Six Sigma Quality Engineering

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Six Sigma Quality Engineering. Week 11 Improve Phase. 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

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## Six Sigma Quality Engineering

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### Six Sigma Quality Engineering

Week 11

Improve Phase

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

Improve

Establish

Optimum

Process

Select

Solutions

Prepare

improvement

Plans

Develop, try out & implement solutions that address root causes

• Improvement Strategies
• Screen Critical Inputs (DOE Plan)
• Refine Model
• Define & Confirm Y = f (x)
• FMEA for Solution
• Cost Benefit Analysis
• Verify Metrics
• Prioritization Matrix
• Document ‘To Be’ Process
• Pilot Solution
• Implementation & Deployment Plans
• Process Documentation

Generate solutions including

Perform cost-benefit

Benchmarking and select

analysis for the

best approach based on

preferred solution

screening criteria

1

2

3

4

5

6

7

8

9

10

A

B

C

D

E

G

F

G

H

I

J

Recommend a solution

involving key

stakeholders.

Use FMEA to identify

Pilot the solution on

risks associated with the

a small scale and

Use DOE and response

solution and take

evaluate the results

surface optimization to

preventive actions

quantify relationships.

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

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.
• 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.
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
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.

The Idea of Confounding

A

B

BC

C

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?

• 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.
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

Design of Experiments

Minitab practice

Design Resolution

The resolution number tells you what factor and interactions will be confounded with one another.