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ME 350 – Lecture 14 – DOE Part 1

Design of Experiments

at Grainger in reference section

covering chapters 17 & 18

- Quality Control
- Gaussian distributions
- Quality Loss Function
- Process Control
- 2k Factorial Design

Goal of Quality Control

Strategic view of Quality Design and Improvement:

Example Experiment

Control variable 1, x1: extruder temperature

Control variable 2, x2: injection time

Output measurement, y: part weight (goal is 25 oz)

Gaussian Distributions

Gaussians have:

- Mean (average), μ
- Standard deviation, σ
- Variance, σ2
- Tolerance:

2σ =

4σ =

6σ =

Variance of a system: σ2 =

Tolerance of a system:σ =

Quality Control: Gaussian Distribution

A part with a “hole” must match up with another containing a “pin.” The hole and pin tolerances () are 15 mil. Thus the clearance and clearance tolerance is (assume Gaussian distribution):

Quality Control: Rework Distribution

Same problem as before (tolerances are 15 mil). Thus the clearance (with tolerance) is:

Quality Loss Function

The deviation of a product from its nominal value typically has a similar deviation in the product performance:

Warranties for transmissions with greater variability are more expensive. They tend to follow a:

Common Approaches to Reduce Variability:

1) Choose an output region with less variability for a given input, or 2) tighten the input

DOE is to enable Process Control

“You can not manage what you can’t measure”

“If you cannot measure it, you can not control it, if you cannot control it, you can not manage it”

- Step 1: state and rank objective(s),
- Which objectives are “nice” and which are “essential”
- How will you measure (i.e. quantify) objective success
- Ranking can depend upon consequence of failure
- If certain objective fails does someone die or does it produce a product cosmetic blemish?
- Objective could be to compare 2 or more venders
- Objective could be to optimize one or more product characteristics.

Setting up DOE for Process Control

- Step 2: brainstorm possible process variables and rank them
- Base ranking on engineering judgment or experience.
- Don’t eliminate any potential variables (i.e. factors)
- Be specific – don’t just put down “temperature” - temperature of what, where, and when?
- Be bold, but not foolish in choosing “high” and “low” settings of each variable for experimentation
- try for as wide a distance as possible but not impractical
- Check for variable (i.e. factors) settings that are impractical or impossible
- e.g. high gas flow but low pressure in gas line

2k Factorial Design – Test Settings

- “k” refers to the number of variables being tested
- Assumes a linear, or near linear output response when changing an input variable -
- Tests points only at the extremes -

DOE Example 1

Objective: better flow of polymer into fine features of mold in injection molding process

Quantify objective?

Variables?

DOE Example 2

Objective: reduce machining (drill, mill, or lathe) costs to make product.

Quantify objective:

Material variables:

Equipment variables:

DOE Example 3

Objective: improve composite part strength

Quantify objective:

Material variables:

Equipment (or process) variables:

22DOE Example: data analysis

Objective is better control part weight: 25 oz.

Variable 1: extruder temperature

high = 200 C low = 150 C

Variable 2: injection time

high = 4 sec low = 2 sec

Experimental Results:

x2

x1

22DOE: determining magnitude of “effects”

E1 – ‘effect’ of variable 1, use the average of “high” minus the average of the “low” values

x2

x1

23 Factorial Design Example

- Study on the alertness of students in the morning
- Variables
- Design Matrix

coffee

sleep

Effect of Variables?- Graphically, the “effect” of variable 1 is the difference between the average results of the planes

Average corners of inscribed regular tetrahedrons of diagonals and subtract

One tetrahedron should include the (-,-,-) corner and the other should include the (+,+,+) corner

Graphical Understanding (cont)Use Matrix Algebra to Solve:

- Eliminating the “insignificant effects” yields the final equation:
- Determining which effects are significant comes next

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