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STA 5126: Applied Statistics Term Project Instructions for Six Sigma, Study Guides, Projects, Research of Statistics

Florida State University (FSU)Statistics

The instructions for a term project in the applied statistics course (sta 5126) focused on six sigma. The project consists of five assignments, each with specific goals and deadlines. Students are required to clarify their project goals, identify measurable variables, collect and analyze data, and improve processes. The document also encourages students to provide feedback for improvement.

Typology: Study Guides, Projects, Research

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STA 5126: Applied Statistics
Section 1: Doug Zahn
TERM PROJECT INSTRUCTIONS
Fall 2003
to hear is to forget
to see is to remember
to do is to understand
(old proverb, sometimes attributed to Confucius)
Table of Contents
Page Number of
observations required
A. General instructions 2
B. An overview of the term project 3
C. What is Six Sigma about? 4
D. Project Assignment 1: Goals and Computer Information 5 5
Due: September 8, 2003 by 1:25 p.m.
E. Project Assignment 2: Define 7 0
Due: September 22, 2003 by 1:25 p.m.
F. Project Assignment 3: Measure 8 15
Due: October 13, 2003 by 1:25 p.m.
G. Project Assignment 4: Analyze 9 0
Due: October 29, 2003 by 1:25 p.m.
H. Project Assignment 5: Improve 11 10
Due: November 12, 2003 by 1:25 p.m.
I. Project Assignment 6: Control 12 10
Due: December 1, 2003 by 1:25 p.m.
J. Project Assignment 7: Oral Report 13 0
Due: December 1, 2003. In class.
Acknowledgments and a Request
I gratefully acknowledge the many contributions that previous students and Teaching Assistants have made to the
Term Project Instructions. Contributions by Karen Kinard and Nancy Davis have been especially valuable.
In the spirit of systematic improvement, please tell me of any places in these instructions where you see room for
improvement: typos to fix, parts to clarify, instructions that could be shortened without loss of clarity, new topics
to address, etc.
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STA 5126: Applied Statistics

Section 1: Doug Zahn

TERM PROJECT INSTRUCTIONS

Fall 2003 to hear is to forget to see is to remember to do is to understand (old proverb, sometimes attributed to Confucius) Table of Contents Page Number of observations required A. General instructions 2 B. An overview of the term project 3 C. What is Six Sigma about? 4 D. Project Assignment 1: Goals and Computer Information 5 5 Due: September 8, 2003 by 1:25 p.m. E. Project Assignment 2: Define 7 0 Due: September 22, 2003 by 1:25 p.m. F. Project Assignment 3: Measure 8 15 Due: October 13, 2003 by 1:25 p.m. G. Project Assignment 4: Analyze 9 0 Due: October 29, 2003 by 1:25 p.m. H. Project Assignment 5: Improve 11 10 Due: November 12, 2003 by 1:25 p.m. I. Project Assignment 6: Control 12 10 Due: December 1, 2003 by 1:25 p.m. J. Project Assignment 7: Oral Report 13 0 Due: December 1, 2003. In class. Acknowledgments and a Request I gratefully acknowledge the many contributions that previous students and Teaching Assistants have made to the Term Project Instructions. Contributions by Karen Kinard and Nancy Davis have been especially valuable. In the spirit of systematic improvement, please tell me of any places in these instructions where you see room for improvement: typos to fix, parts to clarify, instructions that could be shortened without loss of clarity, new topics to address, etc.

A. GENERAL INSTRUCTIONS

Following are general instructions for all work submitted in response to the Term Project Instructions:

  1. All work is to be typed, double spaced on 8.5” x 11” paper using at least 1.0” margins and 12 point or larger type.
  2. Put your name, the date and the title of the assignment on the cover page of each project assignment you submit. Do not put any additional information on this cover page.
  3. All figures and graphs are to be computer-drawn. Label each as “Figure 1”, “Figure 2”, etc. and refer to it in the text as “See Figure 1”, “See Figure 2”, etc. Each figure is to have  a complete title that stands alone and describes what is in the figure,  its axes labeled, and  the source of the data identified. Treat all tables in this way also, referring to them in the text as “See Table 1”, “See Table 2”, etc. Either put your figures and tables in the text, with the text wrapped around them, or put “Insert Table 1 about here” in the text, on its own line, and present all the tables and figures at the end of the document.
  4. Organize your answers in numbered and lettered paragraphs corresponding to the number and letter of the questions being answered. It is critical that you do this so that your work can be accurately graded.
  5. Staple or bind your pages together. Paper-clipped, folded, or loose papers run the risk of being lost or misplaced. Do not submit your work in those ways.
  6. Number all your pages after the cover page. Put the number in the upper right corner of the page. The cover page is page 1.
  7. Use complete sentences and questions. Check your spelling and grammar. Errors in these areas will cost you points in this course and will compromise your credibility in the working world.
  8. Thank you for submitting all your work in the above format. I will be able to give you higher quality feedback on this work than if you do not follow these instructions.
  9. Late work is not professional. A penalty of 5% per business hour or fraction thereof late will be assessed on all project work and on all homework. Use your resources to get all work in on time. Computer problems do not count as emergencies.
  10. Consequences of not following instructions: Not typed - Not double-spaced - English errors -1 per 2 English errors (-10 maximum on each project part) Answers not numbered corresponding to questions - Pages not all numbered - Incorrect cover page - Tables, graphs not completely labeled - Not following other aspects of instructions: comparable consequences

Free Review Opportunity : I will give you coaching with a 24-hour turn-

around time during weekdays on project components (all or part of what is

due) if you give me a draft at least 48 weekday hours before the due date. I

will do my best to catch all errors and I don’t guarantee I will catch all of them.

C. WHAT IS SIX SIGMA ABOUT?

The course will be organized around a semester-long Six Sigma project.

A Six Sigma project is “a highly disciplined and statistically-based approach for

removing defects from products, processes, and transactions, involving everybody

in the corporation…” (Hahn, Hill, Hoerl, and Zinkgraf, 1998). A “defect” is an

undesired outcome of the current process.

The initiative focuses on reducing the number of defects by first identifying

opportunities for defects. The next step is to reduce the number of defects

occurring. The goal of Six Sigma initiatives is fewer than 3.4 defects per million

opportunities.

Six Sigma improvement projects follow a five-step process: Define, Measure,

Analyze, Improve, and Control (DMAIC). Following is a brief description of the

steps involved in the process.

 Define – Select the area that you want to address. Identify the ultimate goal

of the improvement, as distinct from interim measures of it. Identify the

problem that you intend to address. Identify the process that the problem

relates to. Identify what results you want to achieve in the process. Assess the

process to see if it has the potential to produce these results. Assess the

resources available to you to modify the process, and determine if they are

sufficient to produce the desired results.

 Measure – Select the appropriate responses (the “Y’s”) to be improved, based

on customer inputs and other considerations (such as product yield), ensure

that they are quantifiable, and that we can accurately measure them.

Determine what is unacceptable performance (i.e., a “defect”). Gather data to

gauge the capability of your measurement process and the utility of the data it

produces. (also measure x’s)

 Analyze – Gather preliminary data to assess current performance. Analyze the

preliminary data to document current performance (baseline process

capability), and also to begin identifying root causes of defects (i.e., the “X’s”,

or independent variables), and their impact and act accordingly.

 Improve – Determine how to intervene in the process to significantly reduce

the defect levels. Several rounds of improvements may be required.

 Control – Once the desired improvements have been made, put a system in

place to ensure the improvements are sustained, even though significant

resources may no longer be focused on the problem

(Based on Hahn, G.J., Hill, W.J., Hoerl, R.W., and Zinkgraf, S.A., (1997), The Impact

of Six Sigma Improvement: A Glimpse into the Future of Statistics, The American

Statistician, 53 (3), 208-215.)

http://www.kwtunnell.com/IMAGES/ronsnee_3.doc is the location of another discussion of the big picture by Ron Snee. Case studies of Six Sigma on the web sites of consulting firms: http://www.psteering.com/case_studies/default.html, http://www.sixsigmaqualtec.com/Cases/transactional.html#insurance, http://www.gemedicalsystems.com/prod_sol/hcare/resources/library/, are 3 of approximately 12,600 sites found by Google when I searched on six sigma case studies applications.

_____________________

PROJECT ASSIGNMENT 1, Part B: COMPUTER AND SOFTWARE

QUESTIONNAIRE

Name _________________ Major _______________ DUE: 1:25 p.m., September 8,

1. What level of mastery do you have on the following computer applications?

(Check one)

None Heard of it Can use it Can explain

it Word processing software

( Word, WordPerfect, etc .)

Spreadsheet programs

( Excel, Lotus, etc .)

Statistical operations software

( MINITAB,

SAS, SPSS, etc.)

e-mail

Use of the

INTERNET

2. Academic information:

A. What level mathematics have you completed?

________________________________

When? _______________________________________

B. Have you had any previous statistics course(s) in high school or

college? __________

If so, please name the course(s). ____________________________________

When? ________________________________________________

What statistical topics do you recall from this work well enough to be

able to do or to explain?

____________________________________________________________________

3. What is the e-mail address you prefer to use? __________________________

E. PROJECT ASSIGNMENT (PA) 2 : DEFINE

DUE: September 22, 2003 by 1:25 p.m. 70 points The point value of each question is in parentheses in front of it. (5) 1. What process have you chosen to investigate? What opportunities for improvement do you see in this process? Why is it important to address these opportunities for improvement? (20) 2. Voice of the customer: (4 points each) A. Who is one customer of this process (other than yourself)? B. Identify at least one measurable process output variable (Y-variable) of particular interest to you and your customer. This is a variable that can be measured on each cycle of your process. C. Get a baseline measurement of this Y-variable by measuring it at least 5 times D. What is your customer’s specification for this Y-variable? E. Do a Stakeholder Analysis Commitment Chart for your project. Discuss what you have learned from the construction of this chart and what it shows. How is this information of use in guiding your actions on this project? (20) 3. (2) A. Specify the beginning and ending of one cycle of the process you are investigating. Define your cycle short enough (e.g., 1 day) so that you can observe at least 5 cycles for PA 2 (Define), 15 for PA 4 (Measure), 10 for PA 6 (Improve), and 10 for PA 7 (Control). (4) B. Describe in words what is done in one cycle of your process. Describe the activities in the process, not the measurements you will be making. (10) C. Draw a flowchart of one cycle of your process, starting with your beginning point and stopping with your ending point. Make sure your flowchart contains all paths from the beginning to the end of the process and that there are no dead ends in the middle of the flowchart. (4) D. Do a SIPOC analysis of your process.

  1. (5) A. From the flowchart, identify at least two measurable input or process variables (X-variables) under your personal control. These are two variables that can be measured on each cycle of your process. Measure these variables also while you are getting your baseline measurement on your Y-variable. (10) B. Explain the relationships that you hypothesize to exist between your X- and Y-variables.

(5) C. Submit a spreadsheet containing all data collected to date (the “Define data”).

  1. (5) Determine the resources that you have available and are willing to use for the project. What limitations have been placed (by you or by other parties) on this project? (There are limits here, given all the rest that is going on in your life. What are they?)

F. PROJECT ASSIGNMENT 3: MEASURE

DUE: October 13, 2003 by 1:25 p.m. 40 points The questions are worth 10 points each.

  1. Operationally define how you will measure the Y-variable and X-variables you named in Project Assignment 3 in a way that assure that “all data collectors measure a characteristic in the same way.” Develop and present data collection forms that you will use. Hoerl-Snee Section 5.3 (pp. 141-152) may be helpful here.
  2. Validate your measurement system. Describe any steps you have taken here in a way that addresses concerns that your customer(s) may have about the  accuracy,  precision and  stability of your measurement system.
  3. Begin the data collection. Collect data for at least 15 cycles (the “Measure data”). Keep a data collection diary (field diary) of special or unusual events that occurred while you were collecting your data. A. Submit your diary as an appendix to this assignment. B. Submit a spreadsheet containing all data collected to date.
  4. “Continue improving measurement consistency.” Describe your activities in this area, indicating how your measurement process was refined during the collection of the Measure data. (Quotes indicate material quoted from Rath & Strong’s Six Sigma Pocket Guide .)

Regression Analysis Worksheet for Question 6 of Project Assignment 4:

Analyze

Do a multiple regression analysis using all the data you have collected to date on

your response variable (y) and at least two predictor variables (x’s). Do the

following steps:

a. Get to know your data.

i. Plot the histogram for all data to date for each variable. Do a

box plot for each variable. Are there any outliers in your

histograms? If so, what will you do with them?

ii. If your data are collected sequentially in time, do an individual

control chart plot for each variable. What do you see in these

plots? (e.g., process in control or not? Special cause variation?

Assignable? Structural special cause variation?)

iii. Construct scatter plots of all pairs of variables using the Graph >

Matrix Plot command in Minitab. Are these plots linear?

Curvilinear? Do you see any outliers in these plots? If so, what

will you do with them?

b. Formulate the model

i. Write out in symbols the theoretical multiple regression model

that you will ask Minitab to fit to your data. (e.g., a model like

the ones on p. 237, using your variable names, rather that y or

x 1 or x 2 )

c. Fit the model to the data

i. Compute the regression coefficients using Minitab. Write out

this first fitted multiple regression model.

d. Check the fit of the model

i. Plot the residuals to identify any abnormal patterns or atypical

data points. Do at least the four plots named on p. 239:

1. Residuals versus predicted values

2. Residuals versus predictor variables (x’s)

3. Residuals versus time or observation sequence

4. Normal probability plot of residuals

ii. Deal with any abnormalities detected and refit the model until

the residuals look OK.

e. Refit the model to the data

i. Compute the regression coefficients using Minitab and the

residuals and fitted values for the fitted model using the cleaned

up data from Part d. (This will be the same as your original data

if you did not have to do any clean up in Part d.

ii. If one or more of your predictor variables have t-statistics less

than 2.0, eliminate the one with the smallest t-statistic and refit

the model. Continue doing this until all remaining predictors

have t-statistics greater than 2.0.

f. Interpret the results of your regression analysis.

i. What is your R^2? What does this mean?

ii. Write out your final fitted multiple regression model. Interpret

the coefficients in your regression model.

iii. What do you know now that you did not know before doing this

regression analysis of your Measure data?

I. PROJECT ASSIGNMENT 6: CONTROL

DUE: December 1, 2003 by 1:25 p.m. 70 points The questions are worth 5, 10, 30, 10, 5, 5, and 5 points, respectively.

  1. Present a new flowchart of your process that includes the improvement(s) you have made on the basis of PA 4 and PA 5.
  2. Develop and monitor a plan for controlling for the modified process. Gather at least 10 observations on the modified process (the “Control data”). Present your Measure and Control data in a spreadsheet.
  3. A. Do a control chart for your Y-variable using your Measure and Control data. What does this chart tell you? B. Do separate control charts for your Measure and Control data sets. What do these charts tell you? C. Compare the population mean of your process during the Measure phase to the population mean of your process during the Control phase using a hypothesis test (state your null and alternative hypotheses) and a confidence interval. D. What do these two inferential statistical procedures tell you about the changes you made in your process during your project?
  4. Document the benefits and costs of the improvements you made.
  5. How will you continue to monitor the process and hold the gains you have made?
  6. What recommendations do you have for future improvements in the process you studied?
  7. What are the key points you have learned from this Six Sigma project?

J. PROJECT ASSIGNMENT 7: ORAL REPORT

DUE: December 1, 2003 in class 20 points Present a ten-minute oral report to the class summarizing your entire project. INSTRUCTIONS FOR THE ORAL FINAL REPORT: You will have ten minutes to present an oral summary of your project. Answer the following questions:

  1. What question did you study? (Keep in mind that you are much more familiar with your study than we are. Give us enough background so that we understand your question and its importance to you.)
  2. How did you study your question?
  3. What did you learn from your project? A laptop computer (with PowerPoint) and a projector will be available in the classroom. General purpose coaching on giving a short presentation
  4. Dress appropriately.
  5. Speak clearly and loud enough to be heard in the back row.
  6. Be with your audience and not with your notes.
  7. Practice your presentation and time it. Be clear in your own mind before you start what is the one main point that you intend to communicate to us. I will give a “1 minute remaining” warning and will stop you at ten minutes.

5. To get maximum value from your experience, do the presentation as though it

were an integral part of your interview for your first job after completing your

highest degree.