ie 673session 7 - process improvement (continued) 1 process improvement (continued)

IE 673 Session 7 - Process Improvement (Continued)

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Process Improvement

(Continued)

IE 673 Session 7 - Process Improvement (Continued)

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Introduction to Design of Experiments (DOE)

• Quickly optimize processes• Reduce development time• Reduce manufacturing costs• Reduce scrap and rework• Increase throughput• Improve product quality• Make products/processes more robust• Reduce need for control charting

IE 673 Session 7 - Process Improvement (Continued)

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Experimental designs are specific collections of trials run so the information content about a multi-variable process is maximized. With response-surface experimental designs, the goal is to put this information into a picture of the process.

– J. Stuart Hunter -

Definition of DOE

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Important Contributions From Different Approaches

Loss Function X XEmphasis on Variation Reduction X XRobust Designs X XKISS X X XSimple Significance Tests X XComponenet Swapping X XMulti-variate Charts X XModelling X XSample Size X XEfficient Designs X XOptimization X XConfirmation X XResponse Surface Methods X X

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•Process Knowledge

• If what we know about our processes can’t be expresses in numbers, we don’t know much about them.

• If we don’t know much about them, we can’t control them.

• If we can’t control them, we can’t compete.– Motorola University -

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Old Philosophy of Quality

Quality is based on conformance to specifications

Loss due toscrap & rework

Loss due toscrap & rework

LSL USL

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New Philosophy of Quality

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9

LSL USLTarget

L1

L2

L3L3 > L2 > L1

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Taguchi’s Concept

• DESIGN quality into the product and process.• Design the PRODUCT to be least sensitive to

variations rather than trying to control the factors.• Design the product so that its performance

parameters are CLOSEST TO THE TARGET.• Minimize costs within quality constraints rather

than maximize quality within cost constraints.

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Quality Effort by Activity

DevelopmentDesign Manufacturing Solve Problems

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Taguchi’s Quadratic Loss Function

LSL USLTarget

L0

L1 = k(y1 - T)2

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Example

• Let V(out) = 115 Vdc

• y = V(out) m = 115Vdc

• LD(50) = 115 +/- 20 Vdc (Consumer’s Tolerance)

• Repair Cost = $100

• L(y) = k(y - 115) 2

• k = L(y)/(y - m) 2 = $100/20 2

• k = 0.25

• If V(out) = 110 Vdc

• L(110) = 0.25(110 - 115)^2 = $6.25

IE 673 Session 7 - Process Improvement (Continued)

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Example

Suppose adjustment costs $2.00, i.e., the cost to rework.

When should a unit be reworked?

L(y) = 0.25 (y - 115)^2

$2.00 = 0.25 (y - 115)^2

8 = (y - 115)^2

y = 115 +/- 8 ^ 0.5

y = 115 +/- 2.83

IE 673 Session 7 - Process Improvement (Continued)

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• System Design

• Parameter Design

• Tolerance Design

Basis of The Taguchi Method

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Purposeful changes of the inputs (factors) to a process in order to observe corresponding

changes in the output (responses).

What is Designed Experiments?

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Strategies for Experimentation

• Screening

• Modeling (Characterization)

• Sensitivity

• Optimization

• Robust (parameter) Design

• Tolerance Design

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Objectives of an Experimental Design

• Obtain maximum information using minimum resources.

• Determine which factors shift average response, which shift variability, which have no effect.

• Find factor settings that optimize the response and minimize the cost.

• Build empirical models relating the response of interest to input factors

IE 673 Session 7 - Process Improvement (Continued)

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Methods of Experimentation

• Full Factorials

• Fractional Factorials

• Plackett-Burman

• Latin Square

• Hadamard Matrices

• Foldover Designs

• Box-Behnken Designs

• D-Optimal Designs

• Taguchi Designs

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Full Factorial Experiments

• Advantages– Tests all factors at all levels– Evaluates all main effects– Evaluates all interactions

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Full Factorial Experiments

• Disadvantages– Large number of runs– Large number of samples– Takes long time to run– Expensive

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Fractional Factorial Experiments

• Advantages– Fewer runs– Faster to complete– Fewer Samples– Less costly

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Fractional Factorial Experiments

• Disadvantages– Cannot test all factors at all levels– Cannot evaluate all main effects– Cannot evaluates all interactions

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Factorial Versus Taguchi

Factors Levels Factorial Taguchi2 2 4 (22) 43 2 8 (23) 44 2 16 (24) 87 2 128 (27) 8

15 2 32768(215)

16

4 3 81 (34) 9

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Taguchi Designs

• Orthogonal Arrays

• Screening Designs

• Robust Designs

• Minimal Runs

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Layout for Taguchi L-8Column 1 2 3 4 5 6 7Factor A B C D E F GTrial

1 1 1 1 1 1 1 12 1 1 1 2 2 2 23 1 2 2 1 1 2 24 1 2 2 2 2 1 15 2 1 2 1 2 1 26 2 1 2 2 1 2 17 2 2 1 1 2 2 18 2 2 1 2 1 1 2

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ExampleColumn 1 2 3 4 5 6 7 ResponseFactor A B AxB D AxD BxD GTrial

1 1 1 1 1 1 1 1 56 A1 392 1 1 1 2 2 2 2 23 A2 483 1 2 2 1 1 2 2 484 1 2 2 2 2 1 1 295 2 1 2 1 2 1 2 356 2 1 2 2 1 2 1 627 2 2 1 1 2 2 1 508 2 2 1 2 1 1 2 45