study guide” which simulates a variety of problems scenarios, ranging from probability distributions (discrete and continuous), Statistical inference, Regression, Control charts and Design of Experiments can also be used as an effective teaching and practice tool during Six Sigma GB or BB training (66). A companion tool is the “DOE simulator” which can be used to effectively teach (and practice) concepts in Design of Experiments (Factorial designs) is available (67) in the public domain.

The use of case studies is not common in instructor lead class room training however is an important component in web based training (65).

The authors of this paper have come across numerous experiments that are being used to illustrate various statistical concepts as a part of Six Sigma GB and BB training. However these experiments have not been reported in the open literature.

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Proposed Experiments based on US Pennies (coins) and Alka Seltzer

The Central Limit Theorem One of the most important concepts in statistics is the “Central Limit Theorem” which is typically addressed more in BB rather than GB training. This concept is typically illustrated in class using MINITAB (or other) simulation methods. This approach had the advantage of rapidly illustrating the concept while using a variety of “starting” distributions. An experiment which has been described in statistics education literature uses US pennies to illustrate this concept (learning by doing). We have found this to be a very powerful approach to illustrating the concept of CLT. We describe here the details of this experiment and also show some pictures from a class room activity.

The Experiment In order to carry out this experiment one would need coins (typically ones which have been in circulation for a long period of time) which have a marking on the year when they were minted (note this may present problems in some Asian countries- See Appendix for an alternative novel approach). Typically one would need some 500 of these coins to demonstrate this experiment. This being a team exercise, we typically form two teams provided with specific instructions. The first team samples a coin at random (from the large collection) and subtracts the year marked on the coin (say 1965) from the current year (say 2005). Then this coin is paced on a template (shown in Figure 4) at an X-Axis location of 40. If another coin, also sampled randomly is marked 1965, then this coin is placed on the top the first one. This exercise continues till 100-150 coins have been placed on the template. Figure 5 shows how this arrangement may look like after completion. The second team had the task of sampling five coins at random (also from a large collection) and average the difference between the years marked on each coin from the current year (say 2005). If sampled coins at random have the years, 1960, 1978, 2004 and 1953, then we take the average value between, 45 (2005-1960), 27 (2005-1978), 1 (2005-2004) and 52 (2005-1953), which gives the value 25. Then one coin is placed on a new template at an X-Axis value of 25. This exercise continues till 50-60 coins are placed on the template. Figure 6 is a cartoon on how this template may look like after completion.

Figure 4

Figure 5

Figure 6

Illustration of the Central Limit Theorem with US pennies Shown below are pictures from a typical class room experiment involving US pennies. Figure 7 is a picture showing a display based on “individuals” while Figure 8 is a display based on “average” using a sample size of 5.

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Figure 7

Figure 8

Reflections After completing their respective assignments, teams are encouraged to visit the other teams work. As a part of reflections, concept of central limit theorem is discussed and this is followed by a quantitative analysis of data. Graphical analysis for the “individuals” is performed initially. Predictions for the average and standard deviation for the distribution of averages are made before a graphical analysis is undertaken. Histograms for both “individuals” and “averages” are plotted and properties of these distributions evaluated. Questions answered as part of this experiment are:

• Is the data normally distributed for each distribution?

• Measures of central tendency • Standard Error of the Mean

Figure 9 shows a histogram and MINITAB Graphical summary output for individuals. Figure 10 is a similar representation for the distribution of averages (sample size =5) We observe that histogram for the individuals is not normally distributed whereas the distribution of averages (sample size =5) is normal. One can further verify that standard deviation of the sampled distribution (standard deviation of the individuals/√sample size) is 0.99 close to the expected value of 1.2. We can continue this experiment by increasing the sample size to 10 further demonstrating the lowering of variability.

Figure 9

Figure 10

STATISTICAL TOOLS COVERED IN THE PROPOSED SET OF EXPERIMENTS BASED ON ALKA SELTZER

Alka seltzer is an over the counter medicine a product from the Bayer corporation. It is considered to be an antacid and typically taken for heartburns, sour stomach and acid indigestion. The nominal composition of active ingredients is listed to contain, Asprin, Sodium bicarbonate and Citric acid. Bayer corporation maintains a website (68) which describe this product in detail and also provide details for class room demonstrations involving this product. One of the observed properties of this product is the effervescent behavior when this tablet is dissolved in water (a procedure suggested on the label). This gas that evolves in this chemical experiment is Carbon di-Oxide (CO2) which is simply a reaction between citric acid and the bi-carbonate present. The chemical reaction is shown below (“aq” stands for aqueous and “g” for gas):

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H3C6H5O7(aq) + 3NaHCO3(aq) → Na3C6H5O7(aq) + 3H2O + 3CO2(g)

Frequently upon dissolving a tablet of Alka Seltzer in water, one observes a residue which is normal. This residue is the undissolved aspirin in the tablet. It is well known in Chemical literature (69) that kinetics (velocity) of reactions are strong functions of temperature and also surface area. Since we have Sodium bi Carbonate as one of the ingredients, presence of an acid in addition to the citric acid should also influence this reaction. Hence Coke Cola is used as a factor in our DOE’s. It is known, that Coke Cola contains dilute Phosphoric acid as one of its ingredients. It is possible to substitute another acid such as, dilute Sulfuric or Hydro-Chloric acid instead of Coke Cola. It is these features of the Alka seltzer tablet that allows us to design a series of experiments which in turn help illustrate the application of statistical tools. Besides the Alka Seltzer (the Bayer Brand name) other pharmaceutical companies (in the US and elsewhere in the world) market similar products with identical active ingredient compositions. Hence these different brand names can also be considered as variables in designed experiments. Note: these brand names would be called “effervescent Antacids” since Alka Seltzer is a trade mark of Bayer corporation. In all our experiments the following operational assumptions are made:

• The Key Process input variable (KPIV) is the “mass” of the tablets

• The Key process output variable (KPOV) is the time for the Alka seltzer (or Antacid) tablet to dissolve in excess amount of water

• Crushed, broken or chipped tablets are considered to be defective (subject to an incoming inspection) and hence are not used in either KPIV or KPOV based experiments. However defective data are used in attribute hypothesis testing

Advantages in using the Alka Seltzer system in Six Sigma training include:

• It is possible to design a set of experiments that can illustrate over 80 % of the statistical tools (used in GB and BB training) and assumptions involved in their use

• It is inexpensive to perform these experiments • These experiments can be performed any where

in the world without having to ship delicate contraptions

• It is possible to explain the observed results based on basic chemical principles

• Experiments can be laid out to follow the Six Sigma Roadmap (DMAIC)

• Chemicals involved are just Alka Seltzer, water and Coke Cola, hence there is no need for MSDS documents.

• There are no waste treatment problems that one needs to be concerned about

• There are no safety issues to be concerned with Given this background, we have been able to design a series of experiments using Alka Seltzer to illustrate the application of following statistical procedures (application of tools)

• Descriptive statistics Measures of central tendency Measure of spread Normality Confidence intervals

• Process capability • Statistical inference (including test for process

stability and Normality assumption) One proportion test Two proportion test Chi-square test Paired t-test One sample t-test Two sample t-test One way ANOVA

Test for equal variance Tukey Pairwise comparisons

• Regression Fitted line plot (linear and Quadratic) Residual plots

• Design of Experiments Fractional factorial design Fold over design Main effects and interaction plots Response surface designs Contour and wire-frame plots EVOP (Evolutionary operations)

• Destructive Gage R and R Nested ANOVA (design)

In this paper we describe the experiments, its deliverables (including reflections) and typical results. All the output shown is derived from either MINITAB version 13 or 14. Some raw data obtained in our experiments is included in the Appendix section of this paper. Discussion of results, in terms of detailed statistical interpretations, is outside the scope of this work. THE ALKA SELTZER EXPERIMENTS

Given the background on the Alka Seltzer system and scope of work, we now describe the details on how these experiments are conducted (including reflections) during training.

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We start by stating, that CTQ is KPOV, which is the time it takes for a given antacid tablet to dissolve in aqueous solutions. We also state that the key process input variable (KPIV) is the mass of the tablet.

The first set of experiments explores the antacid product (three brand names) for KPIV. Here we provide two analytical balances (good to 0.01 gram) to measure the mass of tablets. Data is obtained for all three brand names.

Constants like LSL (Lower specification limit) and USL (Upper specification limit) are provided so that short term process capability can be evaluated

Deliverables for Lab 1 include:

Data collection plan

Data collection sheets

Do we have a stable process (Reference 70)?

Are KPIV’s normally distributed?

Measures of central tendency for each brand name

Measures of variability in mass for all brand names

Confidence intervals for the mean

Confidence intervals for variance

What is the short term process capability?

Is KPIV for Brand “A” different from KPIV for Band “B” (Are KPIV’s for Brand “A” and “B” derived from the same population)?

Are KPIV’s for the three brand names different from one another (Are KPIV’s for the three brand names derived from the same population)?

What is Cpk for (KPIV) one of the brands?

How did we handle outliers and non normal data?

Reflections

Participants complete the above assignment and address all the deliverables in the form of a standardized Power Point presentation. This includes, stated

objectives for Lab 1, data collection plan (including a p-diagram), observations (data collection templates), data analysis (including graphical analysis), interpretation and lessons learnt. This presentation is then posted in the training room and presented to other teams as a “poster presentation” during reflections.

The trainer takes the opportunity to provide feedback (mostly based on observations made during the experiments), and ask questions. One of these questions is how this learning can be applied to what the participant is currently engaged in or with respect to their chosen Six Sigma project. Questions from other team members are also encouraged. If the trainer feels there is a gap in “understanding”, participants return back to some more instructor led discussion.

In Lab 1, we are able to accomplish aspects of Descriptive statistics and Hypothesis testing (excluding one sample t-test) including ANOVA. The only Hypothesis tests that were not included are those akin to attribute data. This will be described in Lab 2. Lab 4 will describe an experiment involving Alka seltzer where the use one sample t-test and correlation are illustrated.

KPIV data sets for the three brand names is provided in the appendix

Typical Results in Lab 1

We now present some typical results that are associated with this Lab 1 (Note, this lab is associated with KPIV). This includes:

I-MR chars (only one Brand name shown here) for KPIV (mass of the tablet)

Anderson-Darling test for normality (only one brand name shown here)

MINITAB’s Graphical summary for Descriptive statistics (one brand name shown here)

Two sample t-test (MINTAB output and Box plots)

Test(s) Equal variances (MINITAB graph)

One way ANOVA output

Tukey comparisons (KPIV) for three Brands (MINTAB output)

Process capability for KPIV (one brand)

Lab 1: KPIV (mass of antacid tablets)

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Figure 11: I-MR data for Bayer Brand

Figure 12: Normal Probability Plot for Bayer Brand

Figure 13: MINITAB Graphical Summary output for

Bayer Brand

Figure 14: Equal variance tests for the three Antacid Brands (MINITAB output)

Figure 15: Box plots (KPIV) comparing Bayer brand name to Philippine Antacid Brand

Figure 16: MINITAB out put for two sample t-tests

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Figure 17: One way ANOVA (MINITAB) output comparing the US brands and Philippine Brand

Figure 18: Box plots comparing KPIV for three Antacids Brands

For process capability, we specify the LSL to be 3.2 grams and USL to be 3.4 grams. Participants measure KPIV (mass) for one of the brand names with a sample size of 30 tablets. Process stability and normality checks are run before the assessment of process Capability (Cpk)

Figure 19: Process Capability for Bayer Brand name (MINITAB output)

Key conclusions from Lab 1

• Measurement of mass is a stable process

• Mass measurements for all three brand names are normally distributed

• We demonstrate that variances (KPIV) for the three populations are the same

• Two sample t-tests shows that KPIV for Bayer and the Meijers_US brand come from same population

• Two sample t-tests comparing Bayer to the Philippine brand shows that KPIV’s are from different populations

• ANOVA (and Tukey comparisons) confirms the results of two sample t-tests

• Process capability (short term) for the Bayer brand is 2.97

Lab 2: Dealing with defective antacid tablets

In this Lab we explore the use of attribute data. Attribute data is derived by counting the number of tablets that are found to be defective. All tablets used in Lab 1 and Lab 3 and 4 are inspected for chipped, broken or crushed conditions. Typically tablets are damaged due to poor handling. A count of number of defective tablets for each brand is maintained. Total number of tablets used in this study for all brands is also tracked so that proportion defective for all the brands may be computed.

We state (for this Lab) that the expected number of defectives (in the population) should be less than or equal to 0.25 % for all brand names.

The deliverables for this lab are:

• Test each brand name for the claim that proportion defective is less than or equal to 0.25 %

• Can one predict (for the population) if the proportion defective for Bayer brand is the same as that observed for US_Meijers brand name

• Same as above, comparing Bayer vs. Philippine brand

• Can one predict (comparing all three brand names) that one of the brands has an unusually larger or smaller proportion defective?

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Reflections

Reflections in Lab 2 are identical to that in Lab 1. A small knick or a chip is suggested as one the major reasons for outliers detected in Lab 1. Here, the trainer brainstorms with the students on how one would go about validating this hypothesis.

Typical Results in Lab 2

Shown in Figure 20 are one proportion tests for each brand, testing to confirm if the proportion defective for each brand is less than or equal 0.25 %. Failing to reject the null will confirm that our claim is valid.

Similarly two proportion tests to test if proportion defective for Bayer and Philippine brand are derived from the same population is shown in Figure 21.

Lastly a Chi-Square test is run comparing proportion defective for all three brand names. Results are shown in Figure 22.

Figure 20: One Proportion tests (testing for proportion defective > 0.25 %)

Figure 21: Two Proportion tests comparing Bayer vs. Philippine Brand

Figure 22: Chi-Square test comparing, Bayer, US_Meijers and Philippine Brand Antacids

Key conclusions from Lab 2 are:

• We find the claim that damage should be less than or equal to 0.25 % is not true (at 95 % confidence).

• There is no statistical difference between the Meijers and Philippine brand antacid for proportion defective

• Chi-square tests indicate that there is no statistical difference between proportions defective between the three brand names

Lab 3: Comparing two scales for KPIV Lab 2 explored KPIV while Lab 3 extends the experiment to compare (for one Brand name) KPIV measured on two scales (analytical balance). Here we are able to illustrate the application of the paired t-test and correlation tests.

In this Lab, students measure the mass of tablets (typically 10-12) using two analytical balances, keeping track of the sequence. It is important to note that this experiment needs to be completed quickly since the antacids have a tendency to absorb moisture if left exposed in air (a noise source).

Deliverables in this lab are:

• Are the two scales correlated?

• Is KPIV measured dependent on the scale?

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Reflections

The trainer emphasizes the need for using the paired t-test as opposed the two sample t-test in this experiment. Practical situations involving the use of paired t-tests are also discussed. Participants are also asked to consider the effect of exposing the tablets and consequences on data analysis.

Typical Results for Lab 3

The two scales used in this study are referred to as “AND” and “METLER”.

Figure 23: Comparing the “AND” and “Metler” Analytical Balances

Figure 24: MINITAB paired t-test output comparing “AND” & “METLER” scales

Figure 25: MINTAB Box Plot output for paired t-test

Key Conclusions from Lab 3

• The scales are perfectly (positively) correlated and their correlation statistically significant

• KPIV measurements are not dependent on the scale used

Lab 4: KPOV (time for Alka Seltzer to dissolve in aqueous solutions) In an earlier section we pointed out that our definition for the Key Process Output Variable (KPOV) as, time for an Alka Seltzer (or antacid) tablet to dissolve in aqueous solutions.

In dealing with the dissolution process of antacid tablets in aqueous solutions, the rate of chemical reaction is significantly influenced by factors such as temperature, pressure, surface area of the particles and the presence of an acid component. In this lab we explore the effect of temperature on the rate of dissolution of the tablet.

The reaction of Alka Seltzer in water is also exothermic in nature. This implies that one can detect an increase in temperature of the solution during the dissolution process. Hence if one has to treat “temperature” as an independent factor to explore KPOV, it is important to establish the volume of water that will be used in the reaction. The intent is to have enough volume of water whose temperature will not change significantly due to the exothermic process. Students are encouraged to conduct experiments by dissolving Alka Seltzer in, 25, 50, 100 and 200 ml of water, determine KPOV and statistically infer (One way ANOVA with Tukey comparisons) the volume of water that would be used in subsequent experiments (hence the volume of water is a noise factor which can play a significant role at small volume levels). Typically a volume of 100 ml is adequate to carry out each experiment in Lab 4.

Students typically observe that a residue is left behind when Alka seltzer dissolves in water which is normal. Hence it is important to decide on when a tablet is considered to be completely dissolved. Students are encouraged to practice dissolving several tablets and come to a consensus on the “end point” for this dissolution process. We also suggest that more than one person (typically three) monitor KPOV and then allow students to decide to use the mean or median value for data analysis.

To explore the effect of temperature, this lab requires a copious supply for hot water (up to 80 C) and ice. Suggested temperature range is between10 to 65 C. Digital thermometers (good to 0.1 C) are provided to monitor this independent variable. We typically suggest that a minimum of six runs be carried out at each temperature and evaluate KPOV at four set temperature values (say 10, Room temperature around 25 C, 45 and 65 C).

Deliverables in this lab include:

• Is the dissolution process (KPOV) stable?

• Is the data (at all temperatures) normally distributed?

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• Are all brand names equal as far as KPOV is concerned?

• What is Cpk for KPOV?

• What is the prediction model for rate of dissolution as a function of temperature (linear and non-liner models)? How good is the model?

• Validate the model by running an experiment at an arbitrary temperature (selected by the trainer) and comparing it to predictions. What is the Cpk for this run?

• Validate regression assumptions

Reflections

Reflections in this Lab are similar to those in Labs 1 and 2. Frequently students report that data sets are non normal. Typically this can be seen at temperatures greater than 65 C. The trainer requests students to make visual observations of the dissolution process at temperatures in the range 10 to 65 C and compare this to observations at temperatures greater than 65 C. Using these observations it is possible to discuss the change in the mode of dissolution as a “special cause” which can affect tests for Normality (two dissolution mechanisms). Participants are also encouraged to brainstorm an experiment where they can easily demonstrate the effect of pressure on KPOV.

Typical Results in Lab 4

Figure 26: I-Mar Chart for US_Meijers (KPOV) at Room Temperature

Figure 27: Test for Normality for US_Meijers Brand name (KPOV) at Room Temperature

Figure 28: Process Capability for US_Meijers Brand (KPOV) at Room Temperature

Figure 29: One Way ANOVA for KPOV comparing Bayer, US_Meijers and Thai Brands

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Figure 30: Box Plots comparing KPOV’s for Bayer, US_Meijers and Thai brand at Room

Temperature

Figure 31: Regression Output (MINITAB) for Bayer Brand (temperature is the independent variable)

Figure 32: Regression-Fitted line plot for Bayer Brand name (linear fit)

Figure 33: Validating Regression Assumptions

Lab 5: Experiments with treated Alka Seltzer (Antacid) tablets In order to illustrate a one sample t-test with Alka Seltzer (antacid) tablets, we surface treat the tablets to enhance the time it takes to dissolve in water. A thin layer of clear coat (matte finish) is applied on both sides and the tablets allowed to dry. This clear coat (paint) can be purchased from any art store. We state that there is a claim that time for an antacid to dissolve will be greater than 45 seconds. Students run experiments (at room temperature water) with treated samples and perform a one sample t-test to confirm if the samples are derived from a population of tablets with a time to dissolve greater than 45 seconds. Deliverables

• Is the dissolution process stable • Is the data normally distributed • Confirm or refute the claim that time required to

dissolve is greater than 45 seconds Reflections Students are not told that tablets were coated with a clear coat. The trainer probes the class into talking about the root for this increase in dissolution time and turns this discussion into a brainstorming event. Typical Results for Lab 3 are shown below:

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Figure 35: I-MR Charts for Treated Bayer Tablets

Figure 36: Probability plot for treated tablets

Figure 37: MINITAB output for one sample t-test

Figure 38: MINTAB Box plot for one sample t-test

Key Conclusions from Lab 3 are:

• Dissolution process for treated samples is stable

• The data is normal

• The claim is true

Lab 6: Design of Experiments for KPOV The intent of this lab is to build on the learning from the three previous labs. Here we explore the world of “Design of Experiments”. The response variable is stated to be the KPOV (time for the Alka Seltzer tablet to dissolve in aqueous solutions)

We start by exploring a Fractional Factorial design along with data analysis and interpretation of ANOVA and Regression outputs. We follow this experiment fractional with a “Fold over design” to resolve confounding. Following this exercise students explore Response Surface Designs.

The factors that are considered in the Factorial designs are:

• Temperature of the solution

• Surface Area

• Coke concentration

Since the first experiment is a screening (fractional factorial) design, all the factors are explored at two levels. For surface area, students are provided with a pestle and mortar which is used to grind the tablets to a very small size.

A fractional factorial design for this experiment is shown below.

Temperature (deg C) Surface Area Coke Concentration (%)1 1 11 -1 -1-1 1 -1-1 -1 1

This is a resolution three design (shown in coded units) where the main effects are confounded with two factor interactions. There is also a three factor interaction that may be present.

In order to run this experiment, students already know (instructor led lectures) that four runs does not allow for any degree of freedom for the error term. We need a minimum of one extra run to carry out an ANOVA analysis. As a rule of thumb, we instruct that students to run the first set of four experiments (as per the design

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above – keeping in mind to randomize the runs) and replicate the runs which show the highest and lowest response value. With these additional runs, we have two degrees of freedom for the error and ANOVA analysis can be performed.

Typically, we like the factors levels as far apart as possible, say 10 C and 50 C. For surface area, the low setting is taken as un-ground tablet while the high setting is taken as the ground (powder) tablet. For coke concentration we like to choose the low setting as 0 % and high at 30 %.

The fold over for this design is shown below. Note the design below is randomized.

Temperature (deg C) Surface Area Coke Concentration (%)1 -1 1-1 -1 11 1 -1-1 -1 -11 1 11 -1 -1-1 1 -1-1 1 1

This design is free from confounding and it possible to evaluate all the main effects (3), two factor interactions (3) and three factor interaction (1) in nine runs (accommodating for the constant and error term). Since, the earlier design had two replicates, these are used in addition to the above eight runs to complete the analysis. This results in a total of 10 runs also giving the error term two DF’s.

The deliverables for the Factorial design experiments are:

• p-diagram

• Which main effects are significant?

• Are two factor interactions significant?

• Is the only three factor interaction significant?

• Normal probability plot for effects

• Main effects plots

• Interaction plots

• Cube plots

We present the results first for the resolution three design (factional factorial experiment) followed by the results for the Fold Over experiment.

Figure 39 shows the ANOVA output for the fractional factorial design. Since all the factors are significant, it

becomes necessary to carry out a Full factorial or a Fold over design to sort through confounding.

Figure 40, is the ANOVA output for the fold over design where four additional experiments (not to be confused with replicates) have been added to the previous one.

ANOVA output shows that all the main effects, two factor interactions and the only three factor interaction are significant.

Figure 39: ANOVA output for Fractional Factorial Design (note we have added replicates to the base design)

Figure 40: ANOVA output for Fold over design (note we have added replicates)

We use this Lab to demonstrate the application of MINITAB’s DOE graphical capabilities. Figure 41 is the Normal probability plot for effects, Figure 42 is the

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residuals plot, and Figure 43 the main effects plot for the three statistically significant factors, Figure 44 is a plot for the three two way interactions. Figure 45 is a Cube plot representation.

Figure 41: Normal Probability Plot for Effects

Figure 42: Residual Plot for Fold Over Design

Figure 43: Main Effects Plot for Statistically Significant Factors

Figure 44: Interaction plot for Fold over Design

Figure 45: Cube plot for Response (Fold Over Design)

Reflections

The trainer initiates the discussion with the question; can we explain these results from first principles (kinetics of chemical reactions)? Discussion also centers on a firm understanding of the ANOVA output and residual plots. Students take turn in interpreting MINITAB’s graphical outputs including the interaction plots. It is common to see students omit the three factor interaction (intuitively) during DOE analysis and this becomes a teaching moment for the instructor to remind students that one needs to have insights (apriori knowledge) into the system under investigation and when in doubt to include higher order terms. These reflections help in the next Lab where a Response Surface experiment is conducted for two factors at three levels (surface area is not included as a factor since it is practically difficult to get a “mid level” for this factor).

Key conclusions for Lab 6 are:

• Alka seltzer (antacid) system offer a convenient approach to teach DOE techniques

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• All the main effects are statistically significant

• All the two factor interactions are statistically significant

• The three factor interaction is significant

• Residuals are well behaved

• MINITAB’s outputs (graphical) are convenient to represent the results of ANOVA analysis.

Lab 7: Response Surface Analysis for KPOV (Bayer Brand) This lab is an experiment to illustrate the application of Response Surface Designs and analysis. For this lab we have chosen a simple “Central Composite – Face Centered” design (14 runs) where factors are set at three levels. Temperature and Coke Concentration are selected as the factors. A typical design is shown below.

Temperature ( C ) Coke Concentration (%)

65.5 10 32.25 10 32.25 10

-1 10 32.25 20 32.25 0 32.25 10 32.25 10 65.5 0 65.5 20

32.25 10 -1 0

32.25 10 -1 20

The deliverables in this Lab are:

• What is model for Response (KPOV)

• Are the “square” terms significant

• Wire-frame plot for response

We show typical results from this Lab where the students decided to include three replicates at each treatment condition.

Figure 46, is MINITAB’s Regression output for this experiment. This analysis shows that interaction terms and square terms are significant.

Figure 46: Regression output for RSM design

Figure 47: Coefficients for the RSM Model

The model for the dissolution of Alka Seltzer (Bayer Brand) is

temp) conc (coke 0.005 Conc) (Coke 0.063

(temp) 0.012 %) in Conc (coke 2.1-

C) deg in (temp 3.1 - 231 (sec)KPOV

2

2

××+×+

×+×

×=

Figure 48 shows the wire-frame plot for KPOV indicating curvature (square terms in the model)

Figure 48: Surface Contour Plot for KPOV

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REFLECTIONS

Trainer focuses the discussion to the RSM family of designs and the interpretation of the output. Students are encouraged to explore other RSM designs and MINITAB graphical options like contour plots and the use of the Response Optimizer.

LAB 8: PRELIMINARY EVOP EXPERIMENTS FOR KPOV (BAYER BRAND)

Authors have this paper have not fully explored the Alka Seltzer system to be used as a teaching tool for Evolutionary Operations Experiment. In this paper we present our preliminary work on the use of Alka Seltzer system to teach the EVOP technique. In this demonstration we have used the commercially available simplex optimization software called “Evoptimizer” (66). Here we can either choose to minimize, maximize or reach a target for the chosen response. For a detailed account of the EVOP method, readers are referred to the following references (71-72) We have chosen a simple two factor case (temperature and coke concentration) to illustrate the use of simplex optimization procedure. Our objective in this preliminary study is use the simplex optimization to reach a KPOV target. Since we had a reasonable idea (based on previous labs), values for Temperature and Coke Concentration were chosen so that the target would be relative close. We start the process by defining an initial simplex which translates to obtaining KPOV at three different Temperature and coke concentrations. The response values (KPOV’s) are fed into this software tool which then computes a new set of temperature-Coke Concentration pair (X-Y pair) to explore. Experiments are now performed at the suggested X-Y coordinates and KPOV measured. This procedure is continued till the variability in KPOV between two X-Y pair’s are not statistically significant.

Figure 49: Preliminary EVOP Experiment for Bayer

Brand Alka Seltzer (KPOV)

In this paper we show the screen shot from an EVOP experiment where the graph shows trends in KPOV and the coordinates for X-Y are shown in the table above. In a subsequent paper (73) we plan to describe a complete EVOP experiment using the Alka Seltzer system.

Lab 9: Measurement System for KPOV (Destructive Gage R and R) In an earlier section we discussed a variety of hand on experiments that are in vogue for training Six Sigma Green and Black Belts. Hands on experiments for illustrating concepts in MSA fall into two categories:

• For variable response or • For attribute response

The Catapult device, resistance measurements or voltage measurements of batteries are excellent projects to illustrate variable response. For attribute data, several appraisers’ grade possible flaws or defects in a collection of parts which have some good and some defective ones mixed in. % agreement between appraisers is used a measure of Gage R and R. The authors have not come across hands on experiments described in the context of GB or BB training involving the application of MSA for destructive testing. In this lab we chose the response to be the KPOV, which is time for the antacid to dissolve in water. This system is used to illustrate the destructive Gage R and R technique. A detailed account of the destructive Gage R and R method involving nested ANOVA designs is well beyond the scope of this paper, however a we cite one reference are for further reading (74) The basic assumption that we make in this study is that there is no intrinsic compositional or structural difference between tablets (composition, density or porosity). All the variability is assumed to be in KPOV. This is a reasonable assumption to make, given KPIV is found to be a very capable metric (approximately 3). This Gage study involves three operators and ten replicates (sample size =10) per trial and three such trials were conducted. Operators were called in random order to carry out the experiments. Operators initially were coached on the antacid dissolution process and were allowed to try a few samples to measure KPOV (under supervision). Data was analyzed using MINITAB’s menu, “Gage Method – Nested”.

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• Is the Gage adequate to measure KPOV? • What is the component of Reproducibility? • What is the component of repeatability? • What are possible methods for improving Gage

R and R? Reflections A good part of the discussion centers on the homogeneity assumption. Is a high value for Cpk observed for KPIV a sufficient proof for this assumption? Students are encouraged to think of other properties which may have may serve as better metric to justify this assumption. The second part of the discussion is about the observations and how may one go about improving the gage performance. Typical results for this lab are shown in the figures below:

Figure 50: Nested ANOVA Output for Gage R and R

Figure 51: MINITAB’s Graphical Output for Nested Gage R and R

Key Conclusions for this Lab are:

• The Gage R and R is not acceptable

• Tablets and operators are not statistically significant

• Virtually all the contribution is due to repeatability

• Even a higher sample size does not improve Gage R and R (not shown in this study)

• One has to consider an alternative (more sensitive) Gage for KPOV.

An alternative method based on volumetric measurement of Carbon di-Oxide is currently under investigation and results from this Gage will be reported in a future communication.

CONCLUSIONS

This paper describes a series of modular experiments based on a simple chemical system consisting of Alka Seltzer (antacid), water and coke. Using this system we have been able to illustrate the application of most statistical tools taught during Six Sigma training Green Belt and Black Belt training.

The basis for all these experiments (Labs) is the Kolb’s adult learning model augmented by constant and consistent reflections provided at the end of each laboratory. Reflections are further strengthened by participants preparing a poster presentation at the end of each lab

These experiments originally conceived in the kitchen, have been easily translated into the training room. Experiments can be conducted virtually any where in the world with minimum expense and no chemical safety hazards to contend with.

The authors are exploring extensions of the Alka Seltzer experiments to design more complex DOE’s and a novel Measurement System for KPOV.

Our hope is that, more creative but simple experiments to illustrate advanced concepts in statistics will be explored by the Six Sigma Training community (Master Black Belts) and reported in the open literature

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26

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CONTACT

Amurthur Ramamurthy of Visteon Automotive Systems may be contacted either at aramamur@visteon.com or at ram320@yahoo.com.

Arlette Reyes of Visteon Philippines Inc, Philippines, may be contacted at areyes25@visteon.com or at arletteareyes@yahoo.com.

ACKNOWLEDGEMENT

Authors would like to thank Visteon Corporation for presenting opportunities to bring Six Sigma Green belt education at several Asian sites. We would like to acknowledge the efforts of several groups of students who have contributed to our experiences that we have shared in the form of various experiments in this paper.

The readings from various works on adult learning, particularly the work of Dr. David Kolb has helped us both to understand adult learning styles and the art and practice of reflection.

APPENDIX

ILLUSTRATION OF THE CENTRAL LIMIT THEOREM IN THE ABSENCE OF APPROPRIATE COINS

The authors of this paper have experienced the non availability of coins with the year marked on them in some Asian countries. Importing US coins (pennies) into some Asian countries is by no means a trivial matter. Authors describe here a novel scheme to overcome the above constraints. The only requirement for this method is the availability of ½” to 1” (1/8 to 1/16” thick) size circular plastic disks on which a number can be scribed. Poker chips if available will do the job. The idea here is to scribe these plastic disks with “years” marked on them, just like what would appear on a coin. The method to derive the “year” that is to be scribed on each disk is described in the form of a flowchart below.

Shown below are two pictures of plastic disks, one for the distribution of “individuals” and the other derived from averages of five.

Distribution of Individuals

Distribution of Averages (n=5)

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MINITAB Output for Individuals (using disks)

MINITAB Output for Averages (using disks) Histograms and statistics for the above is described below:

Data Sets In this section we include few data sets for the reader to get a feel for the Alka Seltzer (antacid) Labs. The following data sets have been included:

• Lab 1 : KPIV (mass of antacid tablets)

• Lab 3 : Comparing two scales for KPIV

• Lab 4 : KPOV (comparing time for antacid to dissolve in room temperature water)

• Lab 6 : Design of Experiments with Antacid water system (Fractional and Fold Over Designs)

Philippine (gr) US-Meijer (gr) Bayer (gr)3.2957 3.2531 3.24893.2847 3.2511 3.26473.3067 3.2376 3.2473.2803 3.2484 3.26393.2827 3.2761 3.25473.3061 3.2678 3.2323.2751 3.2713 3.26583.2855 3.2643 3.25863.3276 3.2595 3.25623.323 3.2361 3.24123.2904 3.2463 3.26493.286 3.2368 3.22283.2806 3.2398 3.22663.2951 3.2591 3.25793.274 3.2849 3.2743

3.26033.24

3.24173.23443.24973.22283.24413.22573.23223.24783.27163.21883.2583.2471

Lab 1: KPIV data for Three Brand Names

Lab 3: Comparing two Scales for KPIV

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Lab 4: Comparing KPOV for US_Meijers, Thai and Bayer Brand Antacids at room temperature water

Lab 6: Design of Experiments with Antacid water system (Fractional Factorial Design)

Lab 6: Design of Experiments with Antacid water system (Fractional Factorial Fold-Over Design)