This slide deck will help you appreciate the application of statistics (and now data science) in the field of Quality Management and Process Improvement. And why is there a need to produce a consistent "in spec" product at 99.9997% of the time.

1. Six Sigma
Green Belt Training
6
Methusael Brown Cebrian ITIL v3 LSSBB
Certified Lean Six Sigma Black Belt
“You cannot Manage, what you cannot measure” – W. Edwards Deming

2. What is Six Sigma?
- It is a Quantitative, data-driven Define,
Measure, Analyze, Improve, Control
methodology to Process Improvement
based on Statistical and Management tools
to increase efficiency in the process.
- Simply put, it is a way of using data to solve
problems and make businesses more
profitable.
The term “sigma” is used to designate the distribution or spread around the
mean (average) of any process or procedure.


3. • Developed by Motorola, used successfully by Texas
Instruments, Boeing, Honeywell, Lockheed Martin.
• GE, has become the face of Six Sigma due to its wide
adoption throughout the organization.
• Internal Focus: Improve existing processes – manufacturing,
business transaction for service industry.
• External Focus: Listens to Voice of the Customer (VoC).
• Uses trained teams
- Champions: Business Leaders, provide resources and
support implementation.
- Master Black Belts: Experts and Culture-Changers, train
and mentor Black Belts/ Green Belts.
- Black Belts: Lead Six Sigma project teams.
- Green Belts: Carry out six sigma projects related to their
jobs.
Driver for Cost Savings and Customer Satisfaction

4. Six Sigma is:
• An enabler to Business Strategy.
• Places customers at the center of the performance
improvements.
• Fact-based approach for improving business processes and
solving problems.
• A proven methodology and toolset supported by deep
training and mentoring.
• Focused on reducing variability of processes
• Elimination of Defects/Wastes (Mudas).
• A way to develop highly skilled business leaders.
• A means for creating capacity in organizations.
Quality is Everyone’s Responsibility

5. Striving towards Six Sigma
Six Sigma Improves Quality by Reducing Defects and Variation

6. Quality
99% is never good enough!

7. Building on Quality reduces long -term costs
Why do we need to pursue Quality
Initiatives?
• Meet Customer expectations for higher quality.
• Provide a competitive differentiator in the Market.
• Build greater pride and satisfaction within the company.
• Drive other key goals: Productivity and Growth.

8. Delighting Customers
• Making customers successful
• Customer-Centric metrics
• Listens to the Voice of the Customer (Voc)
• Surveys, Interviews, Net Promoter Score
Make customers feel Six Sigma

9. The Kano Model
• A way to evaluate how customer satisfaction is
impacted by an initiative
• Three types of improvements
• Hygiene factor (green). Customer expect this
and is dissatisfied if not fulfilled. Ensuring that these
needs are met should have highest priority.
• Performance factor (blue). There is a
relationship between customer satisfaction and how
well the need is met. Important to ensure
satisfactory performance.
• Delight factor (red). Customers do not expect
this and are thus indifferent if the need is not met.
A way to create additional satisfaction if all hygiene
factors are performing.

10. Definitions

12. The statistical objective of Six Sigma
Reduce Variation and Center Process – Customers feel
variation more than the mean.

14. What is Variation?
• Variation is the extent to which items (things) differ, from
one to the next!
• There will always be some variation present in all
processes.
-Nature – shape, size of leaves, height of trees
-Human – Handwriting, speed of walk, tone of voice etc.
-Mechanical – weight/size/shape of product, content
etc.
We can tolerate this variation if:
- The process is on target (where we want it to be)
- The variation is small compared to the customer
specifications.

15. According to Deming:
• 85%-95% of all variation is Common Cause.
• 5%-15% of all variation is Special Cause.
• Common Cause – variation is random,
stable and consistent over time. It is
expected variation.
• Special Cause – is not random, and
changes over time. It is unexpected
variation. There is undue influence in the
process.
Variation is the enemy of Process Improvement efforts.

16. Common Cause Variation

17. Special Cause Variation

18. 6 Causes of Variation
• Man
• Machine
• Material
• Method
• Measurement
• Mother Nature

19. Process
Any activity that takes inputs, adds value, and
provides an output(s).
Variation exists in the process.

20. Six Sigma improvement approach
Six Sigma is Long Term Commitment to the Philosophy of Quality.

21. The heart of Six Sigma
Historically the Y – with Six Sigma the X’s
Focusing on the X’s relies on a good and steady flow of Data – Metrics!

22. D-M-A-I-C

23. Lean Six Sigma Checklist

24. The Changing Focus of Six Sigma
The GE Experience –> Lean Six Sigma expands the tool set
Six Sigma – a dynamic, living initiative

25. Summary of Introduction:

27. Working with DMAIC!

31. Identify Project Critical To Quality

33. Define Phase Date Version 1.1
The scope of this project will focus on following key aspects:
People
Process
Critical To Quality
Machines
Workplace
Problem / Goal Roles
Sponsor
BB
GB
Shift Managers:
Allan K, Mark L., John Doe
Shift Machine Operators
Rey M , Louie G, Rick L.
Finance Accountant
Julie P.
Project Outcome Milestones
Define 1-Jun-13
Measure 15-Jun-13
Analyze 15-Jul-13
Improve 15-Oct-13
Control 15-Nov-13
Potential Risks
Lack of Buy in from operators
Non-Compliance to governance/policy/SOP and difficult to monitor
Lack of support from Leadership Signature Sponsor Signature BB / GB
We will look at the existing capabilities of the machines to
produce the PCB's according to specifications. Including
the ways it processes the raw materials being fed to it, as
well as its technological limitations to produce a PCB
according to specs.
We will look at the workplace environment involved in the
process of producing PCB's. IF an essential 5S processes
are in place. Some aspects that will be looked at, but is not
limited to: Machine arrangements, distance, tool
placements, lighting, tidiness.
The existing process produces a high number of scraps or waste, which affects the pricing model
for the product as well as the reliability of delivery schedules, we will pursue key areas of interests
such as People, Process, Machines, and Workplace in zeroing down the root causes of the
existing issues. In order to meet the Customer requirements for Volumes, we will embark on a
project using Lean Six Sigma methodologies to improve the existing process by eliminating 98%
from existing Scrap Rates, reduce product cost as well as achieve 100% reliability in delivery
schedule. With the elimination of Scraps in the processes, we will be able to provide room for
future growth in customer demands.
98% Reduction of Scraps
100% Availablity of Machines to Operate
Newly trained Operators
Newly published SOP's, Policy, Guideline and Manuals
Reduced Product Cost
100% Reliability in Delivery Schedule
35% increase in volume capacity
Plant Manager - David Mack
Quality Manager - John Loyd
Methusael B. Cebrian
Core Team
Project Charter
The Quality and Reliability of our process and products are threatened because of the defects
existing in the manufacturing line. Customers are complaining that we can no longer keep up with
our committed scheduled deliveries, which also affects their supply chain. The cost of raw
materials is also at all time high, and a high rate of scraps is no longer acceptable.
The high cost of raw materials and the number of scrap rates, is passed to the customer which
coupled with unreliable delivery schedule makes our customers to look for other suppliers. It is
therefore imperative to engage the problem and eliminate it using Lean Six Sigma methodology
and make our product a reliable and cost competetive one for our customers.
Project Name
Business Case Project Scope
Eliminate Manufacturing Defects Affecting Scrap Rate, Product
Cost and Delivery Schedule.
1-Jul-13
We will look at the skill sets, trainings, and capabilities of
people involved in the process, to follow the existing
instructions, guidelines and SOP's needed to produce the
PCB's.
We will look at the existing methodologies, instructions,
steps if it conforms to the right processes needed to
produce the PCB's according to specifications.

34. Team Charter

35. Five major elements of a Charter

37. Problem and Goal Statements
Together they provide focus and purpose for the team

38. Description of the “pain”

39. Problem Statement

41. The Goal Statement

42. SMART Problem and Goal
Statements

44. Milestones

57. Simplification is the goal of Lean Six Sigma!

60. Example: It is much easier to work on your SIPOC
Chart, if you follow POCIS process.
SUPPLIERS INPUTS OUTPUTS CUSTOMERS
Client Inputs Order order call/email Order Slips
Production Planning Control
Department
Production Planning Control
Department
Order slips/documents from
Clients Internal Production orders
Production Material Control
Department
- Release internal
production order
Production Material Control
Department Production Orders Raw Materials Production Floor
- Release Material and
other Raw materials to
production shop
Production Floor
Raw Materials for PCB
manufacturing Printed Circuit Boards Quality Inspection
- PCB Production Process
Quality Inspection
Output products from
production floor.
Quality Pass, Defects,
Scraps Packaging Facility
Packaging Facility
Final Product ready for
delivery Package PCB's for delivery
- Final Product packaged
and ready for delivery
PROCESS
SIPOC DIAGRAM
Online OrderSystem
Production and Engineering
Documentations
Packaging - delivery to customers
Pre Prod Engineering
Check for Specs tolerance,
Defects
Load Lookup/Look Down
Stencil/PWB
Alignment
Print
Wipe Stencil
Buttom
UnloadSeparate

64. Define – make a case for action
Measure – define success

71. Pareto Chart – 80/20 RULE

83. Failure Modes and Effects
Analysis (FMEA)
Process or
Product Name:
Prepared by: Page ____ of ____
Responsible: FMEA Date (Orig) ______________ (Rev) _____________
Process Step
Key Process
Input
Potential Failure Mode Potential Failure Effects
S
E
V
Potential Causes
O
C
C
Current Controls
D
E
T
R
P
N
Actions
Recommended
Resp. Actions Taken
S
E
V
O
C
C
D
E
T
R
P
N
What is the
process step
What is the Key
Process Input?
In what ways does the Key
Input go wrong?
What is the impact on the
Key Output Variables
(Customer Requirements) or
internal requirements?
HowSevereisthe
effecttothe
cusotmer?
What causes the Key Input to
go wrong?
Howoftendoescause
orFMoccur?
What are the existing controls
and procedures (inspection and
test) that prevent eith the cause
or the Failure Mode? Should
include an SOP number.
Howwellcanyou
detectcauseorFM?
What are the actions
for reducing the
occurrance of the
Cause, or improving
detection? Should
have actions only on
high RPN's or easy
fixes.
Whose
Responsible
for the
recommende
d action?
What are the completed
actions taken with the
recalculated RPN? Be
sure to include
completion
month/year
0 0
0 0
0 0
0 0
Process / Product
Failure Modes and Effects Analysis
(FMEA)
• RPN = Severity * Occurrence * Detection

84. What is FMEA?
• A predictive/ Proactive tool that allows us to
identify potential risk failures in the system
or process, and prevent it from happening.
Opposite of FMEA: Reactive Tool
 Root Cause Analysis
 Pareto Chart

85. Why do we need FMEA?
• Predict possible failure modes in the
process.
• Reduce Risk of Failure
• Prevent Failure from Happening
• Identify Potential Effects of Failure
• Identify Current Controls in place
• Recommended Action.

86. When to Use an FMEA
ANALYZE PHASE
 Determine if there is a High Risk of Failure
and Determine if the failures are
detectable.
IMPROVE PHASE
 Evaluate impact of proposed changes.
CONTROL PHASE
 Determine Which Failure Modes are the
Most Critical to Control ->Include in
Control Plan

98. Who will
Do it?
Type of Operational Measurement Data Tags Needed Data Collection Person(s) What? Where? When? How Many?
Measure Measure Definition or Test Method to Stratify the Data Method Assigned
Name of Xor Y Clear definition of Visual Data tags are Manual? State What Location How The number
parameter attribute or the measurement inspection defined for the Spreadsheet? who has measure is for often of data
or condition discrete defined in such a or automated measure. Such Computer based? the being data the points
to be data, way as to achieve test? as: time, date, etc. responsibility? collected collection data collected
measured product or repeatable results Test instruments location, tester, is per sample
process from multiple are defined. line, customer, collected
data observers buyer, operator,
Procedures for etc.
data collection
are defined.
Define What to Measure Define How to Measure Sample Plan
Data Collection Plan

106. Measurement Systems
Analysis
Where does variation come
from?

107. Measurement Variation
Actual Value
Measured Value
Variation

108. Measuring Process
The Process:
Variable Data
Operators
The Tool
Part To Be
Measured
Measurements

109. Gage R & R Studies
• Measures the Repeatability and Reproducibility of
your measurement process and compares it to the
variation occurring in your part
• Or stated another way, Measures the amount of
error introduced in the measurement process

110. Total Variation in Measurement:
Preferred
Actual Variation in
Product
Operator
Environment
Gage
Process

111. Total Variation in Measurement:
Unacceptable
Actual Variation in
Product
Operator
Environment
Gage
Process

112. Accuracy and Precision
Accuracy: How close to the
measured.
Precision: How repeatable
Examples of:
• Poor accuracy and precision
• Good precision, poor accuracy
Actual
Value
Measured
Value
Accuracy
Repeatability
(Precision)

113. Target Practice
 How could the green player
improve performance?
 How could the yellow player
improve performance?
Which player do you think has
a better chance of becoming a
champion dart player?
Typically, it is easier to shift the average than to reduce variation

114. Understanding Accuracy and
Precision
Target
Target
Target
Target
High accuracy & high precision Low accuracy & high precision
High accuracy & low precision Low accuracy & low precision

115. Gage R&R Example
• One gage
• Two operators
• Measuring the length of a part in meters
twice
• Blind samples
• Spec Limit: +/- 0.1 mm
• Gage Tolerance +/-0.0001 mm

116. The Data

117. Use Minitab
Open Minitab, enter data as shown
Quality Tools: Gage R&R (Crossed)
Follow directions as on following sheets
Minitab uses ANOVA to perform analysis
• ANOVA was discussed in DOE Class

121. The Results

122. StatGuide

126. Statistical Process Control (SPC) is a technique that enables
the quality controller to monitor, analyze, predict, control, and
improve a production process through control charts.
Control charts were developed as a monitoring tool for SPC by
Shewhart.
Statistical Process Control

127. Understanding Variation
The 6 Ms – all variation is from one or more of the
6Ms.
• Man (generic)
• Machine
• Material
• Method
• Measurement
• Mother nature

128. USLLSL
USLLSL
LSL USL
Process Variation = Lost $

129. Common Cause Variation
• Natural, expected variation, Controllable
• Characterized by a stable and consistent pattern of variation over time.
A process operating with controlled variation has an outcome that is
predictable within the bounds of the control limits.

130. Special Cause Variation
• Unnatural, not expected
•Perform root cause analysis and eliminate if possible

131. Remember!
According to Deming:
85% to 95% of all variation is
Common Cause.
5% to 15% of all variation is
Special Cause.

132. “Eighty-five percent of the reasons for failure to meet
customer expectations are related to deficiencies in
systems and process…rather than the employee.
The role of management is to (fundamentally) change
the process rather than badgering
individuals to do better.”
Should We Be Concerned
with Common Cause Variation?
– W. Edwards Deming

133. Types of Data
Discrete Data
• Is Counted
• Can only take certain values
• Example: The number of students in class (you cannot have
a half student)
Continuous Data
• Is measured
• Can take any value (within a range)
• Often involve fractions or decimals.
• Example: A person’s height, Time (hour, minutes, seconds),
weight, length.

134. Control Charts
• Control charts are simple but very powerful tools that can
help you determine whether a process is in control
(meaning it has only random, normal variation) or out of
control (meaning it shows unusual variation, probably due
to a "special cause").
• Control charts have two general uses in an improvement
project. The most common application is as a tool to
monitor process stability and control. A less common,
although some might argue more powerful, use of control
charts is as an analysis tool.

135. Choosing Control Chart using Minitab

136. Commonly used Control Charts
Control Charts for Continuous Data
Xbar-R Charts
• Xbar charts give the average value each operator obtained per part.
• R chart shows the difference between the largest and the smallest
measurement for each part. The R chart is used to evaluate the
consistency of process variation.
• Each subgroup is a snapshot of the process at a given point in time.
The chart’s x-axes are time based, so that the chart shows a history of
the process. For this reason, it is important that the data is in time-order.

137. • The Xbar chart is used to evaluate consistency of process averages by
plotting the average of each subgroup. It is efficient at detecting
relatively large shifts (typically plus or minus 1.5 σ or larger) in the
process average.
• The R chart, on the other hand, plot the ranges of each subgroup. The
R chart is used to evaluate the consistency of process variation. Look at
the R chart first; if the R chart is out of control, then the control limits on
the Xbar chart are meaningless.

138. Control Charts for Discrete Data
C Charts
• Assumes a Poisson distribution (counting or integers)
• Tracks the # defects and presence of Special Causes
• Used when identifying the total count of defects per unit (c)
that occurred during the sampling period, the c-chart allows
the practitioner to assign each sample more than one
defect. This chart is used when the number of samples of
each sampling period is essentially the same.

139. • This chart is used when the number of samples of each
sampling period is essentially the same.

140. Control Limits
The data determine the control limits with Common Cause
variation
UCL
LCL
Ave
Measurement Number
Value

141. Control Limits Differentiate CC and
SC Variation
LCL
Special Cause Variation
UCL
When a process is stable and in control, it displays common cause
variation, variation that is inherent to the process.
If the process is unstable, the process displays special cause variation,
non-random variation from external factors.

142. X bar Control Chart for SPC
Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Centerline = Mean
USL
LSL

143. X bar R Chart - The X bar Part
UCL 74.015
CL 74.001
LCL 73.988
73.980
73.985
73.990
73.995
74.000
74.005
74.010
74.015
74.020
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
S17
S18
S19
S20
S21
S22
S23
S24
S25
Date/Time/Period
X bar Observations
CL = Center Line; this is the average of the
averages (grand average) of each sample
average

144. Control Limits and Spec Limits
CLs are what the process delivers
• Typically +/- 3 sigma from mean
SLs are what the product needs
Hopefully CLs are “tighter” than SLs

145. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rules
Developed by Dr. Walter Shewhart in 1931
Assume Normal Distribution
“3 sigma significant” 1891-1967

146. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 1
• One point more than 3 sigma from mean

147. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 2
• Nine points in a row on same side of the
mean

148. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 3
• Six points in a row all decreasing or all
increasing

149. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 4
• Fourteen points in a row alternating up
and down

150. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 5
• Two out of three points more than two
sigma from the mean on the same side

151. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 6
• Four out of five points more than one
sigma from the mean on the same side

152. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 7
• Fifteen points in a row within one sigma
of mean on either side

153. Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
Shewhart Rule 8
• Eight points in a row more than one
sigma from mean on either side

154. Using the Rules
 Xbar-R charts use 1-8
 C Charts 1-4
Often people will select which rules to chose, 7
and 8 are least often used
Since 3 sigma is 99.7%, if you analyze large
quantities of data you will get rule violations
even with CC variation

155. The Control Chart
Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
x
x
x + A2R
- A2R

156. Example
Stencil Printing Volume
Subgroup size =5
60 subgroups
Develop Xbar - Chart

157. Xbar-R with Minitab:
Enter data (Excel) then…..

159. Discussion?
Sample
SampleMean
554943373125191371
2000
1900
1800
1700
__
X=1870.6
UC L=2007.3
LC L=1733.9
Sample
SampleRange
554943373125191371
600
450
300
150
0
_
R=237.0
UC L=501.1
LC L=0
6
1
Xbar-R Chart of Print Volume Data

161. Stencil Printing Process
The Process:
Variable Data
Process Parameters:
Print Speed
Snap Off
Downstop
Design:
PWB Layout
Stencil Design
Solder Paste Design
Materials:
PWB
Solder Paste
Stencil
Squeegee
The Product:
An Acceptable Board
For Component Placement
Quality Level
(Attribute Data)

162. C Charts: Control Charts for Attribute
Data
Measure attribute data
Ex: X defects per 1000 parts
Can be done manually
xxLCL 3
xxUCL 3

163. Using Minitab
1. Enter defect data in column C-1
2. Then perform operations as above

165. Conclusions?
Sample
SampleCount
28252219161310741
35
30
25
20
15
10
5
0
_
C=13.66
UCL=24.74
LCL=2.57
1
1
1
1
2
1
1
1
C Chart of Defects

166. Analysis

167. Other Control Charts
C and Xbar-R charts are most commonly used
in SPC

168. Process Capability Analysis
Where specs and process capability face off
• Use Capability Sixpack (normal)
• Assumes Normal Distribution
Is your process in spec?
How well is it in spec?
• Cp
• Cpk

169. When the Data are Not Normal
Control chart theory will be misleading
Minitab tests for normality
Fortunately, data are often normal, or can be
normalized with a transformation
X 1 2 3123
Mean

170. Capability Analysis:
What are Cp and Cpk?
Cp – Process Capability ->measures
precision only.
Cp - is a measurement that considers the
spread of the data relative to the
specification limits. As shown in the
following figure, a high Cp value indicates
low process variation.
6 sigma means Cp = 2

171. Cpk – Process Capability Index ->measures precision and
accuracy.
Cpk - is a measurement that considers both the spread of the
data and the shift of the data relative to the specification. As
shown in the following figure, a process may have good Cp
but not meeting specifications (low Cpk).
6 sigma means Cp = 2 and Cpk =1.5

172. Remember!
It is important to note that capability indices are only useful
when the process is stable.
In addition, like all other statistical procedures, capability
indices are only estimates based on the samples collected.
Thus, control charts are often used in conjunction to monitor
the process over time rather than relying on a single number.

173. Good Cp and Cpk
X 1 2 3123
Mean,
99.74% with +/- 3 sigma
LSL USL
Tolerance
Width of Distribution

174. Good Cp, Poor Cpk
X 1 2 3123
Median, Mean, Mode
LSL USL
Width of Distribution
3 standard deviations

175. Cp and Cpk
• Cp = USL – LSL
6
• Cpu = USL – Xbar
3
• Cpl = Xbar - LSL
3
• Cpk = min (Cpu, Cpl )

176. What is the Cp and Cpk
of this Distribution?
X 1 2 3123
Median, Mean, Mode
99.74%
LSL USL
Tolerance
Width of Distribution
Cpl
Cpu
3 standard deviations

177. Current process has 3 standard
deviations between target and USL.
USLLSL
1 Standard Deviation
Target
Process
Center
3
Improved process (reduced variation) has
6 standard deviations between target and
USL.
What 6 Sigma Looks Like
USLLSL
Target
Process
Center
1 Standard Deviation
3
+6
3
SQL = 3.0 SQL = 6.0
-6
Spec limits are
from the
customer Spec limits are
from the
customer
Spec limits are
from the
customer
Spec limits are
from the
customer

178. X
X
10
LSL
15 20
USL
10
LSL
20
USL
18
X
X
USL
10
LSL
16 20
10
LSL
15 20
USL
For σ
= 1.66
For
Cpk = 4
What are Cp, Cpk or σ?
For Cp
= 2.5
For σ
= 1

179. Sugar Concentration in Soda
A manufacturer wants the sugar concentration
in his soft drink to be 10 teaspoons +/- 0.25 at
a 3 sigma level in a 12 oz can
Analyze the data with the Capability Sixpack
Comment on the results

183. Introduction to DOEs
and Regression

184. Objectives
 DOE = Design of Experiment
 To be able to set up, solve and analyze
simple DOEs
 Perform simple Regression analysis

185. Experiments
The experimental method is the foundation of
science and engineering
• Without it we would live short, savage lives
They are a new invention
• Only practiced consistently since Galileo
Aristotle could have avoided the mistake of
thinking that women have fewer teeth than men,
by the simple device of asking Mrs. Aristotle to
keep her mouth open while he counted. ---
Bertrand Russell

186. What is DOE?
Most processes are affected by multiple factors
• Example: Stencil Printing
• Factors: Stencil, paste, snap off speed, print speed, wipe
frequency
With DOE, the effect of all the factors can be
determined with a minimum amount of testing
• The results are “statistically significant,” not an opinion
The old way: one experiment for each factor => not
effective
• Requires much more data, interactions are a problem

187. History
1830 – Gauss
• Curve fitting with least squares
• The “Normal” or “Gaussian” Curve
1908 – “Student” develops t -Test to analyze beer
1920 - DOE Concepts Developed
• First in Agriculture….calculations harder than experiments
1950-80s “Taguchi” Developed
1951 - Central Composite Design
1990’s - D optimal designs
• Experiments harder than calculations

188. DOE: Step 1
Clarifying the process mechanisms is
crucial
Hence, have a brainstorming session to
identifying independent variables (factors)

189. Guidelines for Brainstorming
Team Makeup
• Experts
• “Semi” experts
• Implementers
• Analysts
• Technical Staff who will run the experiment
• Operators

190. Guidelines for Brainstorming
Discussion Rules
• Suspend judgement
• Strive for quantity
• Generate wild ideas
• Build on ideas of others

191. Guidelines for Brainstorming
Leader’s Rules for Brainstorming
• Be enthusiastic
• Capture all ideas
• Make sure you have a good skills mix
• Push for quantity
• Strictly enforce the rules
• Keep intensity high
• Get participation from everybody

192. Conducting a DOE
Steps 1 through 5
1. State the Problem
2. Define the Objective
3. Set the start and end dates
4. Select the Response
– e.g., Solder paste volume
5. Select the factors
– e.g., Print Speed, Separation Speed, Paste,
Stencil, etc.

193. 6. Define the team and resources
7. Select design type
– e.g., Full factorial, etc.
8. Conduct experiment
9. Analyze data
10. Plan and execute further tests from these
results
Conducting a DOE
Steps 6 through 10

194. Score
Random Variation =
Variance: SDR
2
AverageNumberofRounds
Random Variation:
Dr. Ron Golf Score

195. Tiger Dr. Ron Score
 Difference
in averages
Implies that
there is a greater
difference
between Tiger
and Dr. Ron than
among them 2
>> Sr
2
NumberofRounds
STiger
2
Variation from Factors: Tiger and Dr. Ron
SDR
2

196. For example: Phil Mickelson and
Steve Stricker. Then, 2 << Sr
2

MultipleRounds
Golf Score
Sr
2
When Variation from Factor Change is Small…….

197. ANOVA
ANOVA (Analysis of Variance)
• Compares S2 to 2
The F Statistic:
Large F => factors have a significant effect on
result
“Large” varies with sample size, typically > 4
for 95% confidence
2
2
rS
F



198. The Null Hypothesis
H0: The mean response at two different factor
levels is the same.
Example: The Tiger and Dr. Ron score the
same.
Typically, we want to see if we can reject H0 at
a certain “level of confidence”
F ~ 4 can reject H0 with >95% confidence:
• P<0.05

199. DOE Size
The amount of data needed quickly grows with
the number of factors and levels
F = number of factors, L= number of levels
Data Points = LF
• a 6 factor, 4 level experiment = 4096 data
points

200. DOE Size
Must work to minimize # of factors and
levels
“If it’s too big, it won’t get done.”
- Joe Belmonte
Fractional factorial, Taguchi, Plackett-
Burman, and D-Optimal Designs were
created to minimize data collection
But, always with the loss of something

201. DOE Example and Theory
Apple growth
Two Factors: Water and fertilizer are believed
to increase the quantity of apples. It is not
known if there are interactions between the
two factors
Two Levels: For each Factor
Response: Crates of Apples
We will do a “full factorial” experiment

202. The Data
Run Water
(A)
Fertilizer
(B)
Resp1
(100 crates)
Resp2
1 70 100 2.2 2.8
2 70 200 3.2 3.6
3 90 100 5.0 4.6
4 90 200 5.8 5.4

203. Parallel lines => No Interaction!
Apple Production vs Amount of Irrigation
0
1
2
3
4
5
6
60 65 70 75 80 85 90 95
Units of Water
Apples(100Crates/tree)
200 Units
Fertilizer
100 Units
Fertilizer

204. Interaction
Water
Apples
P1
P2
Non Parallel Lines =>
Factor Interaction

205. (2.2-2.5)2 + (2.8-2.5)2
Water Fertilizer

206. Number of responses minus 1
Cross Product Term

207. If we reject Ho
we are wrong
only 5% of the
time.
(4.8+5.6)/2 -(3.4+2.5)/2

208. Still can reject
strongly H0

209. Cross product term
not significant

210. Strong A and B dependence, weak AxB

211. What does ANOVA Do?
ANOVA uses the analysis of variance to
determine if the “treatment” is more
significant than random error

212. Factors in a Chemical Reaction
Feed rate, Catalyst, Stir rate, Temperature and
Concentration are to be evaluated on their effect to
increase the percent reacted
Two levels for each factor are considered:
• Feed rate: 10, 15 (g/min)
• Catalyst: 1, 2
• Stir rate: 100,120 (stirs/min)
• Temperature: 140, 180 (degrees F)
• Concentration: 3, 6 (g/L)

216. Turn off the
randomizer!

218. Now Paste in your Data

220. Note: If you only have one replicate, do not
select more than a 2nd order fit

224. MeanofPercentReacted
1510
75
70
65
60
55
21 120100
180140
75
70
65
60
55
63
Feed rate Catalyst Stir rate
Temperature Concentration
Main Effects

226. Feed rate
21 120100 180140 63
90
75
60
Catalyst
90
75
60
Stir rate
90
75
60
Temperature
90
75
60
Concentration
10
15
rate
Feed
1
2
Catalyst
100
120
Stir rate
140
180
Temperature
Interaction Plot

227. But Always…..
Look at the raw data

228. DOE Class Problem:
using Minitab on your own
Three new additives are being pursued to increase stainless
steel cutlery hardness. Each additive (A,B,C) is tested at
four levels. In addition, two new cold quench
temperatures are tried. The data are “Stainless
DOE/Regression.”
Use DOE techniques (Full Factorial, turn randomizer off, 1
replicate, select 2nd order) to determine which additives
have an effect on the hardness and whether quench
temperature is important. Using factorial plots, comment
on the results. What formulation and treatment would you
suggest from these data to maximize hardness? What
future experiments might you want to do to learn more
about hardness as a function of the factors?

229. Don’t jump ahead, answers are on the next
slide!

230. Analysis of Variance for Rockwell C Hardness, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
A 3 18.141 18.141 6.0471 682.78 0.000
B 3 38.567 38.567 12.8555 1451.5 0.000
C 3 12.227 12.227 4.0755 460.17 0.000
Quench Temp 1 0.0021 0.0021 0.0021 0.24 0.626
A*B 9 0.1127 0.1127 0.0125 1.41 0.196
A*C 9 0.0516 0.0516 0.0057 0.65 0.754
A*Quench Temp 3 0.0220 0.0220 0.0073 0.83 0.483
B*C 9 0.0708 0.0708 0.0079 0.89 0.540
B*Quench Temp 3 0.0052 0.0052 0.0017 0.20 0.899
C*Quench Temp 3 0.0066 0.0066 0.0022 0.25 0.862
Error 81 0.7174 0.7174 0.0089
Total 127 69.9228
S = 0.0941094 R-Sq = 98.97% R-Sq(adj) = 98.39%

231. Session Window Conclusions:
Additives A, B & C are statistically significant.
Need to find optimal level to achieve specified
hardness.
Quench temperature and interactions not
statistically significant.

232. Main Effects plot
2.01.51.00.5
60.0
59.5
59.0
58.5
1.000.750.500.25
3.22.41.60.8
60.0
59.5
59.0
58.5
-100-200
A
Mean
B
C Quench Temp
Main Effects, Rockwell C Hardness

233. Main Effects Conclusions
Additive A achieves optimal hardness between
1.0 & 2.0. Further experimentation with
greater resolution between these points
recommended.
• If cost prohibits, can recommend to use level
1.5, as this produces the hardest steel of
levels tested

234. Additives B & C do not achieve any local or
global optimum. Further experimentation at
higher dosages recommended
• Or if costs prohibit, use the highest levels
Quench temp is not statistically significant.
• Can choose to use level that is cheaper
• This information is just as important
because it allows the business to do what
is cheaper.

235. Interaction Plot
1.000.750.500.25 3.22.41.60.8 -100-200
60
59
58
60
59
58
60
59
58
A
B
C
Quench Temp
0.5
1.0
1.5
2.0
A
0.25
0.50
0.75
1.00
B
0.8
1.6
2.4
3.2
C
Interaction Plot - Rockwell C Hardness

236. Interactions discussion
No interactions statistically significant.
• Seen previously in your session window
• Seen here as there are no non-parallel lines

237. Extra Problem: French Fries
McDonalds is concerned that their French fries are losing favor to Burger
King. They perform a DOE to optimize taste. Professional testers evaluate
the taste of the fries that have been cooked under varying conditions. The
average of 10 tasters is the “response.” Ten is the best rating, one is the
worst. The experiments are performed twice to get two replicates of data.
The factors are: Potato Type: Maine or Idaho, Cooking Oil Type: lard or
vegetable, cooking temperature: 320, 330, 340, 350oF and cooking time
10, 11 or 12 minutes. The results are in the spreadsheet in tab “French Fry
DOE”. Historically, lard has made better tasting fries, but the vegetable oil
is a new version, specifically designed for improved taste.
Analyze and discuss.

239. IdahoMaine
9.2
9.0
8.8
8.6
8.4
LardVeg
350340330320
9.2
9.0
8.8
8.6
8.4
121110
Potato Type
Mean
Oil Type
Temp Cook time
Main Effects Plot for Taste Rating
Data Means

241. LardVeg 350340330320 121110
9.0
8.5
8.0
9.0
8.5
8.0
9.0
8.5
8.0
Potato Type
Oil Type
Temp
Cook time
Maine
Idaho
Type
Potato
Veg
Lard
Oil Type
320
330
340
350
Temp
Interaction Plot for Taste Rating
Data Means

242. Improvement

248. Tool Overview
*It is not expected that all tools be used – the project focus and questions must drive the tool selection.
Define Measure Analyze Improve Control Kaizen
RACI
Stakeholder Analysis
Norms/Ground Rules
SIPOC
Baseline
Measurements
Contract
Project Plan
Review Process
Cost Benefit Analysis
Integrated Flowchart
8 Types of Waste
Pareto Diagram
Kano Model
Customer /Results Matrix
Results/Process Matrix
Operational Definitions
Sampling Plan
Data Collection Form
Measurement Analysis
Control Chart
Process Capability
DPMO
Histogram
Run Charts
Cause and Effect Diagram
Pareto Diagram
Affinity Diagram
Interrelationship Diagraph
Control Chart
Scatter Diagram
Pareto Diagram
Stratification
Hypothesis Testing
Regression Analysis
Tree Diagram
Design of Experiment
Cube Plot
PDSA Test Plans
Brainstorming
Lateral Thinking
5S
Solution and Effect Diagram
Implementation Plan
Gantt Chart
Flow Chart (To Be)
Control Chart
Pareto
Visual Management
Line Balancing
Poke-Yoke
FMEA
Arrow Diagram
Gantt Chart
Risk Assessment
Stakeholder Analysis
Communication Plan
SOP
Control Chart
Control Plan
Training Plan
Force Field Analysis
Cost Benefit Analysis
Final Project Review
Document
Success Story for Publication
Review Process
Communication Plan
Key Tools / Techniques Typically Used in Each Phase