nptel taguchi methods
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Copyright Tapan Bagchi 1
Quality Engineering and Taguchi Methods
Copyright Tapan Bagchi 2
“Robust” Chocolate Bars are better!
Ambient Temperature
PlasticityRobust performance
Poor performance
Copyright Tapan Bagchi 3
Taguchi Methods
(or Quality Engineering
or Robust Design)
Focus is on reducing variability of response
to maximize robustness, generally achieved
through Orthogonal Array Experiments
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The Genesis of DOE
Sir Ronald Alymer Fisher
(1890-1962) was the pioneer
of DOE. He was responsible
for statistics and data analysis
at the Rothamsted Agricultural
Experiment Station in London,
England. Fisher developed
and was the first to use
ANOVA in the statistical
analysis of experimental data.
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Historical Perspective
George E. P. Box (born 1919)
was a student of R A Fisher. He
made several advances to
Fisher’s work in DOE theory
and statistics. The founding
chair of the University of
Wisconsin’s Department of
Statistics, Box was appointed
the R. A. Fisher Professor of
Statistics at UW in 1971.
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Objective of this Lecture:
● To explore the basic ideas of two-level factorial design of
experiments (DOE) and the connection of QE to statistical
process control (SPC)
Key Points:
QE Overview
● DOE can help uncover significant variables and
interactions among variables
● SPC can help uncover process shifts
● Quality engineering tools help the investigator to
discover a path for process improvement
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Typical QE Applications
In manufacturing - improve performance of a
manufacturing process
In process development - improve yields, reduce
variability and cost.
In design - evaluation and comparison of basic
configurations, materials, and parameters
The method is called Taguchi Methods.
The key tool is DOE.
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Taguchi Methods
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C R Rao
You’d know Rao from his
Cramer-Rao Inequality. Rao is
recognized worldwide as a
pioneer of modern multivariate
theory and as one of the world's
top statisticians, with
distinctions as a mathematician,
researcher, scientist, and
teacher. Taught Taguchi.
Author of 14 books and over
300 papers.
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Genichi Taguchi
An engineer who developed
an approach (now called
Taguchi Methods) involving
statistically planned
experiments to reduce
variation in quality. Learned
DOE from Professor Rao.
In 1960’s he applied his
learning in Japan.
In 1980’s he introduced his
ideas to US at AT&T.
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What are Taguchi’s Contributions?
Quality Engineering Philosophy—Targets
and Loss functions
Methodology—System, Parameter,
Tolerance design steps
Experiment Design—use of Orthogonal
arrays
Analysis—use Signal-to-Noise (S/N ratios)
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61
65
8777
79
75
67
60
D
O
B
standard
orderD B O Avg Response
1 - - - 67
2 + - - 79
3 - + - 61
4 + + - 75
5 - - + 65
6 + - + 60
7 - + + 77
8 + + + 87
FACTOR LOW(-) HIGH (+)
D (Driver) regular oversized
B (Beverage) beer water
O (Ball) 3-piece balata
- - - + - -
1 2
3
5
87
4
6+ - +
+ + +
+ + -
- + +
- + -
- - +
D
B
O
Conventional DOE focuses only on
Average Response
QE focuses on Variability of
Response
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Taguchi’s Key Contributions
Quality Engineering Philosophy
Methodology
Experiment Design
Analysis
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The Taguchi Loss Functionand the typically assumed Loss to the Customer
TargetLo Spec Hi Spec
Loss
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Taguchi’s Quality Philosophy
Loss = k(P - T)2
not 0 if within specs
and 1 if outside
On Target Production
is more important than
producing within Specs
LS T US
LS T US
Conventional viewTaguchi’s view
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Taguchi focused on Off-Line Quality Control
Off-Line Quality Control = Improving quality and reducing
total cost in the product or process design stage
Total Cost means cost to society so it includes the cost of
problems in manufacturing and the cost of problems in the
field.
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Definition:
Robust Design—A Design that results in products or services that can function over a broad range of usage and environmental conditions
Taguchi’s key contribution is Robust Design
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Taguchi’s Contributions Contd.
Quality Engineering Philosophy
Methodology
Experiment Design
Analysis
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Taguchi’s Product Design Approach has 3 Steps
1. System Design
Choose the sub-systems, mechanisms, form of the prototype—develop the basic design. This is similar to conventional engineering design
2. Parameter Design
Optimize the system design so that it improves quality (robustness) and reduces cost
3. Tolerance Design
Study the tradeoffs that must be made and determine what tolerances and grades of materials are acceptable
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Parameter Design (the Robust Design step)
● Optimize the settings of the design parameters to minimize its sensitivity to noise–ROBUSTNESS.
● By highlighting ―robustness‖ as a key quality requirement, Taguchi really opened a whole area that previously had been talked about only by a few very applied people.
● His methodology is heavily dependent on design of experiments like Fisher’s and Box’s methods, but the difference he made was that for response he looked at not only the mean but also the variance of performance
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Robust Design—how it is done
Identify Product/Process Design Parameters that Have significant / little influence on Performance
Minimize performance variation due to Noise factors
Minimize the processing cost
Methodology: Design of Experiments (DOE)
Examples - Chocolate mix, Ina Tile Co., Sony TV
Target
Performance () Actual
Performance (P)
Design Parameters (D)
Noise Factors (N): Internal & External
Product / Process
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Taguchi’s Experimental FactorsParameter design step identifies and optimizes the Design Factors
Control Factors – Design factors that are to be set at optimal levels
to improve quality and reduce sensitivity to noise
• Size of parts, type of material, Value of resistors, etc
Noise Factors – Factors that represent the noise that is expected in
production or in actual use of the product
• Dimensional variation
• Operating Temperature
Adjustment Factor – Affects the mean but not the variance of a
response
• Deposition time in silicon wafer fabrication
Signal Factors – Set by the user to communicate desires of the user
• Position of the gas pedal
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Taguchi’s Contributions Contd.
Quality Engineering Philosophy
Methodology
Experiment Design use orthogonal arrays
Analysis
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Several different types of Experimental plans (“designs”) are available to the design engineer—Factorial, Fractional, Central Cuboid, etc. Taguchi used “Orthogonal” Designs
CCenter
SScreening
FFactorial
OOrthogonal
FFFractional
factorial
Focus: Handle many factors
Output: List of Important Factors, Best Settings, Good design
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Full Factorial Array Example: The 23
(8-trial) array
1 2 3 4 5 6 7
1 1 1 1 1 1 1
1 1 1 2 2 2 2
1 2 2 1 1 2 2
1 2 2 2 2 1 1
2 1 2 1 2 1 2
2 1 2 2 1 2 1
2 2 1 1 2 2 1
2 2 1 2 1 1 2
C B -BC A -AC -AB -ABC
Full Factorial Factor Assignments to Experimental Array Columns
Such experiments can find all Main & two- and three-factor Interactions
Array
Columns
Response
A
C
B
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The L8 Orthogonal Array Example: Taguchi used these
1 2 3 4 5 6 7
1 1 1 1 1 1 1
1 1 1 2 2 2 2
1 2 2 1 1 2 2
1 2 2 2 2 1 1
2 1 2 1 2 1 2
2 1 2 2 1 2 1
2 2 1 1 2 2 1
2 2 1 2 1 1 2
C B D A E F G
Orthogonal Array Factor Assignments to Experimental Columns
Such experiments can find all 7 Main effects.
Array
Columns
Response
A
F
DB E
C G
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Taguchi’s Orthogonal Experimental Plan—
7 Factors (A, B, C, D, E, F and G) may potentially
influence the production of defective tiles
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Calculation of Factor Effects
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Main Effects of Process
Factors on %Defects in Tiles
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Alternative Design Notations for
Orthogonal Arrays
Std. Fisher's Original Yates Group Theory TaguchiOrder A B C A B C A B C1 – – – 1 0 0 0 1 1 12 + – – a 1 0 0 2 1 13 – + – b 0 1 0 1 2 14 + + – ab 1 1 0 2 2 15 – – + c 0 0 1 1 1 26 + – + ac 1 0 1 2 1 27 – + + bc 0 1 1 1 2 28 + + + abc 1 1 1 2 2 2
X1 X2 X3 X1 X2 X3
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Taguchi’s OA-based Experimental Design Matrix Notation
Total Number of Runs
k
NL 2
Number of Levels per Factor
Number of Factors
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Linear Graphs for the L8 Array
Linear graphs guide assignment of factors to L8
columns
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Main effects are assigned to columns at nodes in the graph.
Interactions are assigned to the columns on the lines.
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Some Orthogonal Array Designs
―Classical‖(2-level Factorials)
―Taguchi‖
23
24
25
26-3
27-1
…
23-1=L4
27-4=L8
215-11=L16
…
L12
L18
L27
…
See Montgomery (1997), Design and Analysis of Experiments, P. 631
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Taguchi Orthogonal Array Tables
2-level (fractional factorial) arrays
L4(23). L8(2
7), L16(215). L32(2
31), L64(263)
2-level array
L12(211) (Plackett-Burman Design)
3-level arrays
L9(34). L27(3
13), L81(340)
4-level arrays
L16(45). L64(4
21)
5-level array
L25(56)
Mixed-level arrays
L18(21x37), L32(2
1x49), L50(21x511)
L36(211x312), L36(2
3x313), L54(21x325)
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Comments on Taguchi Arrays
Taguchi designs are large screening designs
Assumes most interactions are small and those that aren’t are known ahead of time.
Taguchi claims that it is possible to eliminate interactions either by correctly specifying the response and design factors or by using a sliding setting approach to those factor levels.
Doesn’t guarantee that we get ―highest resolution‖ design.
Instead of designing the experiment to investigate potential interactions, Taguchi prefers to use three-level factors to estimate curvature
Copyright Tapan Bagchi 36
Taguchi’s Robust Design Experiments
Taguchi advocated using
inner and outer array
designs to take into
account noise factors
(outer) and design factors
(inner)
Design factors: I1, I2, I3
Noise factors: E1 & E2
Objective: Maximize
response while minimizing
its variance
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Example: Robust Design OAs of
Starter Motor Parameter Design
Inner array: armature turns, gage of wire, ferric content of alloy
Outer array: battery voltage, ambient temperature
Starter torqueReplicates
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Taguchi’s Contributions
Quality Engineering Philosophy
Methodology
Experiment Design
Analysis Finding the robust design parameter values
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Taguchi’s Analysis uses SN Ratios
To maximize robustness, Taguchi uses signal-to-noise ratios as response variables, for example,
However, it is often more informative to analyze mean and standard deviation separately, rather than combine into a signal-to-noise ratio
analyze stddev in the same manner that we have previously analyzed the mean.
Taguchi’s analysis techniques are often inefficient…
SNt -10logy 2
s2
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SN Ratios are Maximized
To maximize robustness, when Target performance is the best, Taguchi uses the signal-to-noise ratio
When response is to be maximized, Taguchi uses
When response is to be minimized, Taguchi uses
-
n
ySNt
2/1log10
2
2
log10s
ySNt
-
n
ySNt
2
log10
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Taguchi Analysis of Motor Design Data
Robustness is maximized with SN ratio is maximized.
Design (inner array) factor settings that maximize SN ratioare:
I1 (turns) = -1
I2 (gage) = +1
I3 (ferric %) = -1
Note: This system is not additive! Results are approximately OK.
72
74
76
78
80
I1 = -1 I1 = +1 I2 = -1 I2 = +1 I3 = -1 I3 = +1
Inner Array Factors
Torq
ue
10
15
20
25
I1 = -1 I1 = +1 I2 = -1 I2 = +1 I3 = -1 I3 = +1
Inner Array Factor Settings
Sta
ndar
d D
ev T
orqu
e
0
0.0005
0.001
0.0015
I1 = -1 I1 = +1 I2 = -1 I2 = +1 I3 = -1 I3 = +1
Inner Array Factor Settings
S/N
Ratio
of R
espo
nse
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Designers should embrace Taguchi’s philosophy of quality engineering. It makes very good sense.
Note, however, that a key weakness of Taguchi method is its assumption of a ―main factor only‖ (or ―additive‖ model)… Taguchi ignores interactions
Therefore, rather than use inner outer arrays, we may use more efficient and exact methods that are no more difficult to learn and apply to carry Taguchi’s robust design philosophy into practice…
You may use any of the various experimental and optimization techniques available in the literature such as multiple regression/RSM to develop robust designs.
An example of such extension is shown in the next slides.
Epilogue
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Multiobjective Robust Design
by Metaheuristic Methods
Tapan P Bagchi
and
Madhu Ranjan Kumar (1993)
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The Empirical Framework for progressing Knowledge
Weather
EconomyElectronics
Chemistry
Medicine
EngineeringPsychology
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Robust Design search by GA
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