# MATHEMATICS

Instructions
You need to understand how to send your assignments (deliverables)
to your instructor. The tabs (bottom of each sheet) in this
document contain all of the deliverables expected of you.
If you need help along the way, look for these special cells that have a red indicator
in the corner. It looks like the &quot;Read me&quot; box to the right:
The format for all of the deliverables is the same:
The ‘assignment objective’ is in black font.
The next segment is in green font. These are your instructions for that assignment.
The blue font is the data (where applicable) for completing each the assignment.

Software
We are using Excel software for the projects. You may use other software
described below.
You may complete your assignments with any version of Excel software.
All assignments can easily be completed with a basic copy of Excel.
There is also an Add-In feature which is available for Excel that can be helpful,
although it is not required. The Add-In feature comes free with each Excel package,
and Excel 2007. (Slide your cursor over the red-cornered cells to read)

Excel 2003

Project Timeline
Deliverables include:
Project charter (target week 3 or sooner)
Baseline sigma (week 4 or sooner)
Histogram (week 5 or sooner)
Expected variation (week 6 or sooner)
t test ( week 7 or sooner)
Chi square (week 9 or sooner)
ANOVA (week 11 or sooner)
DOE (week 12 or sooner)
Scatter diagram (week 13 or sooner)
Control chart (XmR) (14 or sooner)
Pp Ppk (week 15 or sooner )

Excel 2007

How to submit an Assignment
In response to customers like you, we have added a peach-colored box
for each deliverable. We have done this to make it clear (and consistent) the
areas of the project that will be reviewed to your instructor.
Project:
Deliverable:
Student last name:

Manufacturing Project
Improve phase – gen. sol.
Johnson

What is the control chart telling you?
There is a point out of control at
subgroup #15. I would try to figure
out why that happened. We would
also recalculate the control limits
because there is evidence the
process has changed.

of
xample
E
What is the average of subgroup 1? liverable
a de
What is the average of subgroup 2?
What is the average of subgroup 3?
What is the average of subgroup 4?
What is the average of subgroup 5?
What is the average of subgroup 6?
What is the average of subgroup 7?
What is the average of subgroup 8?

22
34
23
22
25
23
29
27

To send each assignment to your instructor:
Click-and-hold the LEFT mouse button at the TOP-LEFT corner of the
peach-colored box, then while holding down on that button, drag to
the LOWER-RIGHT corner of the box. This will highlight the entire
peach-colored box. Release the mouse button. Do a CTRL-C. This will
copy what has been highlighted.
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor’s email envelope icon
4. Type &quot;Check My Work – Specific assignment&quot; in the SUBJECT box.
5. Click once inside of the message box
6. Do a CTRL-V. This will paste your deliverable into this box.
Don’t be concerned if after you paste it, the appearance of the text is out of
alignment. It will straighten out after you hit SEND.
7. SEND Check your SENT ITEMS folder afterward to see how it straightened out.
DO NOT SAVE THEM FOR THE END.
Procrastinators: The deadline for completing all project deliverables
is 7 days prior to the end of the course.

If you see Data Analysis already listed under the Tools tab, you are set. If you do not see Data Analysis
follow the instructions in the Green tab.
Excel 2003 instructions

Excel 2003 or earlier versions of Excel example

If you see Data Analysis already listed under the DATA tab, you are set. If you do not see Data Analysis
follow the instructions in the Green tab.
Excel 2007 instructions

Excel 2007 example

Manufacturing Project
Lovell Levelers, Inc. is a major provider of specialized parts
for the automotive industry. LLI’s biggest customer, Specific Motors
was not a delighted customer this month. In fact, last
Monday, the executive vice president of Specific Motors headquarters,
Phyllis Kendall was diverted from a return trip from Singapore
to drop in unexpectedly at the LLI plant. There was nothing
Specific Motors was disappointed with the level of quality relative
to the leveler plates. In particular, she was disappointed with the
current average of rejects at the rate of 1,350 defects per million
opportunities (DPMO), and at LLI’s cost of poor quality of just over \$256,000
per quarter. She said the industry standard is &lt;50 DPMO and
if we do not get the level of quality to the industry standard (as a
minimum) within the next six months, LLI should not expect
to keep the business next year.
The student will be a Black Belt working for LLI. The specifics about their company:
CEO
Bill Lovell
GM
Mary Nichols
John Hopps
Finance
Cindy Jenkins
Process owner
Leroy Miller
Master BB
Dennis Kens
Manufacturing
Mitch Freese
Design Engineer
Al Nelson
Quality
Debbie Judson
The deadline for completing all project deliverables is 7 days prior to the end of the course

Objective:
A problem statement needs to be developed.
There needs to be a business case so that management will buy-in to having the team
working on the project. The scope of the project also needs to be decided upon. This is
important to ensure a likely successful completion. If the scope is too broad, a
success may not be realized for years, or may not happen at all.

Instructions for you:
Create a project charter based
&quot;Create a charter?&quot;
upon the information in the introduction. (see &quot;The project&quot; tab below)
In reality, you would fill in a charter with team members’ names, stake holders, etc. We
are not interested in those details for this simulation, but we do want to see what you
come up with for four (4) items: Problem statement, business case, goal and project scope.

How to submit an Assignment
TARGET ASSIGNMENT DATE – Submit in Week 3 or earlier
Project:
Deliverable:
Student last name:

Manufacturing Project
Project charter
Heideloff

Specific Motors is not satisfied with LLI’s performance due to high defect
rate of Leveler Plates and resulting cost increases. By reducing defect rate
to 50 DPMO (indusrty standard), LLI can expect to cut re-work costs by
approximately \$246,518/QTR; \$986,074 Annually. This project will focus on
What is the problem statement?
quality improvement initiatives to achieve anticipated savings.
Specific Motors expects LLI to deliver quality Leveler Plates, meeting or
exceeding rate of 50 DPMO. LLI’s current defect rate of 1,350 DPMO has
cost \$256K/QTR. At this rate, LLI can expect to see an anual hard loss of
What is If LLI cannot reduce defect rate to 50 DPMO within 6 months, LLI
will lose Specific Motors, their largest customer.
Reduce defect rate to 50 DPMO within 6 months

What is the project scope?
Scope for this project includes defect prevention, quality control and
quality assurance practices (from commencement of production through
turnover to customer).

&quot;Problem Statement&quot;

&quot;Goal Statement&quot;

&quot;The project scope?&quot;

To send each assignment to your instructor:
Click-and-hold the LEFT mouse button at the TOP-LEFT corner of the
peach-colored box, then while holding down on that button, drag to
the LOWER-RIGHT corner of the box. This will highlight the entire
peach-colored box. Release the mouse button. Do a CTRL-C. This will
copy what has been highlighted.
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor’s email envelope icon
4. Type &quot;Check My Work – PROJECT CHARTER&quot; in the SUBJECT box.
5. Click once inside of the message box
6. Do a CTRL-V. This will paste your deliverable into this box.
Don’t be concerned if after you paste it, the appearance of the text is out of
alignment. It will straighten out after you hit SEND.
7. SEND Check your SENT ITEMS folder afterward to see how it straightened out.

DO NOT SAVE THEM FOR THE END.
Procrastinators: The deadline for completing all project deliverables
is 7 days prior to the end of the course.

Objective:
We want you to determine baseline sigma for both the current defect level and the
new target defect level. (approximate is okay)
You will need to refer to the tab below entitled &quot;The Project&quot; for this deliverable.

Instructions for you:
Calculate baseline sigma.
Sigma Levels
6 sigma 3.4 dissatisfied customer experiences per million (DPMO)
5 sigma 233 DPMO
4 sigma 6,210 DPMO
3 sigma 66,810 DPMO
2 sigma 308,770 DPMO
1 sigma 697,672 DPMO

How to submit an Assignment
Target Assignment Date – Submit in Week 4 or earlier
Project:
Deliverable:
Student last name:

Manufacturing
Baseline Sigma
Heideloff

Baseline sigma for current defect level::

4.5

Baseline sigma for the new target defect level

5.4

To send each assignment to your instructor:
Click-and-hold the LEFT mouse button at the TOP-LEFT corner of the
peach-colored box, then while holding down on that button, drag to
the LOWER-RIGHT corner of the box. This will highlight the entire
peach-colored box. Release the mouse button. Do a CTRL-C. This will
copy what has been highlighted.
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor’s email envelope icon
4. Type &quot;Check My Work – BASELINE SIGMA&quot; in the SUBJECT box.
5. Click once inside of the message box
6. Do a CTRL-V. This will paste your deliverable into this box.
Don’t be concerned if after you paste it, the appearance of the text is out of
alignment. It will straighten out after you hit SEND.
7. SEND Check your SENT ITEMS folder afterward to see how it straightened out.
DO NOT SAVE THEM FOR THE END.
Procrastinators: The deadline for completing all project deliverables
is 7 days prior to the end of the course.

Objective:
The Black Belt team did a pareto analysis of the data and determined that three factors were causing
over 95% of the problem with the leveler plates. Those factors are,
the length of the plates, the width of the plates, and the thickness of the plates.
You need to know if the data from these three ‘product parameters’ are normally distributed.

Instructions for you:
1. Construct three (3) histograms for the three data sets.
2. Interpret each of the histograms to determine whether the variables are random or normally
distributed.

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