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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 2 k Factorial Design. Goal of Quality Control.

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Me 350 lecture 14 doe part 1
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
Goal of Quality Control

Strategic view of Quality Design and Improvement:

Example experiment
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
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 =

Me 350 lecture 14 doe part 1

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
Quality Control: Rework Distribution

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

Quality loss function
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
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
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
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

2 k factorial design test settings
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
DOE Example 1

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

Quantify objective?


Doe example 2
DOE Example 2

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

Quantify objective:

Material variables:

Equipment variables:

Doe example 3
DOE Example 3

Objective: improve composite part strength

Quantify objective:

Material variables:

Equipment (or process) variables:

2 2 doe example data analysis
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:



2 2 doe determining magnitude of effects
22DOE: determining magnitude of “effects”

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



C ompounded e ffects characteristic e quation
Compounded Effects & Characteristic Equation

  • Compound Effect E12?

  • Characteristic Equation:



2 3 factorial design example
23 Factorial Design Example

  • Study on the alertness of students in the morning

  • Variables

  • Design Matrix

Effect of variables




Effect of Variables?

  • Graphically, the “effect” of variable 1 is the difference between the average results of the planes

Graphical understanding cont1

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
Use Matrix Algebra to Solve: diagonals and subtract

  • Eliminating the “insignificant effects” yields the final equation:

  • Determining which effects are significant comes next