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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
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.

• 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
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
Striving towards Six Sigma
Six Sigma Improves Quality by Reducing Defects and Variation
Quality
99% is never good enough!
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.
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
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.
Definitions
The statistical objective of Six Sigma
Reduce Variation and Center Process – Customers feel
variation more than the mean.
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.
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.
Common Cause Variation
Special Cause Variation
6 Causes of Variation
• Man
• Machine
• Material
• Method
• Measurement
• Mother Nature
Process
Any activity that takes inputs, adds value, and
provides an output(s).
Variation exists in the process.
Six Sigma improvement approach
Six Sigma is Long Term Commitment to the Philosophy of Quality.
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!
D-M-A-I-C
Lean Six Sigma Checklist
The Changing Focus of Six Sigma
The GE Experience –> Lean Six Sigma expands the tool set
Six Sigma – a dynamic, living initiative
Summary of Introduction:
Working with DMAIC!
Identify Project Critical To Quality
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.
Team Charter
Five major elements of a Charter
Problem and Goal Statements
Together they provide focus and purpose for the team
Description of the “pain”
Problem Statement
The Goal Statement
SMART Problem and Goal
Statements
Milestones
Simplification is the goal of Lean Six Sigma!
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
Define – make a case for action
Measure – define success
Pareto Chart – 80/20 RULE
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
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
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.
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
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
Measurement Systems
Analysis
Where does variation come
from?
Measurement Variation
Actual Value
Measured Value
Variation
Measuring Process
The Process:
Variable Data
Operators
The Tool
Part To Be
Measured
Measurements
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
Total Variation in Measurement:
Preferred
Actual Variation in
Product
Operator
Environment
Gage
Process
Total Variation in Measurement:
Unacceptable
Actual Variation in
Product
Operator
Environment
Gage
Process
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)
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
Understanding Accuracy and
Precision
Target
Target
Target
Target
High accuracy & high precision Low accuracy & high precision
High accuracy & low precision Low accuracy & low precision
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
The Data
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
The Results
StatGuide
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
Understanding Variation
The 6 Ms – all variation is from one or more of the
6Ms.
• Man (generic)
• Machine
• Material
• Method
• Measurement
• Mother nature
USLLSL
USLLSL
LSL USL
Process Variation = Lost $
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.
Special Cause Variation
• Unnatural, not expected
•Perform root cause analysis and eliminate if possible
Remember!
According to Deming:
85% to 95% of all variation is
Common Cause.
5% to 15% of all variation is
Special Cause.
“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
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.
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.
Choosing Control Chart using Minitab
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.
• 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.
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.
• This chart is used when the number of samples of each
sampling period is essentially the same.
Control Limits
The data determine the control limits with Common Cause
variation
UCL
LCL
Ave
Measurement Number
Value
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.
X bar Control Chart for SPC
Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Centerline = Mean
USL
LSL
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
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
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
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
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
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
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
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
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
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
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
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
The Control Chart
Sigma 3
Sigma 2
Sigma 1
Sigma 1
Sigma 2
Sigma 3
UCL
LCL
Mean
x
x
x + A2R
- A2R
Example
Stencil Printing Volume
Subgroup size =5
60 subgroups
Develop Xbar - Chart
Xbar-R with Minitab:
Enter data (Excel) then…..
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
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)
C Charts: Control Charts for Attribute
Data
Measure attribute data
Ex: X defects per 1000 parts
Can be done manually
xxLCL 3
xxUCL 3
Using Minitab
1. Enter defect data in column C-1
2. Then perform operations as above
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
Analysis
Other Control Charts
C and Xbar-R charts are most commonly used
in SPC
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
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
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
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
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.
Good Cp and Cpk
X 1 2 3123
Mean,
99.74% with +/- 3 sigma
LSL USL
Tolerance
Width of Distribution
Good Cp, Poor Cpk
X 1 2 3123
Median, Mean, Mode
LSL USL
Width of Distribution
3 standard deviations
Cp and Cpk
• Cp = USL – LSL
6
• Cpu = USL – Xbar
3
• Cpl = Xbar - LSL
3
• Cpk = min (Cpu, Cpl )
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
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
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
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
Introduction to DOEs
and Regression
Objectives
 DOE = Design of Experiment
 To be able to set up, solve and analyze
simple DOEs
 Perform simple Regression analysis
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
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
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
DOE: Step 1
Clarifying the process mechanisms is
crucial
Hence, have a brainstorming session to
identifying independent variables (factors)
Guidelines for Brainstorming
Team Makeup
• Experts
• “Semi” experts
• Implementers
• Analysts
• Technical Staff who will run the experiment
• Operators
Guidelines for Brainstorming
Discussion Rules
• Suspend judgement
• Strive for quantity
• Generate wild ideas
• Build on ideas of others
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
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.
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
Score
Random Variation =
Variance: SDR
2
AverageNumberofRounds
Random Variation:
Dr. Ron Golf Score
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
For example: Phil Mickelson and
Steve Stricker. Then, 2 << Sr
2

MultipleRounds
Golf Score
Sr
2
When Variation from Factor Change is Small…….
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


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
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
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
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
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
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
Interaction
Water
Apples
P1
P2
Non Parallel Lines =>
Factor Interaction
(2.2-2.5)2 + (2.8-2.5)2
Water Fertilizer
Number of responses minus 1
Cross Product Term
If we reject Ho
we are wrong
only 5% of the
time.
(4.8+5.6)/2 -(3.4+2.5)/2
Still can reject
strongly H0
Cross product term
not significant
Strong A and B dependence, weak AxB
What does ANOVA Do?
ANOVA uses the analysis of variance to
determine if the “treatment” is more
significant than random error
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)
Turn off the
randomizer!
Now Paste in your Data
Note: If you only have one replicate, do not
select more than a 2nd order fit
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
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
But Always…..
Look at the raw data
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?
Don’t jump ahead, answers are on the next
slide!
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%
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.
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
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
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.
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
Interactions discussion
No interactions statistically significant.
• Seen previously in your session window
• Seen here as there are no non-parallel lines
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.
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
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
Improvement
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

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Learning Six Sigma

  • 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.
  • 11.
  • 12. The statistical objective of Six Sigma Reduce Variation and Center Process – Customers feel variation more than the mean.
  • 13.
  • 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.
  • 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!
  • 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
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  • 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.
  • 35. Five major elements of a Charter
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  • 37. Problem and Goal Statements Together they provide focus and purpose for the team
  • 38. Description of the “pain”
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  • 42. SMART Problem and Goal Statements
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  • 57. Simplification is the goal of Lean Six Sigma!
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  • 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
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  • 64. Define – make a case for action Measure – define success
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  • 71. Pareto Chart – 80/20 RULE
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  • 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
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  • 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
  • 99.
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  • 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
  • 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
  • 118.
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  • 125.
  • 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
  • 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…..
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  • 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
  • 164.
  • 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
  • 180.
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  • 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
  • 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
  • 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)
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  • 218. Now Paste in your Data
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  • 220. Note: If you only have one replicate, do not select more than a 2nd order fit
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  • 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
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  • 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.
  • 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.
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  • 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
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  • 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