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

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IE 673 Session 7 - Process Impro vement (Continued) 1 Process Improvement (Continued)

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Page 1: IE 673Session 7 - Process Improvement (Continued) 1 Process Improvement (Continued)

IE 673 Session 7 - Process Improvement (Continued)

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Process Improvement

(Continued)

Page 2: IE 673Session 7 - Process Improvement (Continued) 1 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

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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Quality Effort by Activity

DevelopmentDesign Manufacturing Solve Problems

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IE 673 Session 7 - Process Improvement (Continued)

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Taguchi’s Quadratic Loss Function

LSL USLTarget

L0

L1 = k(y1 - T)2

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IE 673 Session 7 - Process Improvement (Continued)

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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

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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

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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Strategies for Experimentation

• Screening

• Modeling (Characterization)

• Sensitivity

• Optimization

• Robust (parameter) Design

• Tolerance Design

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IE 673 Session 7 - Process Improvement (Continued)

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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

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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Fractional Factorial Experiments

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

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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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Taguchi Designs

• Orthogonal Arrays

• Screening Designs

• Robust Designs

• Minimal Runs

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IE 673 Session 7 - Process Improvement (Continued)

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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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IE 673 Session 7 - Process Improvement (Continued)

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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