Lean Sigma’s “Myth Buster”
Introduction to 22 Factorial Design of
Experiments
Clay Walden, Ph.D.
Conference on High Technology
Mississippi Telcom Center, Jackson, MS
November 28, 2007
Myth Buster
Can you distinguish truth from myth?
1.
Only two Coca-Cola executives know
Coke’s secret formula – each one only
knows half.
2.
A light bulb in 1901 burns bright to this
day.
3.
Pull tabs from aluminum cans have special
redemption value for time on kidney
dialysis machines
4.
Great Wall of China is the only man made
object visible from the moon.
5.
In order to implement Six Sigma you need
to hire a pointed head statistician.
Myth Buster “Pretest”
Can you distinguish truth from myth?
1.
Only two Coke-Cola executives know Coke’s the secret
formula – each one only knows half.
1. Myth
2.
Pull tabs from aluminum cans have special redemption
value for time on kidney dialysis machines
2.
Myth
3.
Great Wall of China is the only man made object visible
from the moon.
3.
Myth
4.
A light bulb in 1901 burns bright to this day.
4.
Truth
5.
In order to implement Six Sigma you need to hire a
pointed head statistician
5.
????
Pre-Test Evaluation
• 0-1 Correct: Give Up!
• 2-3 Correct: Recommend enrolling in next “1
sigma” pink belt workshop.
• 4 Correct: Need to find a life outside of
watching “Myth Buster” reruns
Shop Floor Myths
• Like popular culture – “myths” and urban legends
abound on the shop floor.
• Why?
–
–
–
–
–
Shop Floor Myths
• Like popular culture – “myths” and urban legends
abound on the shop floor.
• Why?
– Dynamic and sometimes chaotic environment
– Lots of possible factors – Deming stable processes are an
achievement and NOT a natural state.
– Inadequate measurement systems
– “Shoot from the hip & declare victory” approach to
problem solving.
Generic Myths
• If parts are “in spec” then problem is NOT in manufacturing.
• If parts are “out of spec” then we have found the root cause
of our field failures.
• We have excellent communications between shifts.
• Our workforce will always be generally unskilled and
unmotivated.
• All tasks and operations are equally important.
• ….
• ….
How can we dispel these and other
manufacturnig myths?
Hire a statistician !
EASY
BUTTON
+
+
+
+
Multiple Factor Approach
• Assemble “experts” and thoroughly discuss the candidate
factors.
– Engineering
– Maintenance
Good subject matter experts are
essential, not just engineers.
– Operations
• Good Opportunity for Cause and Effect diagram (Fishbone)
• Use a group consensus technique like multi-voting to find the
top “few” factors, at least from the team’s perspective.
– Each person has $100 to “spend” on the factors in order of their
importance.
– Very successful in building group consensus.
– Always do a “sanity check” never “blindly” follow the approach.
Now what do you do ?
• Most industrial settings, interested in making
conclusions regarding multiple factors.
• Trial and Error
• Typical “OFAT” Approach
– very carefully vary one factor at a time so that we
can isolate the impact of each.
– Any problems?
• DOE is a better way … Why?
Example Problem
• Problem: Gas mileage for car is 20 mpg. Would like to
get >30 mpg.
• Factors:
Measurement
–
–
–
–
–
–
Method
Machine
Driving habits
Gage Error
New tires
Tire pressure
Speed
Type of Gas
MPG
Type of Gas
Driving habits
weather
New driver
Materials
Man
Mother Nature
OFAT Example
Speed (A)
Tire Press. (B)
Mileage
OFAT “Reasonable Approach”
OFAT (One-Factor-At-A-Time)
“One Factor @ a Time”
• Inefficient use of sample size.
• Interactions can not be investigated.
Power of 22 Factorial Design
Speed (A)
Tire Pressure (B)
55
30
55
35
65
30
65
35
MPG
Factorial Design – each level of one factor is found in
combination with each level of the other factors.
Allowing both Main Effects and Interactions to be
estimated
Interactions?
• Interactions occur when the effect of one
factor depends upon the level of another
factor.
• Example, Drug “A” reduces blood pressure
when used by itself, Drug “B” reduces anxiety
when used by itself. If Drug A and B are used
together may lead to a heart attack or stroke.
Interactions
• Are understanding interactions important
to improving manufacturing processes?
Yield of a chemical process is impacted by
operating temperature and reaction time.
The impact of changing temperature on
yield depends upon the reaction time.
22 Factorial Example – Main Effect
Lubrication (B)
Hardness (A)
“low”
(i.e., dirty)
“high”
(i.e., clean)
“low”
10
20
“high”
30
40
Objective: two factor experiment focusing on the impact of hardness and
lubrication on process yield (%).
Main Effects:
Effect of Hardness (A): average change in response (yield) as hardness goes from
a low to high level.
Effect of Lubrication (B): average change in response (yield) as lubrication goes
from a low to high level.
22 Factorial Example
Lubrication (B)
Hardness (A)
“low”
(i.e., dirty)
“high”
(i.e., clean)
“low”
10
20
“high”
30
40
Main Effects:
Main Effect of A:
Main Effect of B:
Interaction AB:
A = (30+40)/2 – (10+20)/2 = 20
B = (20+40)/2 – (10+30)/2 = 10
AB = (40+10)/2 – (30+20)/2 = 0
Notice: the effect of A is the same no matter what the level of B. This indicates there is
no interaction effect.
Plot of Effects – Main Effect
50
Lub “high”
40
Yield
Lub “low”
30
20
10
“low”
Hardness
“High”
Hardness
Parallel lines indicate the absence of an interaction effect
Effect of hardness on yield is the same regardless of whether clean or dirty lub is
used.
22 DOE Example - Interaction
Hardness (A)
“low”
“high”
Lubrication (B)
“low”
(i.e., dirty)
10
30
“high”
(i.e., clean)
20
0
Changed response from 40,
notice impact on effects
calculation and effects plot.
Plot of Effects - Interaction
50
40
Yield
Lub “low”
30
20
10
Lub “high”
“low”
Hardness
“High”
Hardness
Intersecting lines indicate an interactive effect.
Effect of hardness on yield depends on whether you are using clean or dirty lub.
Myths – “Small Motor Plant”
• “Our new rpm/amps tester provides us with a
reliable evaluation of product performance.”
• “Use a special “calibrated” rubber hammer to reduce
shaft TIR.
• “Current Method of aligning commutator, while not
perfect, is adequate.”
• “Reason for the 40% failure rate must be in the
ancient heat treating process. We can’t solve the
problem, because the company is unwilling to
invest.” – Catalogue Engineer (Shigeo Shingo)
Myths Busted … “Small Motor Plant”
• Exposed by …
– Measurement System Analysis
• Cyclical error found which takes up 50% of tolerance
– Design of Experiment on the Shop Floor – 23 factorial 40
runs (1 day)
• “Rubber Hammer” process not capable
• Tested new alignment method verses “old method”
• Resulted in …
– Reducing defect rate from 40% to 0%
– ~ $500K per year in savings
Myths – Acme Tube & Pipe
• “Any combination of plugs and dies from the tool crib
will work.”
• “A high degree of variation in tube eccentricity at the
press is inherent.”
• “We need to better train our operators and
maintenance personnel to repair “breakers”
quicker.”
Busted … Acme Tool & Tube
• Exposed by …
– Design of Experiment on the Shop Floor –
factorial (2 day)
• Lub ID critical
• Match correct “plug and die”
• Standardized work and 5S in tool crib
• Resulted in …
– Reducing “breaker rate” from 12% to 5%
– $2,700,000 per year in savings
Catapult Dynamics
Producing our nation’s next generation of missile
defense systems!
Catapult Design
Factors:
CTQ: Range:
1) Type of Projectile – golf,
whiffle, ping pong
2) # of rubber bands
3) Release angle – 250, 400,550,
700, 850, 1000
4) Launch Arm position – 1, 2,
3
5) Cup Position (Fix at top of
arm)
6) Upright Position – 1, 2, 3, 4
Arm
Pos 3
Upright
Pos 4
Specification: +/- 1”
Arm
Pos 1
Upright
Pos 1
Target: 75”
Release
Angle
700
Catapult Factory
• Use 6 Sigma Problem Solving Approach
– DMAIC
• Objective reduce process variation and center on
target (75 inch).
• Plant Resources
– Personnel: 3 operators, 1 inspector, 1 Recorder
– Equipment: ping pong balls, tape measure, pad, pen.
Myth or Truth?
Catapult Dynamics
• Variation caused by repeated use of the rubber band
is unavoidable.
• Production task is quite simple and should be
automated.
• Poorly skilled and unmotivated workforce
• If the company really cared about quality they would
invest in a new highly automated CNC catapult.
• Testing can best be done when only factor is changed
at a time. ….
Design of Experiments
• Select two key factors
– each factor at 2 levels.
– Replicate the experiment
– 8 runs are required – which ones?
• “Randomize the trails” (why?)
• Analyze the results (i.e., plot the data)
• Make recommendations for standard work
within the process.
Plot of Effects - Interaction
50
Factor B “high”
40
Response 30
20
Factor B
“low”
10
“low”
Factor A
“High”
Factor A
The effect of Factor A on distance depends upon the level of
factor B.
Plot of Effects – Main Effects
50
40
Response 30
Factor B
“low”
20
Factor B “high”
10
“low”
Factor A
“High”
Factor A
The effect of Factor A on distance does not depend upon the level
of factor B.
Plot of Effects
90
Factor B
“low”
80
Response 70
60
Factor B
“high”
50
“Low”
Factor A
“High”
Factor A
Key Take-a-Way
Catapult Dynamics
Myth: You must hire a pointed head
statistician to use Six Sigma
+
+
+
Busted !
+