Six Sigma Black Belt Course Work
The following links provide an idea about the content of each course of the program. Please be aware that course content is subject to change, according to the criteria of the department and the instructor that offers the course; nevertheless, you can expect those changes to be minimal.
- IEE 570 Advanced Quality Control
- IEE 572 Design of Engineering Experiments
- IEE 578 Regression Analysis
Alternately:
STP 530 Applied Regression Analysis or
- IEE 581 Six Sigma Methodology
- IEE 585 Six Sigma Methodology Capstone Experience
QBA 525 Applied Regression Models
For the IEE 598 Six Sigma Methodology Capstone Experience course, the student works on a real industrial or business problem, usually obtained in his/her workplace, and reports project progress during the semester.
IEE 570 ADVANCED QUALITY CONTROL
Textbook & Materials
Introduction to Statistical Quality Control, 5th edition, by D.C. Montgomery, John Wiley & Sons, New York, 2005
Modern data analysis requires use of the computer. The software package utilized in this course is Minitab. Other statistical packages can often be substituted and may be used for your homework, but you should be able to interpret Mintab output. You will be asked to interpret Minitab output for exams.
Calculator
Reference/Review
Applied Statistics and Probability for Engineers, 3rd edition, by D.C. Montgomery, G.C. Runger, John Wiley & Sons, New York, 2003
About the Course
This course covers topics in quality control that have been widely used in many industries (including service industries). Specifically, it focuses on control charts as the core for statistical process control. Basic and more advanced charts are presented. Also, special applications (such as multiple stream processes and integration with closed-loop control) are presented. The objective is for students to understand the concepts, operation, and role of these techniques.
Prerequisite: one previous course in engineering statistics. Students do not need previous exposure to quality control, but introductory knowledge of hypothesis testing, confidence intervals, probability, and some familiarity with matrix algebra is required.
Requirements
The final grade in the class is determined by two mid-term examinations (30% each) and a final examination (40%).
Recommended homework exercises are provided. These are not submitted nor graded. A minimum number of exercises are assigned; more exercises should be worked as necessary to master the material. Additional exercises will be presented in class. Students may be requested to present solutions. Students are encouraged to work suggested homework exercises in groups. All work other than homework is expected to be a student’s own. Academic integrity is expected.
Exams are open book/notes and emphasize the interpretation of computer output and model-building concepts. The final exam is comprehensive and will require a calculator.
|
Week |
Topic |
Text Reference |
Homework Problems |
|
1 |
Introduction to quality control |
Chapter 1 |
|
|
2 |
Review of basic statistics |
Chapter 2 and 3 |
Select based on your background |
|
3 |
Introduction to statistical quality control |
Chapter 4 |
4-5, 4-11, 4-21, 4-32 |
|
4 |
Control charts for variables, Xbar, R, S, and Individuals charts |
Chapter 5 |
5-3, 5-11, 5-13, 5-52, 5-61 |
|
5 |
Control charts for attributes, P and U charts |
Chapter 6 |
6-1, 6-9, 6-65, 6-41, 6-56 |
|
6 |
Process and measurement capability analysis |
Chapter 7 |
7-4, 7-10, 7-19, 7-28, 7-42 |
|
7 |
Process and measurement capability analysis |
|
|
|
8 |
Time-weighted control charts, CUSUM and EWMA |
Chapter 8 |
8-4, 8-13, 8-19 |
|
9 |
Short production runs, multiple streams |
Chapter 9-1 to 9-5 and 9-8 to 9-9 |
9-1, 95, 9-17 |
|
10 |
Overview of other methods-tool wear, change points, nonparametrics |
|
|
|
11 |
Multivariate control charts, |
Chapter 10 |
10-1, 10-10, 10-15, 10-22 |
|
12 |
Multivariate control charts |
|
|
|
13 |
Integration of SPC and closed-loop control |
Chapter 11 |
11-3, 11-6, 11-7 |
|
14 |
Integration of SPC and closed-loop control |
Chapter 14 |
|
|
15 |
Review, last class |
|
|
|
|
Final Exam |
|
|
IEE 572 DESIGN OF ENGINEERING EXPERIMENTS
Textbook & Materials
Design and Analysis of Experiments, 6th edition, by D.C. Montgomery, John Wiley & Sons, New York, 2005
Student version of Design-Expert V6 software
Student Solutions manual for the textbook
Computer software packages (Design-Expert, Minitab) to implement the methods presented will be illustrated extensively; students will have opportunities to use it for homework assignments and the term project. The Design-Expert computer software package can be used to solve many of the problems in the textbook.
Course materials are available from the ASU Bookstore or directly from the publisher. All three required items are available as a bundled package; see the Wiley website (http://www.wiley.com/WileyCDA/) for details.
About the Course
All experiments conducted by engineers and scientists are designed experiments; some of them are poorly designed, and others are well-designed. Well-designed experiments allow you to obtain reliable, valid results faster, easier, and with fewer resources than with poorly-designed experiments. A well-designed experiment can lead to reduced development lead time for new processes and products, improved manufacturing process performance, and products that have superior function and reliability.
This is a basic course in designing experiments and analyzing the resulting data. It is intended for engineers, physical/chemical scientists and scientists from other fields such as biotechnology and biology. The course deals with the types of experiments that are frequently conducted in industrial settings.
The course objective is to learn how to plan, design, and conduct experiments efficiently and effectively, then analyze the resulting data to obtain objective conclusions. Both design and statistical analysis issues are discussed. Opportunities to use the principles taught in the course arise in all phases of engineering and scientific work, including technology development, new product design and development, process development, and manufacturing process improvement. Applications from various fields of engineering (including chemical, mechanical, electrical, materials science, industrial, etc.) will be illustrated throughout the course.
The course schedule and outline contains assigned reading topics from the textbook and suggested homework problems. In addition to the textbook reading assignments, students may also want to read some of the supplemental text material for each chapter on the publisher-maintained webpage [link: http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471733040.html] for the book. See the text preface for more details.
Prerequisite: basic working knowledge of statistical methods. A formal course in engineering statistics at the level of ECE 380 is the official prerequisite, but this specific course is not essential. Students will need to know how to compute and interpret the sample mean and standard deviation, have previous exposure to the normal distribution, be familiar with the concepts of testing hypotheses (the t-test, for example), constructing and interpreting a confidence interval, and model-fitting using the method of least squares. Most of these ideas will be reviewed as they are needed.
|
Class |
Topic |
Text Reference |
Suggested Exercises |
|
1 |
Introduction to DOX, begin review of basic statistical concepts |
Chapters 1 & Chapter 2 (Sections 2-1 through 2-4) |
2-5, 2-12 (work part c using a normal prob. plot), 2-15 |
|
2 |
Continue statistics review; the t-test and confidence intervals |
|
|
|
3 |
Introduction to the analysis of variance (ANOVA) |
Chapter 3 (Sections 3-1, 3-2, and 3-3) |
3-4, 3-6, 3-8 |
|
4 |
Some practical aspects of planning experiments |
Suggested reading: Coleman, D. E. and Montgomery, D. C. (1993), “Planning for a Designed Industrial Experiment”, Technometrics 35(1), pp. 1-12. Also see the supplemental text material |
|
|
5 |
More about ANOVA; multiple comparisons, residuals and model adequacy checking |
Sections 3-4, 3-5, and 3-6 |
3-1, 3-3 |
|
6 |
More about ANOVA; checking model assumptions, the Box-Cox method |
Chapter 15, Section 15-1.1 |
|
|
7 |
Choice of sample size in designed experiments |
Section 3-7 |
3-15, 3-17 |
|
8 |
The randomized complete block design (RCBD) |
Chapter 4 (Section 4-1) |
4-2, 4-5, 4-6 |
|
9 |
RCBDs, Latin squares, etc. |
Section 4-2 |
|
|
10 |
Introduction to factorial designs |
Chapter 5 (Sections 5-1, 5-2, and 5-3) |
5-5, 5-6 |
|
11 |
Factorials, continued |
Sections 5-4, 5-5, 5-6 |
5-17, 5-21 |
|
12 |
2k factorial designs, introduction |
Chapter 6 (Sections 6-1 through 6-7) |
6-1, 6-5 |
|
13 |
2k factorial designs, continued |
|
6-6 |
|
14 |
2k factorial designs, continued |
|
6-18, 6-19, 6-26, 6-27 |
|
15 |
Quiz 1 |
|
|
|
16 |
Blocking and confounding in two-level factorial designs |
Chapter 7 (Sections 7-1 through 7-6) |
7-1, 7-4, 7-7, 7-9 |
|
17 |
Blocking and confounding in the 2k, continued |
|
|
|
18 |
2k-p fractional factorial designs, introduction |
Chapter 8 (Sections 8-1 through 8-6) |
8-3, 8-4, 8-6 |
|
19 |
2k-p fractional factorial designs, continued |
|
8-24 |
|
20 |
2k-p fractional factorial designs, continued |
|
8-28 |
|
21 |
2k-p fractional factorial designs, continued; Second Project Report Due |
|
8-27 |
|
22 |
2k-p fractional factorial designs, continued |
|
8-5 |
|
23 |
2k-p fractional factorial designs, continued |
|
8-33 |
|
24 |
Response surface methods and designs (an overview) |
Chapter 11 (Sections 11-1 and 11-3) |
11-8 |
|
25 |
Quiz 2 |
|
|
|
26 |
Random factors in experiments |
Chapter 13, Section 13-1 |
13-1, 13-4 |
|
27 |
Random factors in factorial experiments, mixed models |
Section 13-2, 13-3, 13-5, 13-6 |
13-9, |
|
28 |
Nested & split-plot designs |
Chapter 14, Sections 14-1, 14-2 and 14-3 |
14-1, 14-3 |
|
29 |
Nested and split-plot designs |
Chapter 14, Sections 14-4 and 14-5 |
14-19 |
Grading
Your grade in the course will be determined by the two quiz scores (25% each), the final exam (25%) and the term project (25%).
Term Project
The term project is performed in teams of up to three people. The project consists of planning, designing, conducting and analyzing an experiment, using appropriate DOX principles. The major requirement is that the experiment must involve at least three design factors. Each of the interim reports requires information about the problem, the factors, the responses that will be observed, and the specific details of the design that will be used. Students will be given feedback on these reports that should help them complete the final experiment and analysis, and prepare the final report. Two written interim project reports are required, along with a final written project report. Due dates are on the course outline above.
The context of the term project experiment is limited only by the imagination. In previous classes, students have conducted experiments directly connected to their own research projects. The project is a nice way to get extra-mileage from this course; it can help students finish their research sooner. For industrial participants or those with an internship in industry, a project that they are involved with at work is a good possibility. If all else fails, a “household” experiment may be conducted, such as how does varying factors such as type of cooking oil, amount of oil, cooking temperature, pan type, brand of popcorn, etc. affect the yield and taste of popcorn). However, your instructor may have seen all the possible popcorn experiments than can be run, so be creative. The textbook web site has several examples of term projects from previous classes. These will give you a good idea about the types of experiments that have been conducted by previous groups of students, and how their reports were prepared. Some of these projects may be selected for class discussion/presentation, if time permits, and/or included on the department website. If you are willing to donate your project, please submit an electronic copy of the final report to your instructor.
IEE 578 REGRESSION ANALYSIS
Textbook
Introduction to Linear Regression Analysis, 3rd edition, by D.C. Montgomery, E.A. Peck, and G.G. Vining, John Wiley & Sons, New York, 2001
Reference/Review
Engineering Statistics, 3rd edition, by D.C. Montgomery, G.C. Runger, and N.F. Hubele, John Wiley & Sons, New York, 2004
About the Course
This is a basic course in regression analysis and model-building for engineers and physical/chemical scientists. It specifically focuses on building empirical models for relating an observed response to one or more predictor or regressor variables. Regression methods based on linear least squares are the primary technique presented, although some attention will be given to other parameter estimation techniques.
Modern regression analysis requires use of the computer. The software package utilized in this course is Minitab. Other statistical packages may be used for your homework, however, students will need to interpret Mintab output for exams. Additionally, the class will also illustrate some SAS output for features not supported by Minitab; students will not be required to learn SAS.
Prerequisite: one previous course in engineering statistics. Students do not need previous exposure to regression, but introductory knowledge of hypothesis testing, confidence intervals, and familiarity with matrix algebra is required.
Grading
The final grade is determined by two mid-term examinations (50%), a final examination (25%), and a term project (25%).
Requirements
Recommended homework exercises are provided with solutions. These are not submitted nor graded. A minimum number of exercises are assigned; more exercises may be necessary to master the material. Additional exercises will be presented in class before exams to show you typical questions and solved in class.
Exams are open book/notes and emphasize the interpretation of computer output and model-building concepts. A calculator is needed. The final exam is comprehensive.
The term project is a final data analysis that requires use of the methods presented throughout the term (details are provided below). Students are encouraged to work suggested homework exercises in groups. Other than the homework, the work is to be your own. Academic integrity is expected.
Term Project
The term project consists of finding a real-world application of regression model-building, then fitting and checking the adequacy of the model. Students must submit a report summarizing their model-building approach and illustrating the validity of the chosen model. The data set must be “real”; that is, you cannot use data from a statistics textbook—or some other source—where it is highly likely that the author fabricated the data.
Good sources of data include research projects currently being conducted in your department, data collected as part of thesis and dissertation research, data from a work environment (if not a full-time student), or data published in a journal article in which the authors either did not do any regression modeling or they did not do it very well. There are many examples of the latter situation, so journals are a fairly nice source of data, if all else fails. Data sets must be discussed with the instructor before starting the project. Generally, the data set should include at least five candidate regressor variables (more are preferred). Some categorical regressors that require indicator variables would make the project more interesting, but these are not required.
|
Class |
Topic |
Text Reference |
Homework Problems |
|
1 |
Introduction and introduction to computer software |
Chapter 1 |
|
|
2 |
Least squares fitting for simple linear regression |
Chapter 2 (through Sec. 2.8) |
2.1, 2.2, 2.4, 2.5, 2.12 |
|
3 |
More about the simple linear regression model, predictions, correlation |
Sec. 2.9, 2.10 |
2.10, 2.17 |
|
4 |
Multiple regression, least squares and inference, use of computer software |
Chapter 3 (through Sec. 3.4) |
3.1, 3.5, 3.10, 3.15, 3.16 |
|
5 |
Multiple regression, fitting and inference continued, predicting new responses—interpolation vs. extrapolation |
Sec. 3.5, 3.6 |
3.6 |
|
6 |
Model adequacy checking; residuals and plots, outliers, detection and treatment, lack of fit |
Chapter 4 |
4.1, 4.4, 4.7, 4.18, 4.22 |
|
7 |
Transformations for model inadequacy |
Chapter 5 |
5.1, 5.2, 5.16 |
|
8 |
Influential observations and leverage |
Chapter 6 |
6.5, 6.12, 6.15 |
|
9 |
Mid-Term Examination 1 |
|
|
|
10 |
Building regression models; adding polynomial terms |
Chapter 7, Sec. 7.1, 7.2 & 7.4 |
7.2, 7.3, 7.6, 7.7, 7.19, 7.20 |
|
11 |
Building regression models; adding polynomial terms-continued |
|
|
|
12 |
Polynomials, and regression models with indicator variables |
Chapter 8, Sec. 8.1 & 8.2 |
8.3, 8.4, 8.5, 8.13 |
|
13 |
Variable selection methods |
Chapter 9 |
9.1, 9.2 (use all regressors as candidates) |
|
14 |
Variable selection methods-continued |
|
|
|
15 |
Multicollinearity in regression, diagnostics and ridge regression |
Chapter 10 (through Sec. 10.5.4) |
10.6, 10.7 |
|
16 |
Mid-Term Examination 2 |
|
|
|
17 |
Validating regression models, overview of robust fitting of regression models |
Chapter 15, |
15.1, 15.9 |
|
18 |
Nonlinear regression methods overview |
Chapter 12 |
12.6, 12.7 |
|
19 |
Projects Due |
|
|
|
20 |
Last day of class, Final Exam to be scheduled during exam week |
|
|
IEE 581 Six Sigma Methodology Seminar
Textbooks
George, M.L. (2002). Lean Six Sigma: Combining Six Sigma Quality with Lean Production Speed. McGraw-Hill, New York, NY.
Snee, R.D. and Hoerl, R.W. (2003). Leading Six Sigma: A Step-by-Step Guide Based on Experience with GE and Other Six Sigma Companies. Financial Times Prentice Hall, Upper Saddle River, NJ.
2004 Business Criteria for Performance Excellence, published by the Baldrige National Quality Program. Individual copies are available at no cost from BNQP. Information on obtaining individual copies of the criteria free of cost can be found at the following website: http://baldrige.nist.gov/Business_Criteria.htm
|
Class |
Topic |
|
1 |
Introduction to Six sigma, course overview, the DMAIC process |
|
2 |
Introduction to Six sigma, course overview, the DMAIC process |
|
3 |
Define, including project selection and management, project failure modes |
|
4 |
Define, including project selection and management, cost of quality |
|
5 |
Define, including project selection and management, financial impact of projects |
|
6 |
Measure |
|
7 |
Measure |
|
8 |
Analyze; applications of basic statistical tools |
|
9 |
Analyze; dealing with categorical data |
|
10 |
Improve |
|
11 |
Improve |
|
12 |
Control |
|
13 |
Teams; fundamentals, dynamics, leadership, facilitation |
|
14 |
Teams; fundamentals, dynamics, leadership, facilitation |
|
15 |
Making presentations to non-statisticians |
|
16 |
Making presentations to non-statisticians |
|
17 |
Mid-term exam review, questions, project planning discussion |
|
18 |
Mid-Term Exam |
|
19 |
The history of six sigma |
|
20 |
Design for six sigma |
|
21 |
Design for six sigma |
|
22 |
Lean and six sigma |
|
23 |
Lean and six sigma |
|
24 |
Six sigma in service and transactional businesses |
|
25 |
Six sigma in service and transactional businesses |
|
26 |
Applications of categorical data analysis in transactional businesses |
|
27 |
Quality management systems and six sigma |
|
28 |
Quality management systems and six sigma |
|
29 |
Summary & review |
|
30 |
Final Exam |
Reading & Resource List
Books
Hoerl, R.W. and Snee, R.D. (2002). Statistical Thinking: Improving Business Performance. Duxbury, Pacific Grove, CA.
Pyzdek, T. (1999). “The Complete Guide to Six Sigma”, QA Publishing, L.L.C., Tucson, AZ.
Pyzdek, T. (2003). The Six Sigma Project Planner: A Step-by-Step Guide to Leading a Six Sigma Project through DMAIC. McGraw-Hill, New York, NY.
Articles
Hoerl, R.W. (2001). “Six Sigma Black Belts: What Do They Need to Know? (With discussions and response)”. Journal of Quality Technology 33(4), pp.391-435. (This article is free to the general public on the journal's site: http://www.asq.org/pub/jqt/past/vol33_issue4/)
Hahn, G.J.; Doganaksoy, N.; and Hoerl, R. (2000). “The Evolution of Six Sigma”. Quality Engineering 12(3), pp. 317-326.
Anderson-Cook, C. M., Editor (2005). Special Issue, “New Directions for Six Sigma in the New Millennium”, Quality and Reliability Engineering International, Vol. 21, No. 3, April. This issue contain several useful articles on various aspects of six sigma methodology and practice. It may be found at the journal website, www.interscience.wiley.com.
IEE 585 Six Sigma Methodology Capstone Experience
Course participants will develop and complete a Six Sigma Black Belt project. The project will be typical of projects used to certify Six Sigma black belts in industry, and will involve both oral and written presentation of results. The project expectations are as follows:
- Must use the DMAIC approach
- Must demonstrate effective use of the appropriate statistical tools
- Must demonstrate payback or bottom line business impact to the sponsor
- Must demonstrate other Six Sigma skills as appropriate (project management, leadership, presentation, etc.)
- Must be written in an acceptable manner (see guidelines)
- Must be presented orally to the sponsor.