Lowest point of expected variation

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 Specif

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
Read me
in the corner. It looks like the "Read me" box to the right:
Simply slide your cursor over the red-cornered cell and you will get more information.
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
to complete your projects, but please 'report' your answers in the Excel format
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,
although it may not be currently loaded into your copy.
Following are the simple instruction for loading the Excel Add-ins for both Excel 2003
and Excel 2007. (Slide your cursor over the red-cornered cells to read)

Excel 2003

Excel Novice - Please read

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

Read this!
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.
Go to your Villanova website and follow this sequence:
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor's email envelope icon
4. Type "Check My Work - Specific assignment" 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.
Please 'hand-in' your assignments throughout the course.
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.

Read this!

This spreadsheet tab provides illustrations of adding the DATA ANALYSIS capability to your Excel software.
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

This spreadsheet tab provides illustrations of adding the DATA ANALYSIS capability to your 2007 Excel software.
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
routine about this visit. She made it explicitly clear that
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 <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
Sponsor
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
"Create a charter?"
upon the information in the introduction. (see "The project" 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

What is the business case?
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
$1.02M. your goal statement?
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).

"Business Case?"

"Problem Statement"

"Goal Statement"

"The project scope?"

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.
Go to your Villanova website and follow this sequence:
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor's email envelope icon
4. Type "Check My Work - PROJECT CHARTER" 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.

Please 'hand-in' your assignments throughout the course.
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 "The Project" 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.
Go to your Villanova website and follow this sequence:
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor's email envelope icon
4. Type "Check My Work - BASELINE SIGMA" 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.
Please 'hand-in' your assignments throughout the course.
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.

Data:
Length
10.63
10.65
10.66
10.66
10.67
10.68
10.68
10.68
10.68
10.69
10.69
10.69
10.69
10.69
10.69
10.70
10.70
10.70
10.70
10.70
10.71
10.72
10.72
10.72
10.72
10.72
10.72
10.73
10.73
10.73
10.74
10.74
10.75
10.75
10.77
Upper Spec
Lower Spec
Target

Width

11
10.5
10.75

7.66
7.45
7.55

7.51
7.52
7.53
7.53
7.53
7.53
7.54
7.54
7.54
7.54
7.54
7.54
7.54
7.55
7.55
7.55
7.55
7.55
7.55
7.55
7.55
7.55
7.55
7.55
7.56
7.56
7.56
7.56
7.56
7.56
7.57
7.57
7.57
7.58
7.58

Thickness
0.538
0.539
0.540
0.541
0.541
0.542
0.543
0.543
0.543
0.545
0.545
0.545
0.545
0.545
0.545
0.545
0.546
0.546
0.546
0.546
0.546
0.546
0.546
0.546
0.547
0.547
0.547
0.548
0.548
0.549
0.549
0.551
0.552
0.553
0.554

Histograms in Excel 2003

Excel 2007 - 2 Options

Histograms in Excel 2007

More on Bin Ranges

0.56
0.54
0.55

How to submit an Assignment
Target Assignment Date - Submit in Week 5 or earlier
YOU DO NOT NEED TO SEND THE ACTUAL HISTOGRAMS
Project:
Manufacturing
Deliverable:
Histogram
Student last name:
Heideloff
Is 'length' normally distributed?
Is 'width' normally distributed?
Is 'thickness' normally distributed?

Yes
Yes
Yes

YOU DO NOT NEED TO SEND THE ACTUAL HISTOGRAMS
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.
Go to your Villanova website and follow this sequence:
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor's email envelope icon
4. Type "Check My Work - HISTOGRAM" 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.
Please 'hand-in' your assignments throughout the course.
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.

Instructor:

Option #1 (Quick and Dirty draft of a histogram)
1) Click DATA tab
2) Go to ANALYSIS category on the DATA tab
3) Click on DATA ANALYSIS (If you do not see DATA ANALYSIS, refer to the EXCEL EXAMPLES tab at the bottom of
this spreadsheet for instructions in loading the DATA ANALYSIS features.)
4) Select HISTOGRAMS and then click OK
5) The cursor should be blinking in the "Input Range" box
6) Highlight your data
7) Click in "New Worksheet Ply"
8) Skip the bin range option, and other options
9) Check the "Chart Output" box
10) Click OK
11) You may drag your mouse over the corner of the graph to enlarge it.
Option #2 (A More polished copy where you determine the bin ranges)
1) Click DATA tab
2) Go to ANALYSIS category on the DATA tab
3) Click on DATA ANALYSIS (If you do not see DATA ANALYSIS, refer to the EXCEL EXAMPLES tab at the bottom of
this spreadsheet for instructions in loading the DATA ANALYSIS features.)
4) Select HISTOGRAMS and then click OK
5) Determine the range of the data set, from your smallest to your largest data value
6) Add one value (in the unit you are measuring) for 'range with inclusion' (Example: .14 (range) + .01 = .15)
7) Determine the appropriate number of bars for your sample size (Example: < 50 data points use 5, 6 or 7 bars)
8) Calculate both the beginning and ending point of each cell and list the beginning and ending points of each bin
in separate cells. For example, if you have a range of .15, you could have 5 cells with .03 data value per cell.
9) Now you have an idiosyncrasy of Excel. Excel will give you the option of designating the bin ranges.
But, you should give Excel the ENDING value of each bin rather than the beginning value. Highlight the cells that
include the ending value of each bin under the BIN RANGE option.
10) Highlight your complete data set under the INPUT RANGE option
11) Check on CHART OUTPUT and where you want the histogram chart located. (New worksheet or imbedded)
12) Click OK
13) You may drag your mouse over the corner of the histogram chart to enlarge it.
14) When Excel drafts histograms, the bars do not adjoin. Ideally, we want the bars of a histogram to adjoin
because we are graphing continuous data. To make the bars adjoin, right click on top of bars and choose FORMAT
DATA SERIES. In Excel 2007, you go directly to setting GAP WIDTH to zero.
15) To change the color scheme of the histogram, right click somewhere outside of the bars in the graph and
choose
FORMAT PLOT AREA. You can choose many color formats.
16) When you plan the cell intervals, there are no data points in the MORE category, so you may delete it, because
the MORE category is often confusing to people. DO NOT delete the MORE category if it has data points in it.
17) Only go through these more detailed steps if you are interested in a polished Histogram. Otherwise run a
quick draft of the histogram with Option #1.
If you would like to print this tip, right click on the cell and select EDIT COMMENT. Then just highlight and copy
the text, and paste in a document for printing.

Objective:
Your boss wants to know the limits of expected variation. You know there is another shipment
coming in next week and based upon this week's run, you can calculate/predict the limits
of expected variation by calculating the mean and standard deviation.

The Mean and StDev in Excel 2003
The Mean and StDev in Excel 2007
Expected variation

Instructions for you:
1. Calculate the average for length, width and thickness.
2. Calculate the standard deviation for each.
3. From these calculations, determine the expected variation. ( Use + or - 3 sigma)
You may complete this assignment by hand, as taught in the lecture. You may use Excel, or you
may use a calculator or other software. We explain the fundamentals of the calculations, so that
you learn the mechanics and the meaning of standard deviation. This basic approach gives you an
understanding of standard deviation, which then allows you to be flexible in the tools that you use.

Data:
Data

Upper Spec
Lower Spec
Target

Length
10.67
10.74
10.68
10.72
10.66
10.69
10.70
10.72
10.69
10.68
10.72
10.70
10.70
10.73
10.75
10.73
10.69
10.68
10.70
10.77
10.72
10.69
10.66
10.69
10.63
10.68
10.73
10.74
10.65
10.69
10.70
10.72
10.75
10.71
10.72
11
10.5
10.75

LENGTH
###
###
###
Decimal places in Excel
###
Excel STORES the full decimal value of a number in its cells. ###
But, you can adjust how many decimal values
###
are VISIBLE in your spreadsheet. For example,
###
if your average/mean was 2.4557643, Excel
###
could display that number. Or, you can set your spreadsheet ###
number to display the value to 4 decimal places, 2.4558.
###
Following are the instructions for re-setting the number of
###
decimal places that are visible in Excel for both Excel 2003 and
###
Excel 2007. NOTE: Try to not use 'rounded' data during your###
calculations. In your final result, you may round to one
###
more decimal place than your raw data.
###
###
Excel 2003
###
###
Excel 2007
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###

Width
Thickness
7.51
0.551
7.57
0.546
7.55
0.546
7.53
0.554
7.53
0.546
7.56
0.542
7.52
0.545
7.58
0.538
7.55
0.552
7.53
0.547
7.56
0.546
7.58
0.545
7.55
0.546
7.55
0.548
7.54
0.546
7.57
0.543
7.54
0.548
7.55
0.545
7.55
0.553
7.56
0.539
7.54
0.549
7.56
0.541
7.56
0.543
7.55
0.545
7.54
0.549
7.55
0.546
7.56
0.545
7.57
0.540
7.54
0.541
7.55
0.545
7.54
0.547
7.55
0.543
7.53
0.545
7.54
0.546
7.55
0.547
7.66
7.45
7.55

0.56
0.54
0.55

How to submit an Assignment
Target Assignment Date - Submit in Week 6 or earlier
Project:
Deliverable:
Student last name:

Manufacturing
Expected variation
Heideloff

Mean for LENGTH:::
Standard deviation for LENGTH:::
What is the lowest point of expected variation?
What is the upper point of expected variation?

10.7029
0.0305
10.6114
10.7944

Mean for WIDTH:::
Standard deviation for WIDTH:::
What is the lowest point of expected variation?
What is the upper point of expected variation?

7.5489
0.0157
7.5018
7.5960

Mean for THICKNESS:::
Standard deviation for THICKNESS:::
What is the lowest point of expected variation?
What is the upper point of expected variation?

0.5457
0.0036
0.5349
0.5565

Help

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.
Go to your Villanova website and follow this sequence:
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor's email envelope icon
4. Type "Check My Work - EXPECTED VARIATION" 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.

Please 'hand-in' your assignments throughout the course.
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:
There is thought among some people at your facility that the old method
and the new method are producing product at different thicknesses.
You DO NOT WANT the methods to be different. In fact, you want
the methods to be producing products that are the same. To address this, you
suggest using a T test. If the methods are significantly different, you have a problem.
If the null is NOT rejected--that is good news! The team agrees that a sample size
of 25 is adequate for the test. Remember...You are hoping the null does not
get rejected. The team decides a significance level at 0.05 for the test.

Instructions for you:
Step 1. You need 4 numbers:
Old method's average:
m .012576
New method's average: X-bar
(you need to calculate it from the data below)
Standard deviation of sample data 's'
(you need to calculate it from the data below)
n number of samples 'n'
(you need to count them yourself from the data below)
Step 2. State the null and alternate hypothesis.
Step 3. Calculate the T test statistic from the formula found in the t test lecture
in your white manuals.
Step 4. Determine the critical T value
[Hint: (n - 1) is 25 - 1 = 24 df] and considering a 95% confidence.
Step 5. What is your conclusion?
"How did you come up with µ?"
"How can I find x-bar?"
"How can I find S?"
"Hypothesis statement?"
"How much help is Excel for this?"
"My conclusion?"
"I'm lost in calculating the Test Statistic"
"What's the difference between 1-tail or 2?"

Data:
New method
0.009
0.010
0.011
0.011
0.010
0.011
0.011
0.013
0.008
0.012
0.010
0.013
0.014
0.012
0.009
0.014
0.011
0.015
0.011
0.012
0.015
0.011
0.011
0.012
0.008

How to submit an Assignment
Target Assignment Date - Submit in Week 7 or earlier
Project:
Deliverable:
Student last name:

Manufacturing
T Test
Heideloff

Old method average:::
New method average:::
Standard deviation (s):::
n = :::
State the null hypothesis:::

State the alt. hypothesis:::

T test statistic:::
One tail or two?
Critical value(s):::
Reject the null? (yes, or no?):::

0.0126
0.0114
0.0019
25

Check
Check
Check

The new method thickness is equal to the old
method thickness

The new method thickness is NOT equal to the
old method thickness
-3.1795
Two
2.0640
Yes

Please write the hypothesis conclusion:::
Since the test statistic falls in the left-hand reject region, the
null hypothesis is rejected. With 95% confidence it concludes
that the two methods are producing different thicknesses.

Check
Check

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.
Go to your Villanova website and follow this sequence:
1. COMMUNICATE
2. CLASS ROSTER
3. Click on your instructor's email envelope icon
4. Type "Check My Work - t test" 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.
Please 'hand-in' your assignments throughout the course.
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:
Going down the DMAIC road, you and your team are continuing to try
to get a handle on what is causing additional defects in the
leveler plates. You are trying to reduce the variation in that process.
One of the team members suggested that defects of type A or B is
dependent upon the test sites. In other words, he thinks that one or
more of the three test sites may be influencing the defect...