Six Sigma Quality Engineering

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Six Sigma Quality Engineering

• Week 11
• Improve Phase

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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

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Six Sigma - DMAIC Roadmap
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Improve Phase

• 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
Establish Optimum Process
Select Solutions
Prepare improvement Plans
Develop, try out implement solutions that
address root causes

• FMEA for Solution
• Cost Benefit Analysis
• Verify Metrics
• Prioritization Matrix

• Improvement Strategies
• Screen Critical Inputs (DOE Plan)
• Refine Model
• Define Confirm Y f (x)

• Document To Be Process
• Pilot Solution
• Implementation Deployment Plans
• Process Documentation

• Key Deliverables
• Solutions
• Risk Assessment on Solution
• Pilot Results
• Implementation Plans

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Improve Phase
Generating Solutions
Cost-Benefit Analysis
Design of Experiments
A
4
B
1
C
3
D
2
Selecting the Solution
Implementation
Piloting
Assessing Risks
Full scale
Test
Original
Develop Execute a full plan
for implementation and
change management
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• Design of Experiments

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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
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Full Factorial Designs

• Full Factorial Examines factor effects and
  interaction effects. These become large rather
  quickly.
• 22 Full Factorial 2 factors, 2 levels 4 runs
• 23 Full Factorial 3 factors, 2 levels 8 runs
• 24 Full Factorial 4 factors, 2 levels 16 runs
• 25 Full 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.

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Example of a 23 Full Factorial Design
Run
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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.
• 27 Full Factorial 7 factors, 2
  levels 128 runs
• 2(7-1) 1/2 Fractional Factorial 7 factors, 2
  levels 64 runs
• 2(7-2) 1/4 Fractional Factorial 7 factors, 2
  levels 32 runs
• 2(7-3) 1/8 Fractional Factorial 7 factors, 2
  levels 16 runs
• 2(7-4) 1/16 Fractional Factorial 7 factors, 2
  levels 8 runs

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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
  DoEs lead to smaller Full Factorial DoEs.

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Basic Experimental Terms
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The Idea of Confounding
A
B
C
BC
AB
AC
ABC
-1 -1 1 1
-1 1 -1 1
2 (a) 3 (b) 5 (c) 8 (abc)
1 - 1 -1 1
1 1 1 1
1 -1 -1 1

-1 -1 1 1
-1 1 -1 1
Same Signs
Was Y affected by A or by the interaction of B
and C?
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Basic Experimental Terms
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Basic Experimental Terms
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Basic Experimental Terms
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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

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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

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• Design of Experiments
• Minitab practice

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Design Resolution
The resolution number tells you what factor and
interactions will be confounded with one another.
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Questions? Comments?