all of the problems within the six sigma black belt

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 2007

Excel Novice - Please read

Project Timeline
Follow the submission scheduled posted on the Main Discussion Board!! Remember that the entire project must be
100% correct and complete by no later than midnight EST one week (7 days) BEFORE the last day of class.
THIS MEANS THAT ALL REQUIRED CORRECTIONS MUST HAVE BEEN COMPLETED CORRECTLY - JUST TURNING
IN THE ASSIGNMENT IS NOT SUFFICIENT IF THERE ARE ANY ERRORS ON IT. Most people require 2 - 3 attempts
per assignment to make all necessary corrections - so plan your time accordingly!
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 8 or sooner)
ANOVA (week 9 or sooner)
Scatter diagram (week 10 or sooner)
DOE (week 11 or sooner)
Control chart (XmR) (12 or sooner)
Pp Ppk (week 13 or sooner )

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.
What is the average of subgroup 1?
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
Read
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 - ASSIGNMENT NAME - PROJECT NAME" 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.
8. DO NOT SEND ANY ATTACHMENTS UNLESS YOUR INSTRUCTOR SPECIFICALLY ASKS YOU TO!!
VERY IMPORTANT!! Be sure to submit your assignments for grading as you complete
each one and following the submission scheduled posted on the message board - DO
NOT WAIT UNTIL THE END OF THE COURSE TO SEND THEM ALL IN. NOTE THAT THE
ENTIRE PROJECT MUST BE 100% CORRECT BY ONE WEEK BEFORE THE END OF
CLASS OR YOU WILL FAIL THE PROJECT AND THE COURSE. This means that you must
submit ALL of your assignments far enough in advance of the project completion
deadline to allow time for all necessary corrections to be made. Following the
submission schedule is the best way to ensure that you have enough time to finish the
project by the completion deadline - failure to meet the submission due dates can result
in failing the course. Very few assignments are correct on the first submission and many
require multiple rework attempts, so don't procrastinate!

this!

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) that has created a cost of poor quality of just over $256,000
per quarter for them. She said the industry standard is 50 DPMO and
if we do not get the level of quality to the industry standard within the next
six months, LLI will lose Specific Motors as a customer.
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 having all project assignments 100% correct 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.
Be sure to review the week 2 virtual class for more information on project charters before you submit this!

How to submit an Assignment

TARGET ASSIGNMENT Submission DATE - Submit in Week 3 or earlier
Project:
Deliverable:
Student last name:

Manufacturing 2013 LAJ
Project charter
Your LAST name here

What is the business case?
"Business Case?"
Type in your business case here. Use no more than 2 sentences.
What is the problem statement?
"Problem Statement"
Type in your problem statement here. Use no more than 2 sentences.
What is your goal statement?
"Goal Statement"
Type in your goal statement here. Use no more than 2 sentences.
What is the project scope?
Type in the scope here. Be sure to express your scope in terms of the
process.

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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

"The project scope?"

Objective:
We want you to determine the sigma levels with the Motorola 1.5 sigma shift for both the current and
target defect levels identified for this project.
You will need to refer to the tab entitled "The Project" to be able to complete this deliverable.

Instructions for you:
Determine the approximate baseline and target sigma levels (to 1 decimal place) based on the
DPMO and with the Motorola shift.
Be sure to review the week 3 virtual class for more information on sigma levels before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 4 or earlier
Project:
Manufacturing 2013 LAJ
Deliverable:
Baseline Sigma
Student last name:
Your last name here

HINT!

TAKE YOUR SIGMA LEVEL ANSWERS TO 1 DECIMAL PLACE. USE
WHOLE NUMBERS FOR THE DPMO.
What is the current PPM / DPMO?
What is the baseline sigma for the current defect level?

Check

What is the target PPM / DPMO?
What is the sigma value for the target defect level?

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 - 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 having all project deliverables 100% correct
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 it is reasonable to assume that 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 assumption of normality is reasonable.

Data:
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
Upper Spec
Lower Spec
Target

Width

11
10.5
10.75

7.66
7.45
7.55

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

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

Histograms in Excel 2003
Histograms in Excel 2007
More on Bin Ranges

0.56
0.54
0.55

Be sure to review the week 3 & 4 virtual classes for more information on judging normality before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 5 or earlier
DO NOT SEND THE ACTUAL HISTOGRAMS UNLESS YOUR INSTRUCTOR ASKS FOR THEM.
Project:
Manufacturing 2013 LAJ
Deliverable:
Histogram
Student last name:
Your LAST name here
Is 'length' approximately normally distributed?
Is 'width'approximately normally distributed?
Is 'thickness' approximately normally distributed?

Yes or No
Yes or No
Yes or No

How do I determine if it's
approximately normal?

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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

HINT!

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, and assuming that the process is normally distributed,
you can calculate/predict the limits of expected variation by calculating the mean and standard deviation
for this data and then using the properties of the normal distribution to estimate the limits of the expected variation.

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

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

Upper Spec
Lower Spec
Target

11
10.5
10.75

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

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

0.56
0.54
0.55

Be sure to review the week 3 and 4 virtual classes for more information on expected variation before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 6 or earlier
Project:
Deliverable:
Student last name:

Manufacturing 2013 LAJ
Expected variation
Your last name here

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

HINT!!

Help

Check
Check
Check
Check

ROUND ALL FINAL RESULTS TO
3 DECIMAL PLACES.
Check
Check
Help
Check
Check

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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

Check
Check
Check
Check

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 have the same average. If the method averages are significantly
different, you have a problem! To address this, you suggest using a T test.
If the null is NOT rejected--that is good news! The team agrees that a sample size
of 25 is adequate for the sample from the new process for this test. You already know
the mean for the old process. The team decides to use a significance level of 0.05 for the test.

Instructions for you:
Step 1. You need 4 numbers:
Old method's average:
m = 0.0126
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
Be sure to review the week 3 and 5 virtual classes for more information on descriptive statistics and t tests before you
submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 7 or earlier
Project:
Deliverable:
Student last name:

Manufacturing 2013 LAJ
T Test
Your last name here

Old method average:
New method average:
Standard deviation (s):
n=

Enter here
Enter here
What is s?
What is n?

Round all your final results to
4 decimal places.

Check
Check
Check

State the null hypothesis:::
Write the null hypothesis here.

State the alt. hypothesis:::
Write the alternative hypothesis here.
T test statistic:
One tail or two?
Critical value:
Reject the null? Yes or No

What is it?
1 or 2?
What is it?
Yes or No

Check
Round your final results to 4
decimal places.

Check

State your bottom-line conclusion in the words of the problem addressed
by this study. HINT: What would you say to your Sponsor?
Type your conclusion bottom-line conclusion in the words of
the problem here.

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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

HINT!

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.
There are three test sites that are designed to detect both Type A and Type B defects.
People have suggested that the number of Type A or B defects detected depends on
which test site is doing the testing. In other words, one or more of the test sites
may not be using the same criteria, method, etc. to detect Type A or B defects and this
is causing the defect rate to be reported inconsistently across the three sites.
You have been asked to test the defect rates from the three test sites and settle the debate.
One way to find out is through the use of the Chi-Square test for independence.
Test at 95% confidence.

Chi Square

Instructions for you:
We highly recommend working through the practice example in yellow below
before tackling this deliverable.
1. State the practical problem.
2. State the null and alternate hypotheses.
3. Compute the chi-square statistic.
4. Determine the chi-square critical value.
5. What conclusions can you draw?

"Hypothesis statement?"
"Write-up my conclusion?"

Sample Exercise in shaded area (not required, but helpful)
See manufacturing project assignment data in blue below this example
Some help for you using an practice example:
You first need to calculate the expected values. It is best to make
a table as step 1. For example, males and females watch various
TV stations. Let's say that we want to find out if gender is dependent
or independent of television station preferences.
The practice data follows:
WKBW WBEN
WGR
Totals
Males
62
54
25
141
Females
44
50
15
109
Totals
106
104
40
250
Step 1. Calculate each of the 'expected values.' We will do
the first two for you.
a. Probability of viewer being male is 141 / 250 = 0.564
(refer to the cells in the table above)
b. Probability of viewer preferring WKBW is 106 / 250 = 0.424
c. Probability of viewer preferring WKBW AND being male
is 0.564 x 0.424 = 0.239
d. Expected number of viewers in this cell is 0.239 x 250 = 59.8
etc…
a. Probability of viewer being female is 109 / 250 = 0.436
b. Probability of viewer preferring WKBW is 106 / 250 = 0.424
c. Probability of viewer preferring WKBW AND being
female is 0.436 x 0.424 = 0.185
d. Expected number of viewers in this cell is 0.185 x 250 = 46.3
etc…
Repeat this for all six cells. To check your work, the totals
(across and down) should add up very close to the (across and
and down) totals of the observed values. Here is how your
chart should appear when finished: The 'expected values
are in [brackets.]

Males
Females
Totals

WKBW
WBEN
WGR
Totals
62 [59.8] 54 [58.8] 25 [22.5] 141
44 [46.3] 50 [45.3] 15 [17.5] 109
106
104
40
250

Step 2. Compare the OBSERVED [EXPECTED]
Example: For the first cell (Males/WKBW), the formula is:
Observed minus [Expected] Squared divided by [Expected] as follows:
(62-59.8)2 divided by 59.8 = 0.0809
For the 2nd value…(54-58.8)2 divided by 58.8 = 0.3918
For the 3rd value… (25-22.5)2 divided by 22.5 = 0.2778
For the 4th value… (44-46.3)2 divided by 46.3 = 0.1143
For the 5th value… (50-45.3)2 divided by 45.3 = 0.4876
For the 6th value… (15-17.5)2 divided by 17.5 = 0.3571
Step 3. Add those chi-square values and you should get 1.7095
This is your calculated chi-square statistic.
Step 4. Determine the significance level. (e.g., .05 or .01 or .1)
This is up to the discretion of the team and the team's choice is based
upon what level of risk they are willing to live with.
Step 5. Determine the Degrees of Freedom (df) for the rows and
the columns. You will need this to find the critical value in
the table in the textbook.
df=(number of rows minus 1) multiplied by
the (number of columns minus 1) So, in this particular
case it would be (2-1 multiplied by 3-1) = 2
Step 6. Go to the chi-square table in a textbook and determine
the critical value. You already know
the calculated statistic (1.7095). All you need now is that critical
value to see if the calculated statistic is greater than that critical
value. If it is greater than the critical value, you can reject the
null. If not, then you fail to reject the null.

Data:
Data for this deliverable:
Site 1
Defect Type A
8
Defect Type B
9

Excel 2003
Site 2
8
10

Site 3
7
8

Excel 2007

Please review the week 7 virtual class on chi square tests for more information before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 8 or earlier
Project:
Deliverable:
Student last name:
Site 1 / Type A expected:
Site 2 / Type A expected:
Site 3 / Type A expected:::
Site 1 / Type B expected:
Site 2 / Type B expected:::
Site 3 / Type B expected:
Chi Square statistic:::
One tail or two?
Critical value:::
Reject the null? (Yes or No)

Manufacturing 2013 LAJ
Chi Square
Your LAST name here

Round all final
results to 2 decimal
places.

Check
Check
Check
Check
Check
Check
Check

1 or 2
Check
Yes or No

State your bottom-line conclusion in the words of the problem addressed
by this study. HINT: What would you say to your Sponsor?
HINT!
Type your bottom-line conclusion in the words of the problem here.

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 - Chi Square" 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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

Objective:
In an effort to stabilize the process, there has been some discussion about 3 machines
that appear to be causing variation in the mean part thicknesses (measured
prior to plating). It appears that these 3 machines may be producing parts with different average
material thickness even though they are supposed to be producing parts with the same average thickness.
It was suggested that a One-Way ANOVA be used to compare the mean thicknesses
produced by these 3 machines. You will be checking for significant differences between
the mean material thicknesses produced by these 3 machines. Use a 5% level of significance.

Instructions for you:
Using the data below construct a one-way ANOVA. To do so, occurs
in two major steps--the table step, followed by the ANOVA step.

Excel 2003

Excel 2007

Data:
Machine 1 Machine 2
Machine 3
0.546
0.573
0.573
0.526
0.592
0.57
0.587
0.571
0.527
0.563
0.556
0.572

Some help:
Key to terms:
ANOVA
CM
df
F
MS
SS

ANalysis Of VAriance
Correction for the Mean
degrees of freedom
F statistic used to compare with the F-table value (aka 'critical value')
Mean Square
Sum of Squares

Make a table…then fill in the ANOVA using the numbers from the table.
Step 1. Make a table (it is pretty easy)
Table to assist in the calculations of ANOVA
Sum
n Sum2/nSum ?X2?X2
Machine 1
0.546
0.526
0.587
0.563
Help
Help
Help
Help
Machine 2
0.573
0.592
0.571
0.556
Help
Help
Help
Help
Machine 3
0.573
0.57
0.527
0.572
Help
Help
Help
Help
Totals
Help
Help
Help
Help
Step 2. Determine total df.
Help
Step 3. Determine df FACTORStep 3. Determine dfFACTOR
Help
2

Step 4. Calc. CM which is: (?X) /n (which is NOT THE SAME AS ?X2 listed above) Step 4. Calc. CM which is:
Help
Step 5. Calculate SSTOTAL: ?X2TOTAL – CM = Step 5. Calculate SSTOTAL: ?X2TOTAL – CM =
Help
Step 6. Calculate SSFACTOR: SUM2/nTOTAL (from chart above) – CM = Step 6. Calculate SS FACTOR: SUM
Help
Step 7. Calculate SS ERROR: SSTOTAL – SSFACTOR = Step 7. Calculate SSERROR: SSTOTAL – SSFACTOR = Help
Step 8. Calculate MSFACTOR: SSFACTOR divided by dfFACTOR = Step 8. Calculate MSFACTOR: SSFACTOR divided by df
Help
Step 9. Calculate dfERROR: The dfTOTAL…subtract from that the df FACTORStep 9.

: The dfTOTAL…subtract from that the df

Calculate dfERROR

Step 10. Calculate MSERROR: SSERROR divided by dfERROR = Step 10. Calculate MSERROR: SSERROR divided by df
Help
Step 11. Calculate the F statistic: MS FACTOR divided by MSERROR =

Help

Step 12. The ANOVA table below should be filled in by now with the
exception of the F CRITICAL value.
SS
df
MS
Calc . F
ANOVA
Factor
Error
Total
Step 13. Look up the F-table value.
Help
Step 14. What is your conclusion?

F Crit.

Be sure to review the week 8 virtual class for more information on One-Way ANOVA before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 9 or earlier
Project:
Deliverable:
Student last name:

Manufacturing 2013 LAJ
ANOVA
Your LAST name here

Round your results to 5 decimal places.
What is the SUM of SQUARES (SS) for FACTOR?
What is the SUM of SQUARES (SS) for ERROR?
What is the SUM of SQUARES (SS) TOTAL?
What is the Degrees of Freedom (Df) for FACTOR?
What is the Degrees of Freedom (Df) for the ERROR term?
What is the Degrees of Freedom (Df) TOTAL?
What is the MEAN SQUARED (MS) for FACTOR?
What is the MEAN SQUARED (MS) for the ERROR term?
What is the F Calculated value?
What is F Critical value (from the table)?
Will you reject the null? Yes or No

SS-Factor
SS-Error
SS-Total
DF-Factor
DF-Error
DF-Total
MS-Factor
MS-Error
F-Calculated
F-Critical
Yes or No

Check
Check
Check
Check
Check
Check
Check
Check
Check
Check

State your bottom-line conclusion in the words of the problem addressed
by this study. HINT: What would you say to your Sponsor?
HINT!
Type your bottom-line conclusion in the words of the problem here.

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 - ANOVA" 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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

Objective:
A team member has been saying since day one that there is a correlation between
temperature and the thickness. Should the team have listened? Construct a scatter
diagram and calculate the correlation coefficient to see if she is correct.

Instructions for you:
Construct a scatter diagram to see if she is correct. And, if she is, we may have found
a smoking gun toward a solution.

Data:
Data:

Temp
154
153
152
152
151
151
151
151
151
151
151
151
151
151
151
151
150
150
150
150
150
150
150
150
149
149
149
148
148
148
147
147
146
146
145

Thickness
0.554
0.553
0.552
0.551
0.549
0.549
0.548
0.548
0.548
0.547
0.547
0.547
0.547
0.547
0.547
0.546
0.546
0.546
0.546
0.546
0.546
0.545
0.545
0.545
0.545
0.545
0.545
0.545
0.543
0.543
0.542
0.542
0.541
0.54
0.538

Scatter diagrams in Excel 2003
Scatter diagrams in Excel 2007
Correlation Coefficient - Excel 2003
Correlation Coefficient - Excel 2007

Be sure to review the week 9 virtual class on scatter plots for more information before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 12 or earlier
DO NOT SUBMIT THE SCATTER DIAGRAM UNLESS YOUR INSTRUCTOR ASKS FOR IT.
Project:
Manufacturing 2013 LAJ
Deliverable:
Scatter Diagram
Student last name:
Your last name here
ROUND RESULTS TO
3 DECIMAL PLACES.
What is the correlation coefficient?
Is there strong correlation?
HINT!
Yes or No
IF there is strong correlation, is it positive or negative?
(Answer with positive, negative or N/A)

Positive, Negative or N/A?

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 - SCATTER" 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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

Objective:
Although many things have been learned to this point and we have made progress, but we are not quite there.
Earlier in the project the team determined that thickness was the main problem relating to the high level
defects in the leveler plates. The analysis has been completed. Now, we want to IMPROVE the process.
You recommend using a design of experiments approach to hopefully realize a breakthrough improvement.
The team brainstorms a long list of possible reasons why the thickness is not capable. From that list, the
team has reduced it down to five factors they want to include in an experiment. They suspect
interactions, so they conclude a full factorial will be required. They refer to the resolution matrix (found in your
reading materials and in the Fractional Factorial Designs Lecture) and they find they can
learn about the effects of those five factors in 32 experiments.
The factors for the experiment were Depth, Temp, Pressure, R.P.M. and Time.

Instructions for you:
From the factorial experiment (below) calculate the interactions to determine confounding.
1. Fill in the interaction columns. (shaded in peach color) You will need to do
this to answer #1 in the peach-colored area below.
2. Is the initial design below a resolution III, IV, V or Full Factorial (no resolution)?
3. The initial design below is a design that an consultant is recommending. Unfortunately, you learn some bad news.
Your management has set your budget only allowing for 8 runs because the trials cost $600 a piece.
Big Hint: One of the factors MAY be dropped from the study for economic reasons.
What specific experimental design would you recommend? (You do not need to decide which factor to drop at this point.)
4. Using the resolution matrix found in your online textbook, what is the resolution for the design you're recommending?
5. Based on your new recommendation, what will the confounding pattern be in your results?

"I'm lost"

Data:
Factor
Depth
Temp
Pressure
R.P.M.
Time

(-)
85
140
850
4400
30

(+)
150
155
2500
4800
45
I try to enter + or - and it does not work.

Trial
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

Factor Factor Factor Factor Factor A X B A X C A X D A X E B X C B X D B X E C X D C X E D X E
C
A
B
D
E
+
+
+
+
Entering +
+
or - does
+
+
not work
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

Be sure to review the week 9 and 10 virtual classes on DOE for more information before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 11 or earlier
DO NOT SUBMIT THE DESIGNED EXPERIMENT!!
Project:
Manufacturing 2013 LAJ
Deliverable:
DOE Design Choice
Student last name:
Your last name here
1. What is the sign (+ or -) for the AxC interaction for the 4th trial?
2. What is the resolution as shown above? (III, IV, or V, or Full)

+ or - ?
III, IV, V or Full?

3. Given the teams goals and budget, what is
your recommendation for the final design of Type your SPECIFIC recommendation here and use the
correct notation for the design you recommend.
this experiment? BE SPECIFIC AND USE THE
CORRECT DESIGN NOTATION AND/OR
TERMINOLOGY!!
4. What would the new resolution be under your
recommendation in #3 above? (III, IV, or V) :::
5. What will the generic confounding
pattern be for your final design?
(NOT the design generators or alias
sets!)

III, IV, or V?

Describe the GENERIC confounding pattern for this
design resolution. HINT: We do not want the alias sets
or design generators.

DO NOT SUBMIT THE DESIGNED EXPERIMENT
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 - DOE" 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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

"I'm lost"
HINT!
HINT!

HINT!

HINT!

Objective:
Lovell Levelers just reported that Specific Motors is a satisfied customer. The leveler plate
quality is no longer an issue. In fact, they have not seen a single defect in six months!
Phyllis Kendall made another surprise visit, but this time for a more pleasant reason.
She presented each member of the team with a crisp, new $100 bill as a show of appreciation.
But she also pointed out that we need to have a way to ensure that this problem will not
crop up again. The team is one step ahead of her and explained that the thickness of the
leveler plates is being monitored and controlled with an on-going XmR (Individuals and Moving Range)
chart so that any assignable causes of variation will be detected and addressed quickly.
The parameters affecting the product thickness are also being monitored with a capability study.

Instructions for you:
We want to make sure you can calculate control limits. You may construct the
control chart by hand, or you may use a charting function in Excel. There are blank forms in the
back of your notebook .

Control Charts in Excel 2003
Control Charts in Excel 2007
1.
2.
3.
4.

What is the upper control limit for the range?
What is the upper control limit for the individuals?
What is the lower control limit for the individuals?
What would you do with the process?
a. What would you recommend?
b. Is the measurement system discriminate?
c. Is thickness in statistical control?

Help

"I have no idea
about this one"
"I have no idea
about this one"

Data:
Thickness data for XMR control chart
0.551
0.546
1a. Calculate R-bar
0.547
0.548
Self check
0.547
0.547
1b. Calculate the
0.538
upper control limit
0.546
for the range
0.542
"How do I do that?"
0.543
Self check
0.545
0.547
2 & 3. Calculate the
0.543
control limits for the
0.548
individuals
0.545
"How do I do that?"
0.554
Self check
0.549
0.546
0.545
0.553
0.549
0.541
0.542
0.545
0.546
0.552
0.546
0.546
0.545
0.547
0.548
0.547
0.545
0.54
0.545

Calculating R-bar in Excel 2003

Calculating R-bar in Excel 2007

Be sure to review the week 11 virtual class for more information on SPC and measurement discrimination before you submit this!

Target Assignment Submission Date - Submit in Week 13 or earlier
YOU DO NOT NEED TO SUBMIT THE XmR CHART
Project:
Manufacturing 2013 LAJ
Deliverable:
XmR Chart
Student last name:
Your last name here
Calculated R-Bar:
Upper control limit for the range:
Upper control limit for the individuals:
Lower control limit for the individuals:

Type in R-bar
Type in UCL-R
Type in UCL-x
Type in LCL-x

Is there adequate discrimination? Explain your
answer: Which chart did you use and exactly how
many strata are there on that chart? How many
should there be?

ROUND YOUR
FINAL RESULTS TO
4 DECIMAL
PLACES.

Type your answer here. Include which
chart you used and how many strata
there are on that chart.

Is the Moving Range chart stable? Justify your answer using ALL of the tests for stability
covered in the online textbook and virtual class on SPC. NOTE: IF YOU SAY THE CHART IS
UNSTABLE, SPECIFY WHICH TEST(S) IT FAILS AND WHERE ON THE CHART IT FAILS BY
REFERENCING THE SPECIFIC DATA POINTS THAT FAIL BY NUMBER (NOT VALUE).

Check
Check
Check
Check

Help

Help

Type your answer here. If you say the chart is unstable, specify which test(s) it fails and
where on the chart by referencing the specific data point numbers.

Is the Individuals chart stable? Justify your answer using ALL of the tests for stability
covered in the online textbook and virtual class on SPC. NOTE: IF YOU SAY THE CHART IS
UNSTABLE, SPECIFY WHICH TEST(S) IT FAILS AND WHERE ON THE CHART IT FAILS BY
REFERENCING THE SPECIFIC DATA POINTS THAT FAIL BY NUMBER (NOT VALUE).
Help
Type your answer here. If you say the chart is unstable, specify which test(s) it fails and
where on the chart by referencing the specific data point numbers.

Based upon what the control chart is telling you, what would you do next?
Help
Type your answer here.

How to submit an Assignment
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 - XmR Chart" 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 having all project deliverables 100% correct
is 7 days prior to the end of the course.

Check

Objective:
So far, so good. The process has been in control for the past four months. Phyllis isn't
as well versed in Six Sigma as the team is, and it is her nature to question everything.
So she has asked for a capability study to be performed on the 7 key process factors that
affect leveler thickness and wants to see this for the past 35 days of production.
You are on the spot, but confident. You pull up the past 35 day's worth of data and you
calculate Pp and Ppk for each of the 7 factors. Is Phyllis going to be happy or is she
going to be more skeptical? That is the 'question of the day.'
Crunch the numbers--and you will find out. By the way--finish this deliverable correctly
AND MAKE ALL OF THECORRECTIONS REQUIRED ON THE PREVIOUS ASSIGNMENTS
and you are finished with the project! Congratulations!!!

Instructions for you:
"Is it possible for me to do a self-check?"
Instructions for you:
1. Construct histograms for each of the parameters. Note: The
first parameter 'thickness' is the product parameter.
The remaining parameters are process parameters that are thought to affect thickness.
2. Are the processes random (normally distributed)?
3. Calculate Pp and Ppk for each. Note: The upper and lower specifications
are listed at the bottom of each column. You will need these to do the calculations.
4. Are the processes acceptable?
"I'm lost"
"Can I do this with the Data Analysis Toolpak in Excel 2003?"
"Can I do this with the Data Analysis Toolpak in Excel 2007?"

Data:
Data:

Upper Specs
Lower Specs

Thickness
0.548
0.550
0.552
0.554
0.552
0.547
0.547
0.552
0.549
0.548
0.549
0.549
0.550
0.551
0.549
0.550
0.551
0.550
0.550
0.553
0.548
0.552
0.551
0.550
0.549
0.551
0.551
0.550
0.551
0.550
0.549
0.550
0.551
0.549
0.550

Time
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115
115

Temp Pressure
145
1300
146
1400
146
1500
147
1500
148
1500
148
1500
148
1500
149
1400
149
1800
149
1600
150
1600
150
1600
150
1600
150
1600
150
1600
150
1600
150
1600
150
1600
151
1600
151
1800
151
1800
151
1400
151
1400
153
1700
149
1700
152
1700
148
1700
147
1700
150
1700
151
1700
151
1800
151
1800
152
1900
152
1900
154
1900

0.125 dim.
0.121
0.122
0.122
0.123
0.123
0.124
0.124
0.124
0.125
0.125
0.125
0.125
0.125
0.128
0.128
0.125
0.129
0.126
0.126
0.126
0.126
0.126
0.126
0.126
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.128
0.128
0.129
0.130

0.23 dim.
0.229
0.230
0.230
0.231
0.231
0.231
0.231
0.231
0.231
0.231
0.231
0.231
0.230
0.230
0.234
0.233
0.235
0.229
0.234
0.232
0.232
0.232
0.232
0.232
0.232
0.232
0.232
0.232
0.233
0.233
0.233
0.233
0.234
0.234
0.235

R.P.M.
4400
4400
4400
4400
4450
4450
4450
4450
4450
4450
4450
4450
4450
4500
4500
4500
4550
4600
4650
4650
4650
4700
4700
4700
4700
4700
4700
4700
4700
4700
4700
4750
4750
4750
4800

HB

Thickness
0.5600
0.5400

Time
140
100

Temp
160
140

0.125 dim.
0.1350
0.1150

0.23 dim.
0.2400
0.2200

R.P.M.
8000
2000

HB
500
300

Press
2600
900

400
402
404
404
406
406
406
408
408
408
410
410
410
410
410
411
410
410
409
409
410
412
412
412
412
412
412
412
412
414
414
414
414
416
418

Be sure to review the week 3 and 12 virtual classes for more information on judging normality and Process Capability & Performance
before you submit this!

How to submit an Assignment

Target Assignment Submission Date - Submit in Week 14 or earlier
YOU DO NOT NEED TO CREATE CONTROL CHARTS TO COMPLETE THIS ASSIGNMENT!!
DO NOT SEND THE ACTUAL HISTOGRAMS UNLESS YOUR INSTRUCTOR ASKS YOU TO.
Project:
Manufacturing 2013 LAJ
Deliverable:
Pp Ppk
Student last name:
Your LAST name here
INSTRUCTIONS: (1) IF YOU SAY THE DISTRIBUTION IS NOT APPROXIMATELY NORMAL, GIVE THE
CORRECT NAME FOR THE PATTERN YOU SEE IN YOUR HISTOGRAM. (2) BASE YOUR DECISION ON
ACCEPTABILITY ON THE ASSUMPTIONS AND CRITERIA FOR Pp and Ppk DISCUSSED IN THE RECORDED
LECTURES AND VIRTUAL CLASSES ON CAPABILITY. YOU DO NOT NEED TO CREATE CONTROL

HINT!

CHARTS FOR THIS ASSIGNMENT!!
Thickness

Time

Temp

Pressure

0.125 dim

0.230 dim

R.P.M.

HB temp

Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?
Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?
Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?
Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?
Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?
Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?
Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?
Pp
Ppk
Approximately Normal?
If not normal, what is the shape?
Acceptable?
Why is it acceptable or not acceptable?

Check
Yes or No
Yes or No
ROUND YOUR Pp and Ppk
FINAL RESULTS TO 2
DECIMAL PLACES.

Check

Yes or No
Yes or No

Yes or No
Yes or No

IF YOU ANSWER "NO" TO
Check
ANY QUESTIONS ABOUT
NORMALITY, DESCRIBE
THE SHAPE YOU SEE USING
THE CORRECT
TERMINOLOGY.
Check

Yes or No
Yes or No

HINT: REMEMBER THAT
TWO ASSUMPTIONS
MUST BE MET IN ORDER TO
USE THESE FORMULAS
Check
CORRECTLY.

Yes or No
Yes or No

Check
Yes or No
Yes or No

Check
Yes or No
Yes or No

Check
Yes or No
Yes or No

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 - Pp, Ppk" 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 having all project deliverables 100% correct
is 7 days prior to the end of the course.