robust parameter design

5/20/2018 robust parameter design

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Taguchi

Robust Parameter Design


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Robust Parameter Design (Taguchi Design)

A three step method for achieving robust design (Taguchi)

System design

Parameter design

Tolerance Design


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System Design New concepts ideas and methods are generated to provide new and

better products

For egs. judgment of selected materials, parts based on science andtechnology.

Innovation and knowledge management

New product development etc.


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Parameter Design

To determine the factor levels that produce the best performance

of the product/process under study.

The objective is to make the design Robust!

The optimal parameter levels can be determined throughexperimentation


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Tolerance Design

Fine tune the results of parameter design by tightening the

tolerance of factors with significant influence on the product.

Identifying the need for better materials,

buying newer equipment, spending more money for inspection etc.


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The Taguchi Process

1. Problem Identification

Locate the problem source not just the symptom

2. Brainstorming Session

The purpose is to identify critical variables for the quality of the product (CTQ) or service inquestion (referred to as factors by Taguchi)

Control factors variables under management control

Noise factors uncontrollable variation

Define different factor levels (three or four) and identify possible interaction between factors


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Determine Design characteristics

1. Smaller -the-better

2. Nominal-is-best

3. Higher-the-better

The design characteristics are related to CTQ.


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3.Experimental Design

Using factor levels and objectives determined via brainstorming

Taguchi advocates off-line-experimentation as a contrast totraditional on-line or in-process experimentation

Care should be taken to selecting number of trials, trial conditions,how to measure performance etc.


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4. Experimentation

Various rigorous analysis approaches like ANOVA and Multiple

Regression can be used. Customized methods are available like Taguchidesign (Orthogonal Arrays).


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5. Analysis

The experimentation provides best levels for all factors

6. Conforming Experiments (confirmatory runs)

The results should be validated by running experiments with all

factors set to optimal levels


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Design using Minitab


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Linear graph of (L4 2

3

)

1 23


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Linear graphs of orthogonal design (L8)


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Inner Array and Outer Array


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Computing Quality Loss Function (QLF)

Define

C = The unit repair cost when the deviation from target takes place

= Tolerance interval (allowable parameter variation from target to SL)

V = Deviation from target

L(V) = the loss in monetary form (The quality loss)

The Loss Function

L(V) = C(V/)2


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Example::The repair cost for an engine shaft is 1000. The shaft diameter isrequired to be 101 mm. On average the produced shafts deviates 0.5mm from target.

Determine the mean quality loss per shaft using the Taguchi QLF.

Solution: L(0.5) = C*(V/)2 = 1000*(0.5/1)2 = 1000*0.25 = 250 perunit


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Quality Characteristics

Nominal the best (dimension of a part with modest variance) (foodproducts, medical instruments etc.)

Smaller the better (minimum shrinkage in garments, minimum noisein A/C)

Larger the better (maximum expected life of a component)


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Signal to noise ratio (S/N)

The signal to noise ratio measures the sensitivity of the quality characteristics

being investigated in a controlled manner to those external influencing

factors (noise factors) not under control.

The aim of any experiment is always to determine the highest possible S/Nratio for the result.

A high value of S/N implies that the signal is much higher value of S/N implies

that the signal is much higher than the effects of the noise factors.

signal/noise = amount of energy for intended function/amount of energywasted


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Calculation of signal to noise ratio

S/N = -10 log 10 (MSD)

MSD = mean square Deviation

For NTB, MSD = Sum (observation target) 2/N

For STB, MSD = (y12+y2

2+y32+yn

2)/N

The unstated target value is zero.

For LTB, MSD = reciprocal of STB


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Example

Customer satisfaction was measured in a hospital . The factorsconsidered are

(i) waiting time in queue (short,long)

(ii) politeness of the doctor (rude,polite)

(iii) availability of the medicines(yes,no)

Since three factors are involved and each at two levels; also nointeractions would be studied, L4 (2

3 ) design was chosen


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Taguchi Analysis: res1 res2 versus A B C

Smaller is better

Level A B C

1 -13.93 -16.87 -14.87

2 -16.10 -13.16 -15.16

Delta 2.17 3.72 0.29

Rank 2 1 3

Response Table for Means

Level A B C

1 5.000 7.000 5.500

2 6.500 4.500 6.000

Delta 1.500 2.500 0.500

Rank 2 1 3


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Graphical display

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-13

-14

-15

-16

-17

21

21

-13

-14

-15

-16

-17

A

Mea

nofSNratios

B

C

Main Effects Plot for SN ratios

Data Means

Signal-to-noise: Smaller is better

21

7

6

5

21

21

7

6

5

A

MeanofMeans

B

C

Main Effects Plot for Means

Data Means


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Predicted values

S/N Ratio Mean

-11.9240 3.5

Factor levels for predictions

A B C 1 2 1


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Example 2 measuring students satisfaction


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Data set


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Taguchi Analysis: response versus A B C D E F G

Response Table for Signal to Noise Ratios

Larger is better

Level A B C D E F G

1 32.93 31.89 32.05 33.28 32.83 33.01 32.14

2 32.09 33.13 32.98 31.75 32.19 32.01 32.88

Delta 0.84 1.24 0.93 1.53 0.64 1.00 0.73

Rank 5 2 4 1 7 3 6

Response Table for Means

Level A B C D E F G

1 45.00 39.75 40.25 46.50 44.50 44.75 40.75

2 40.50 45.75 45.25 39.00 41.00 40.75 44.75

Delta 4.50 6.00 5.00 7.50 3.50 4.00 4.00

Rank 4 2 3 1 7 5.5 5.5


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Graphical Analysis

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45.0

42.5

40.0

21 21

21

45.0

42.5

40.0

21 21

21

45.0

42.5

40.0

A

MeanofMeans

B C

D E F

G


Data Means

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33.0

32.5

32.0

21 21

21

33.0

32.5

32.0

21 21

21

33.0

32.5

32.0

A

M

eanofSNratios

B C

D E F

G

Main Effects Plot for SN ratiosData Means

Signal-to-noise: Larger is better


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Predicted values

S/N Ratio Mean

35.9660 60


A B C D E F G

1 2 2 1 1 1 2


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CASE STUDY:: Retail Sector


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21

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12

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21 21

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21 21

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A

MeanofM

eans

B C

D E F

G


Data Means

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21 21

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21 21

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A

MeanofSNratios

B C

D E F

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Main Effects Plot for SN ratiosData Means

Signal-to-noise: Larger is better


A B C D E F G

2 2 2 2 2 1 2


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Q/A

robust parameter design

Documents

design robust

results of parameter

experimental design

design characteristics1

tolerance design fine

optimal parameter levels

best levels

taguchi process1