robust parameter design
DESCRIPTION
Robust Parameter DesignTRANSCRIPT
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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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A
Mea
nofSNratios
B
C
Main Effects Plot for SN ratios
Data Means
Signal-to-noise: Smaller is better
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A
MeanofMeans
B
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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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A
MeanofMeans
B C
D E F
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Main Effects Plot for Means
Data Means
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eanofSNratios
B C
D E F
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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
Factor levels for predictions
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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CASE STUDY:: Retail Sector
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CASE STUDY:: Retail Sector
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CASE STUDY:: Retail Sector
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CASE STUDY:: Retail Sector
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CASE STUDY:: Retail Sector
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MeanofM
eans
B C
D E F
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Main Effects Plot for Means
Data Means
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MeanofSNratios
B C
D E F
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Main Effects Plot for SN ratiosData Means
Signal-to-noise: Larger is better
Factor levels for predictions
A B C D E F G
2 2 2 2 2 1 2
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CASE STUDY:: Retail Sector
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Q/A