Objectives
Overview of Design of Experiments• A structured method to learn about a process by changing
many factors at the same time.• It occurs in Improvement Phase.• Fractional factorial experiments are used for initial screening• Full factorial experiments are smaller and more precise
Graphical Analysis• Main effects plots• Interaction plots• Cube plots
Statistical Analysis• P value for main effects and interactions
Six Sigma - DMAIC Roadmap
Define Metrics
Define Metrics
444
Understand the
Customer
Understand the
Customer
333
Define Project
Boundaries
Define Project
Boundaries
222
DefineDefine
Problem Statement
Macro Map & SIPOC
Voice Of Customer(VOC)
Objective Statement
CTQ Tree/List
Metrics Determined: Primary, Secondary & Consequential
Financial Metric(s) and Forecast
Business Metrics
De
fine
Ga
te
Refine the Project
Refine the Project
555
Data Collection
Plan
Data Collection
Plan
666
MeasureMeasure
Project Description
Refine key projectmetrics
Data Collection Matrix
Cause & Eff ect Tools
Detailed Process Map (Non Value Added Flow Analysis if applicable)
Analysis of measurement system variation
Capability summary
Capability Estimates
Exploratory Analysis
Exploratory Analysis
999
Analyze Cause & Eff ect
Analyze Cause & Eff ect
111111
Statistical I nvestigationStatistical
I nvestigation
101010
FMEA
Graphical techniques
Non value added flow analysis
Statistical analysis (Refer to Statistical Tool Kit)
Potential Causes & Eff ect Matrix/ Summaries
AnalyzeAnalyze
Me
asu
re G
ate
Establish Optimum Process
Establish Optimum Process
131313
Prepare Improvement
Plan
Prepare Improvement
Plan
151515
Select SolutionsSelect
Solutions
141414
ImproveImprove
Screen Critical
I nputs (DOE/Pilot)
Refine model (Search for interactions if applicable)
Define & Confirm Y=f(x)
FMEA for solution
Cost Benefit Analysis
Verify applicability of metrics (primary, secondary, consequential & financial)
Document to Be Process
Pilot Solution
Implementation Plan
Deployment Plan and process documentation
Imp
rove
Ga
te
An
alyze
Ga
te
Confirm Improvement
Confirm Improvement
161616
Sustain the Gain
Sustain the Gain
181818
Control X’s and Monitor
Y’s
Control X’s and Monitor
Y’s
171717
ControlControl
Before after analysis
ID VA/NVA activities
Summary of Standardized practices
Control Plan reviewed and assigned to process owner
Establish monitoringand reporting system(s)
Evaluate long term results
Formal Closure with Team, Champion, and Process Owner(s)
Co
ntro
l Ga
te
Develop Contract and Form
Team
Develop Contract and Form
Team
111
Business Case
I dentify BB/GB, Team
Establish Roles/Resp.
Project Charter Signed
Determine Process
Capability
Determine Process
Capability
888
Analyze Measurement
System
Analyze Measurement
System
777
Confirm Cause & Eff ect
Confirm Cause & Eff ect
121212
I nvestigate Causality (DOE/Statistical Studies)
Determine magnitude of variation
DOE/Pilot Plan (if applicable)
Confirmation Study for causality
Pro
ject C
om
ple
tion
xx/xx/xx
EstablishOptimumProcess
SelectSolutions
Prepareimprovement
Plans
FMEA for Solution
Cost Benefit Analysis
Verify Metrics
Prioritization Matrix
Document ‘To Be’ Process
Pilot Solution
Implementation & Deployment Plans
Process Documentation
Improvement Strategies
Screen Critical Inputs (DOE Plan)
Refine Model
Define & Confirm Y = f (x)
Improve Phase
ImproveDevelop, try out &
implement solutions that address root
causes
Key Deliverables Solutions Risk Assessment on
Solution Pilot Results Implementation Plans
Goal: Develop, try out, and implement solutions that address root
causes
Output: Planned, tested actions that eliminate or reduce the impact of
the identified root causes
Improve Phase
Cost-Benefit AnalysisGenerating Solutions
Generate solutions includingBenchmarking and selectbest approach based on
screening criteria
A
B
C
D
4
1
3
2Perform cost-benefit
analysis for thepreferred solution
Assessing Risks
Use FMEA to identifyrisks associated with the
solution and takepreventive actions
Piloting
Test Full scale
Original
Pilot the solution ona small scale and
evaluate the results
2 4 8 6 10
G
1 3 5 7 9A
B
CD
FE
JIH
G
Implementation
Develop & Execute a full planfor implementation andchange management
Selecting the Solution
Recommend a solutioninvolving keystakeholders.
Design of Experiments
Use DOE and responsesurface optimization toquantify relationships.
What is a Designed Experiment?
A method to change all the factors at once in a structured pattern to determine their effects on the output(s)
The structured pattern is known as an orthogonal array
A B A X B
1 -1 -1 1
2 1 -1 -1
3 -1 1 -1
4 1 1 1
0 0 0
Full Factorial Designs
Full Factorial: Examines factor effects and interaction effects. These become large rather quickly.
• 222 2 Full Factorial = 2 factors, 2 levels = 4 runsFull Factorial = 2 factors, 2 levels = 4 runs• 23 3 Full Factorial = 3 factors, 2 levels = 8 runsFull Factorial = 3 factors, 2 levels = 8 runs• 224 4 Full Factorial = 4 factors, 2 levels = 16 runsFull Factorial = 4 factors, 2 levels = 16 runs• 225 5 Full Factorial = 5 factors, 2 levels = 32 runsFull Factorial = 5 factors, 2 levels = 32 runs
Used after initial screening experiments or where the process is simple or well known. The experiment is run to optimize the process using a vital few factors.
Example of a 2233 Full Factorial Design
Run
Fractional Factorial Designs
Fractional Factorial: Examines factor effects and a carefully selected portion of interaction effects.
Shrinks the number of runs for each fraction by one half.
• 227 7 Full Factorial Full Factorial = 7 factors, 2 levels = 128 runs = 7 factors, 2 levels = 128 runs• 22(7-1) (7-1) 1/2 Fractional Factorial = 7 factors, 2 levels = 64 runs1/2 Fractional Factorial = 7 factors, 2 levels = 64 runs• 22(7-2) (7-2) 1/4 Fractional Factorial = 7 factors, 2 levels = 32 runs1/4 Fractional Factorial = 7 factors, 2 levels = 32 runs• 22(7-3) (7-3) 1/8 Fractional Factorial = 7 factors, 2 levels = 16 runs1/8 Fractional Factorial = 7 factors, 2 levels = 16 runs• 22(7-4) (7-4) 1/16 Fractional Factorial = 7 factors, 2 levels = 8 runs1/16 Fractional Factorial = 7 factors, 2 levels = 8 runs
Fractional Factorial Designs
Uses interaction column settings to estimate the effects of main factors.
Used for initial screening designs to isolate the important (vital few) factors.
One DoE leads to another. Fractional Factorial DoE’s lead to smaller Full Factorial DoE’s.
Basic Experimental Terms
The Idea of Confounding
AA BB ABAB2 (a)
3 (b)
5 (c)
8 (abc)
1
- 1
-1
1
-1
1
-1
1
-1
-1
1
1
CC-1
-1
1
1
ACAC
1
-1
-1
1
BCBC-1
1
-1
1
1
1
1
1
ABCABC
Same Signs
Was “Y” affected by A or by the interaction of B and C?
Basic Experimental Terms
Basic Experimental Terms
Basic Experimental Terms
General Comments
In general, industry considers 3rd and 4th order interactions to be negligible.
Fractional Factorial experiments “pool” the effects of interactions to estimate residual error.
No replicates are run - USE WITH CAUTION! Use Fractional Factorial Experiments for screening, then
follow up with Full Factorial Designs. Keep your experiments simple
Be Proactive!
DOE is a proactive tool. If DoE output is inconclusive:
• You may be working with the wrong variables• Your measurement system may not be capable• The range between high and low levels may be insufficient
There is no such thing as a failed experiment• Something is always learned• New data prompts asking new questions and
generates follow-on studies
The resolution number tells you what factor and interactions will be confounded with one another.
Design Resolution
Questions? Comments?
