Compute the Values Using Minitab Computer Science Task

Size of sample_uchart
Number of defects_uchart
2000
15
2000
24
2000
24
2000
17
2000
21
2000
21
2000
21
2000
23
2000
28
2000
17
2000
40
2000
27
2000
28
2000
10
2000
39
2000
26
2000
20
2000
16
2000
31
2000
50
2000
12
2000
24
2000
34
2000
75
2000
27
2000
21
LEAN Six SigmaHomework 2
Please submit ONLY ONE MS Word or PDF file which includes your solutions for all problems.
Problem 1. Consider the data saved in data 1_HW2.csv and answer the following questions:
(a) Draw a histogram of the data. (3 points)
(b) How would you describe the shape of the histogram? (3 points)
(c) Draw a probability plot for normality test. (3 points)
(d) Determine whether the data follow a normal distribution. (3 points)
Problem 2. Consider a sample of fat content (in percentage) of 5 randomly selected hot dogs
2.67, 4.62, 4.14, 3.81, 3.83
Assume that the population distribution of fat content is normal. Suppose that the true average fat content
is 4. Carry out a hypothesis testing with a significance level of .05 to determine whether the sample data
contradict this belief:
(a) State the appropriate hypotheses including the null hypothesis and the alternative hypothesis. (2 points)
(b) Determine the appropriate test statistic (Hint: z test or t test) (2 points)
(c) Determine the rejection region. (3 points)
(d) Calculate the test statistic. (3 points)
(e) Determine if the test statistic lie in the rejection region and make your conclusion. (3 points)
1
TOP LEVEL PROCESS MAP & SIPOC
Project Title:
Project No.
S
Improving the Photocopy Process
EIN 6935 /4451 LEAN Six Sigma
1.
Place original
in the Copier
2.
Set Number
of copies
Prepared by: Walter Silva / Christos Nicolaou
Date (Orig) 06/11/2020
Rev (-)
3.
Enter size
required
4.
Set Light/
Dark settings
5.
Press
Button
Copies
Present
??
Page 1 of 1
yes
6.
Retrieve
copies
no
7.
Troubleshoot
INPUTS
Original Paper
OUTPUTS
INPUTS
OUTPUTS
INPUTS
Proper Alignment
Selection of
Proper Setting
Correct number of
copies
Selection of
Proper Setting
Size of original
document
Operator
Paper Orientation
Operator
Operator
OUTPUTS
INPUTS
Selection of
Correct paper tray
Proper Setting
Image Contrast of
original
Operator
OUTPUTS
Sharp image
INPUTS
OUTPUTS
INPUTS
OUTPUTS
Start Button
Complete Print
Cycle
Printed Copies in
the exit tray
Correct number of
copies
Operator
Mirrored Copies
Copier
No artifacts
Proper Alignment
Correct Contrast
X,C,N, SOP
SUPPLIER
INPUT
SOP
Document Owner
Original Paper
N
Paper Orientation
N
Person
SOP
SUPPLIER
Machine
SUPPLIER
X,C,N, SOP
SUPPLIER
INPUT
Proper Alignment
Copier
N
Machine
Selection of
Proper Setting
N
0
Operator
2.
Set
Number of
copies
OUTPUT
CUSTOMER
Correct number of
copies
Machine
0
0
0
0
0
0
0
0
INPUT
OUTPUT
INPUT
OUTPUT
CUSTOMER
Sharp image
Copier
Selection of
Proper Setting
Size of original
document
Operator
X,C,N, SOP
CUSTOMER
0
0
X,C,N, SOP
1.
Place
original in
copier
OUTPUT
Correct paper tray
3.
Enter size
required
CUSTOMER
Copier
X,C,N, SOP
SOP
SUPPLIER
Machine
0
Selection of
Proper Setting
Image Contrast of
original
4.
Set Light/
Dark
settings
0
0
0
0
Operator
0
0
0
0
0
0
0
INPUT
OUTPUT
INPUT
OUTPUT
5.
CUSTOMER
X,C,N, SOP
SUPPLIER
6.
0
0
CUSTOMER
E
C
Operator
Start Button
Copier
Operator
5.
Press
Button
Complete Print
Cycle
Machine
N
Copier
Printed Copies in
the exit tray
6.
Retrieve
copies
Correct number of
copies
0
0
0
0
0
0
0
Proper Alignment
0
0
0
Correct Contrast
Copier
List
X
C
N
SOP
Mirrored Copies
No artifacts
Operator
CAUSE & EFFECT MATRIX
Project Title:
Improving the Photocopy Process
Project No.
EIN 6935 /4451 LEAN Six Sigma
Prepared by: Walter Silva /
Christos Nicolaou
Page 1 of 1
C&E Matrix Date (Orig) 06/11/2020
3
Output Variables (Y’s), Customer
Expectations, CTS’s
Correct
Contrast
6
No artifacts
6
Mirrored
Copies
9
Complete
Print Cycle
6
Sharp image
6
Correct
paper tray
3
Correct
number of
copies
6
Proper
Alignment
Rating of Importance to Customer
NOTE: These ratings can change based on team
perspective.
Total
No.
Process Step
Process Inputs (x’s)
1
2
3
6
7
11
12
13
Place original in Copier
Place original in Copier
Place original in Copier
Set Number of copies
Set Number of copies
Enter size required
Enter size required
Enter size required
Original Paper
Paper Orientation
Operator
Selection of Proper Setting
Operator
Selection of Proper Setting
Size of original document
Operator
1
6
9
1
1
6
6
1
1
1
9
9
1
1
1
6
1
1
1
6
6
1
1
1
1
1
1
1
1
1
1
3
6
3
1
1
6
6
1
1
3
3
3
1
3
1
1
1
1
1
1
1
1
1
1
1
57
135
135
87
114
135
117
1
1
6
1
6
9
1
1
168
16
17
18
Set Light/ Dark settings
Set Light/ Dark settings
Set Light/ Dark settings
Selection of Proper Setting
Image Contrast of original
1
1
1
1
1
1
6
9
3
1
1
1
6
6
9
9
147
147
Operator
1
1
1
9
3
1
6
9
165
21
22
23
Press Button
Press Button
Press Button
Start Button
Operator
Copier
1
1
1
1
1
1
1
1
9
3
1
1
1
1
1
1
117
63
1
9
6
6
9
1
6
6
246
26
Retrieve copies
Printed Copies in the exit tray
1
1
1
1
1
1
1
1
45
228
117
240
246
459
222
234
132
DO NOT DELETE
Drop Down Window List
9
6
3
1
Rev (-)
Comments
CAUSE & EFFECT MATRIX
Project Title:
Improving the Photocopy Process
Project No.
EIN 6935 /4451 LEAN Six Sigma
Prepared by: Walter Silva /
Page 1 of 1
Christos Nicolaou
C&E Matrix Date (Orig) 06/11/2020
Rev (-)
3
Output Variables (Y’s), Customer
Expectations, CTS’s
Correct
Contrast
6
No artifacts
6
Mirrored
Copies
9
Complete Print
Cycle
6
Sharp image
6
Correct paper
tray
3
Correct
number of
6
Proper
Alignment
Rating of Importance to Customer
NOTE: These ratings can change based on team
perspective.
No.
Process Step
Process Inputs (x’s)
1
Press Button
Copier
1
9
6
6
9
1
6
6
2
Enter size required
Operator
1
1
6
1
6
9
1
1
3
Set Light/ Dark settings
Operator
1
1
1
9
3
1
6
9
246
168
165
4
5
6
7
8
9
10
11
12
13
14
15
Set Light/ Dark settings
Set Light/ Dark settings
Place original in Copier
Place original in Copier
Enter size required
Enter size required
Press Button
Set Number of copies
Set Number of copies
Press Button
Place original in Copier
Retrieve copies
Selection of Proper Setting
Image Contrast of original
Paper Orientation
Operator
Selection of Proper Setting
Size of original document
Start Button
Operator
Selection of Proper Setting
Operator
Original Paper
Printed Copies in the exit tray
1
1
6
9
6
6
1
1
1
1
1
1
1
1
1
1
1
1
1
9
9
1
1
1
1
1
6
1
6
6
1
1
1
1
1
1
6
9
1
1
1
1
1
1
1
1
1
1
3
1
1
1
3
1
9
6
3
3
1
1
1
1
6
6
3
3
1
1
1
1
1
1
6
6
1
3
1
1
1
1
1
1
3
1
9
9
1
1
1
1
1
1
1
1
1
1
147
147
135
135
135
117
117
114
87
63
57
45
228 117 240 246
DO NOT DELETE
Drop Down Window List
9
6
459
222 234 132
Total
Comments
3
1
Failure Modes and Effects Analysis Spreadsheet
Introduction:
This spreadsheet was designed to simplify the Failure Mode and Effects Analysis process.
What is a Failure Modes and Effects Analysis?
It is
*
*
*
*
a structured approach to:
Identifying the ways in which a product or processes can fail
Estimating the risk of specific causes with regard to these failures
Prioritizing the actions that should be taken to reduce the chances of failure
Evaluating the design validation plan (Product) or the current control plan (Product) for preventing these failures
The
*
*
*
purposes of performing such an analysis are:
To identify potential failure modes and rate the severity of their effects
To rank order potential deficiencies
To help focus on prevention
Why perform a Failure Modes and Effects Analysis?
The general benefits of using these tool are:
* Improves the quality, reliability, and safety of products and processes in a proactive manner
* Helps to increase customer satisfaction, by addressing failures that keep us from meeting critical customer
requirements in processes or products
* Reduces product development timing and cost
* Identifies potential process risks
About this spreadsheet…
Follow these simple instructions and you will master the art of FMEA development in no time!!
1) On the Failure Mode & Effects page, fill in the information at the top to identify the analysis.
2) Start filling out the spreadsheet from left to right. It is recommended that you define all the causes of a
particular failure mode and effect before moving to the next failure mode. In doing so, you will avoid having to
insert rows, and other spreadsheet manipulation. There is a drop down window to assist you select a number from a
FMEA Worksheet
Process/Product
Failure Modes and Effects Analysis Worksheet
Project Title:
Improving the Photocopy Process
Prepared by: Walter Silva / Christos Nicolaou
Project No.
EIN 6935 /4451 LEAN Six Sigma
FMEA Date (Orig) 06-11-2020
Page 1 of
1
Rev (-)
Failure Modes Process Step
Key Process Input
What can go wrong?
Effects
Causes
Press Button
Copier
No paper output
Must redo copy
Paper Jam
Press Button
Press Button
Copier
Copier
No paper output
Artifacts (smears) present
Must redo copy
Must redo copy
Out of paper
Copier toner
Preventive Maintenance
SOP #123
None
Copier Panel Control
Current Controls
Enter Size Required
Operator
Select Lower Quantity
Must run copier for missing
quantity
Operator Error
None
Enter Size Required
Operator
Select Higher Quantity
Throw away excess quantity
Operator Error
Enter Size Required
Operator
Keypad malfunctioned
Must run copier for missing
quantity
Wear
Enter Size Required
Operator
Keypad malfunctioned
Throw away excess quantity
Wear
Enter Size Required
Operator
Select wrong setting
Must redo copy
Operator Error
Set Light/ Dark settings
Operator
Copier malfunctioned
Must redo copy
Calibration
None
Preventive Maintenance
SOP #123
Preventive Maintenance
SOP #123
None
Preventive Maintenance
SOP #123
Page 7
Process/Product
Failure Modes and Effects Analysis
(FMEA)
Improving the Photocopy Process
Project No.
EIN 6935 /4451 LEAN Six Sigma
Potential Failure
Mode
Copier
Press Button
Copier
Press Button
Copier
Enter Size Required
Operator
Enter Size Required
Operator
Enter Size Required
Operator
Enter Size Required
Operator
#REF!
Operator
#REF!
Set Light/ Dark
settings
Potential Causes
O
C
C
What is the impact
on the Key Output
Variables (Customer
Requirements) or
internal
requirements?
No paper output
Must redo copy
9
Paper Jam
6
No paper output
Must redo copy
3
Out of paper
Must redo copy
6
Copier toner
6
3
What is the process What is the In what ways does
step under
process Input the process step go
investigation?
under
wrong?
investigation?
Press Button
S
E
V
Potential Failure
Effects
Artifacts (smears)
present
Select Lower
Quantity
Select Higher
Quantity
Keypad
malfunctioned
Keypad
malfunctioned
Select wrong
setting
Copier
malfunctioned
Must run copier for
missing quantity
Throw away excess
quantity
Must run copier for
missing quantity
Throw away excess
quantity
What causes the
process step to go
wrong?
How often does cause or FM
occur?
Process Input
FMEA Date (Orig) 06-11-2020
How Severe is the effect to the
customer?
Process Step
Current Controls
What are the existing
controls and procedures
(inspection and test) that
prevent either the cause
or the Failure Mode?
Should include an SOP
number.
D
E
T
Preventive Maintenance
SOP #123
6
3
None
3
Copier Panel Control
Operator Error
1
Operator Error
6
R
P
N
Actions
Recommended
Resp.
Rev (-)
Actions Taken
S
E
V
O
C
C
D
E
T
R
P
N
What are the
Whose
What are the
actions for reducing Responsible completed actions
the occurrence of
for the
taken with the
the Cause, or
recommende
recalculated
improving
d action? RPN? Be sure to
detection? Should
include
have actions only
completion
on high RPN’s or
month/year
easy fixes.
324
0
9
81
0
6
108
0
None
9
54
0
None
3
54
0
6
36
0
6
36
0
Preventive Maintenance
SOP #123
Preventive Maintenance
SOP #123
6
Wear
1
6
Wear
1
Must redo copy
3
Operator Error
3
None
3
27
0
Must redo copy
3
Calibration
1
Preventive Maintenance
SOP #123
6
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
DO NOT DELETE
Drop Down Window
Page 1 of 1
Prepared by: Walter Silva / Christos Nicolaou
How well can you detect
cause or FM?
Project Title:
9
6
3
1
Page 8
Process/Product
Failure Modes and Effects Analysis
(FMEA)
Prepared by: Walter Silva /
Christos
Page 1 of 1
Nicolaou
FMEA Date (Orig) 06-11-2020
Rev (-)
Improving the Photocopy Process
Project Title:
EIN 6935 /4451 LEAN Six Sigma
Project No.
Process Step
Process Input
Potential Failure
Mode
Potential Failure
Effects
S
E
V
Potential Causes
O
C
C
Current Controls
D
E
T
R
P
N
Press Button
Copier
No paper output
Must redo copy
9
Paper Jam
6
Preventive Maintenance
SOP #123
6
324
0
Must redo copy
6
Copier toner
3
Copier Panel Control
6
108
0
Must redo copy
3
Out of paper
3
None
9
81
0
6
Operator Error
1
None
9
54
0
3
Operator Error
6
None
3
54
0
6
36
0
6
36
0
Press Button
Copier
Press Button
Copier
Enter Size
Required
Enter Size
Required
Enter Size
Required
Enter Size
Required
Enter Size
Required
Set Light/ Dark
settings
Operator
Operator
Operator
Operator
Operator
Operator
Artifacts (smears)
present
Artifacts (smears)
present
Select Lower
Quantity
Select Higher
Quantity
Keypad
malfunctioned
Keypad
malfunctioned
Select wrong
setting
Copier
malfunctioned
Must run copier for
missing quantity
Throw away excess
quantity
Must run copier for
missing quantity
Throw away excess
quantity
Must redo copy
Actions Taken
S
E
V
O
C
C
D
E
T
R
P
N
Wear
1
6
Wear
1
3
Operator Error
3
None
3
27
0
1
Preventive Maintenance
SOP #123
6
18
0
Calibration
DO NOT DELETE
Drop Down Window
Resp.
6
3
Must redo copy
Preventive Maintenance
SOP #123
Preventive Maintenance
SOP #123
Actions
Recommended
9
6
3
1
Page 9
Process/Product
Failure Modes and Effects Analysis
(FMEA)
Improving the Photocopy Process
Project Title:
Press Button
Press Button
Copier
Copier
Copier
Enter Size Required
Operator
Enter Size Required
Operator
Enter Size Required
Operator
Enter Size Required
Operator
Enter Size Required
Operator
Set Light/ Dark
settings
Operator
No paper output
Artifacts (smears)
present
Artifacts (smears)
present
Select Lower
Quantity
Select Higher
Quantity
Keypad
malfunctioned
Keypad
malfunctioned
Select wrong
setting
Copier
malfunctioned
S
E
V
Potential Failure
Effects
What is the impact
on the Key Output
Variables (Customer
Requirements) or
internal
requirements?
9
Must redo copy
6
Must redo copy
Potential
Causes
What causes the
process step to
go wrong?
Paper Jam
Copier toner
O
C
C
6
3
D
E
T
Current Controls
What are the existing
controls and procedures
(inspection and test) that
prevent either the cause
or the Failure Mode?
Should include an
SOP number.
Preventive Maintenance
SOP #123
6
6
Copier Panel Control
Actions
Recommended
Resp.
Actions Taken
Rev (-)
S
E
V
O
C
C
D
E
T
i
R N
P
What are the
Whose
What are the
actions for reducing Responsible completed actions
the occurrence of
for the
taken with the
the Cause, or
recommended
recalculated
improving
action?
RPN? Be sure
detection? Should
to include
have actions only
completion
on high RPN’s or
month/year
easy fixes.
324
108
Refer to
improvement plan
attached (item #1)
Refer to
improvement plan
attached (item #2)
Refer to
improvement plan
attached (item #3)
Refer to
improvement
plan attached
(item #1)
Refer to
improvement
plan attached
(item #2)
Refer to
improvement
plan attached
(item #3)
Refer to
improvement plan
9
attached (item #1)
Refer to
improvement plan
6
attached (item #2)
Refer to
improvement plan
attached (item #3)
162
3
486
3
3
54
54
6
324
9
81
6
Operator Error
1
None
9
54
0
3
Operator Error
6
None
3
54
0
6
Wear
1
6
36
0
6
Wear
1
6
36
0
Must redo copy
3
Operator Error
3
None
3
27
0
Must redo copy
3
Calibration
1
Preventive Maintenance
SOP #123
6
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
Page 10
= Impact
Factor x
Effort
162
None
6
Selection
Score
6
3
9
Effort
3
Out of paper
Preventive Maintenance
SOP #123
Preventive Maintenance
SOP #123
Impact Factor
1 = HIGH $,
manpower &
=
time
9 = LOW $,
RPN (initial) –
PRN (improved) manpower &
time
3
Must redo copy
Must run copier for
missing quantity
Throw away excess
quantity
Must run copier for
missing quantity
Throw away excess
quantity
DO NOT DELETE
Drop Down Window
R
P
N
How well can you detect cause or
FM?
Potential Failure
Mode
What is the process What is the In what ways does
step under
process Input the process step
investigation?
under
go wrong?
investigation?
Press Button
FMEA Date (Orig) 06-11-2020
How often does cause or FM
occur?
Process Input
How Severe is the effect to the
customer?
Process Step
Page 1 of 1
Prepared by: Walter Silva / Christos Nicolaou
EIN 6935 /4451 LEAN Six Sigma
Project No.
0
Size of sample_uchart
Number of defects_uchart
2000
15
2000
24
2000
24
2000
17
2000
21
2000
21
2000
21
2000
23
2000
28
2000
17
2000
40
2000
27
2000
28
2000
10
2000
39
2000
26
2000
20
2000
16
2000
31
2000
50
2000
12
2000
24
2000
34
2000
75
2000
27
2000
21