Description
The Taguchi Method
? Born in Japan, 1924
? Electrical Engineer
? Worked during 1950’s to improve Japan’s
post-WWII telephone communication
system
? Father of the “Taguchi Method” and “Robust
Engineering”
? Not a mathematician?
? You can still successfully apply Taguchi
Method concepts to your service/
manufacturing business.
? Basic concepts are simple.
? Just keep reading.
? “In the next century, the capability of
developing robust technology will be
essential to the competitiveness of any
manufacturing enterprise.” (Tsai)
? Substitute “robust services” and “robust
manufacturing.” You need this.
? “The product performance must be immune
to the noise variable”
“Being within specifications”
“Conformance to requirements”
“Fitness for use”
“Customer satisfaction”
? Taguchi defines quality as:
“the loss imparted to society from the time a
product is shipped to the customer”
? Taguchi is first to articulate that:
“No amount of inspection will ever improve the
quality of a product.”
Quality must be “engineered in” since it
cannot be “inspected out.”
•
• •
Off-Line Quality Control
Improving Quality and Reducing Total Cost
right in the Design Stage
Total Cost
it includes the cost of problems in manufacturing
and the cost of problems in the field.
Taguchi focuses mostly on
Off-Line Quality Control
? CUSTOMER SATISFACTION
? Design to the highest standards early in
the process to eliminate all non-random
errors
? Quality Loss = Loss to Society
quantified through “Quality Loss
Function”
? Variation (+/-) from optimal measure
results in a loss.
$
Design
$$
Service Delivered
$$$$$$$$$$
Post Service Delivery
? Ways to measure service:
1. Returning customers
2. Number of complaints
3. Number of compliments
4. Employee attitude
? Quality Should be designed into the product and
not inspected into it
? Quality is best achieved by minimizing the
deviation from the target
? The cost of quality should be measured as a
function of deviation from the target / standard
and the losses should be measured system –
wide.
Concept of Quality
• Traditional concept:
– Good in the limit and bad
outside the limit
– Step function
– loss off the limit
• Taguchi concept:
– Good only at target
– Continuous, quadratic
loss even within limit
– penalizes a product for
being “off target
m+ A m ÷ A
m
Loss
Pass
Fail
m+ A
m÷ A
m
Loss
This represents a paradigm shift in the way in which
companies measure the “goodness” of a product
? Deviation from
target results in
loss.
? Lower than target
? Greater than target
? Both lose
A
L
= k(y-m)
2
A = k(A
o
)
2
k= A/ (A
o
)
2
L = A(y-m)
2
/ (A
o
)
2
B = A(o)
2
/ (A
o
)
2
o = B (A
o
)
2
----
A
m-o m+o
B
Classification of Quality Characteristics
• Nominal value is the best:
Example: Diameter of a shaft
L = o * (y-m)
2
• The smaller, the better:
Example: Impurity in drug
L = o * y
2
• The larger, the better:
Example: Strength of structure
L = o / y
2
m-A m m+A
A
o
y
A
o
0 A
y
A
o
0 A
y
? Quantify the Loss
? Warning:
Next slide contains
math formulas
? But give it a try!
L = k(y-m)
2
L = Loss
k = constant =
cost to correct
tolerance
2
y = reported value
m = mean value (average)
? Company C received an average of 10 complaints
per month last year. In November they received 15
complaints. Management sets an acceptable
level at 2 (tolerance).
? It costs the company $50 directly per complaint to
correct the problems. They determined the cost in
lost sales to be $100.
? Total cost per complaint: $150
k = $150/2
2 =
$37.50
L = 37.50 (15-10)
2
= 37.50 (5)
2
= 37.50 (25)
= $937.50 is loss for the
month of November
Case Example: SONY Color TV
• Ashi Newspapers on April 17, 1979 reported that:
– Identical sets were assembled in Japan & US with same
design, same parts and same process control
– US customers preferred TV’s assembled in Japan to those
assembled in US, because of better color
– No sets assembled in US was out of specs while 0.3% of
sets assembled in Japan shipped was out of specs, thus
defective.
SONY Color TV (Cont’d)
• Color density distribution:
Color Density
Distribution
US-built sets:
100% within limit
Japan-built sets:
.3% out of limits
y
m-5 m m+5
• The objective in robust design is to:
improve the quality of a product by minimizing the
effects of variation without eliminating the causes (since
the causes are either too difficult or too expensive to
control)
• Robust design is employed in product and process
design to improve product manufacturability and
reliability by making products insensitive to
environmental conditions and component variations
• The end result is a robust design, i.e.,
? a design that has minimum sensitivity to variations in
uncontrollable factors
Product Configuration
Material & Manufacturing
Variations
Usage Variation
Selected Values of
Design Variables
Performance
Variation
P-diagram
? Basic goal:
? Reduce variation in performance parameter due to
variation in noise by selecting the best set of design
variable values
? Here, noise refers to both:
? Materials & manufacturing variations
? Usage variation
? Taguchi advocates a 3 step,
off-line quality control method
for product design
Step 1. System Design
? concept design and synthesis
? innovation and creativity
Step 2. Parameter Design
? parameter sizing to ensure
robustness to variations
Step 3. Tolerance Design
? establish product and process
tolerances to minimize costs
? Goal in Parameter Design:
Identify design parameter settings which minimize the
sensitivity of a design to variations
? Step 1: Identify factors and ranges of interest
Classification of Factors
• Control Factors Design factors that are to be set at
optimal levels to improve quality
and reduce sensitivity to noise
• Noise Factors Factors that represent the noise
that is expected in production or
in use
• Adjustment Factor Affects the mean but not the
variance of a response
• Signal Factors Set by the designer to
communicate desires of the user
Product Design Process Design
Outer Noise Consumer’s usage conditions
Low temperature
High temperature
Temperature change
Shock
Vibration
Humidity
Ambient Temperature
Humidity
Seasons
Incoming material variation
Operators
Voltage change
Batch to batch variation
Inner Noise Deterioration of parts
Deterioration of material
Oxidation (rust)
Machinery aging
Tool wear
Deterioration
Between
Product
Noise
Piece to piece variation where they
are supposed to be the same, e.g.,
Young’s modulus
shear modulus
allowable stress
Process to process variation where
they are supposed to be the same, e.g.,
variations in feed rate
Controllable
Factors
All design parameters, e.g.,
1 dimensions
2 material selection
All process design parameters
All process setting parameters
? Managers’ job:
? Identify the Problems
? Brainstorm
? Contribute to experiment design
? Facilitator’s job:
? Design experiment
? Run experiment
? Analyze results
? Confirm experiment
? What do managers and/or employees see that
need improvement?
? Identify critical variables in the service that
affect quality.
? Open and honest discourse with all people
involved.
? Decide which factors are controllable and
which are not.
? Using results from brainstorming session,
facilitator will design an experiment.
? Management must understand this part, and
needs to fully support the resources needed
for it.
? Use of ANOVA requires managers understand
its use.
? Facilitator, although in charge of the
experiment, must assure management’s
understanding of the process.
? Factors closest to target specification
identified.
? Means to reduce controllable variation
produced.
? Set up new system using data from
experiment.
? Test and validate results.
? Full Factorial Design - the total no. of
experiments required to run all possible
combinations of all the levels for each of
the factors
? Fractional Factorial Design- a portion of
total combinations
? If orthogonality is maintained the
fractional factorial matrices would be
called as Orthogonal Arrays.
Orthogonal Array (L
8
(2
7
))
L
N
(2
k
)
Number of Factors
Number of Levels Per Factors Total Number of Runs
Taguchi’s Orthogonal Array Tables
• 2-level arrays
– L
4
(2
3
). L
8
(2
7
), L
16
(2
15
)
L
32
(2
31
), L
64
(2
63
)
• 3-level arrays
– L
9
(3
4
). L
27
(3
13
), L81(3
40
)
• 4-level arrays
– L
16
(4
5
). L
64
(4
21
)
• 5-level array
– L
25
(5
6
)
• Mixed-level arrays
– L
18
(2
1
x3
7
), L
32
(2
1
x4
9
),
L
50
(2
1
x5
11
)
– L
36
(2
11
x3
12
), L
36
(2
3
x3
13
),
L
54
(2
1
x3
25
)
Taguchi developed OAs to identify factors
influence without loss of accuracy.
No. of factors OA
2 to 3 L4
4 to 7 L8
8 to 11 L12
12 to 15 L16
For 2- levels
No. of factors OA
2 to 4 L9
5 to 7 L27
Selection Rules …
For 3- levels
Analysis
• Find the main effects of the process parameters on the
response
• Conduct Analysis of Variation (ANOVA) to separate the
experimentally observed variations into a number of
specific parameter
• Based upon the ANOVA result determine which factors
and interactions are significant
Analysis (Cont’d)
Taguchi uses signal to noise (S/N) ratios as response variables.
Signal to Noise Ratio
• A single response which makes a tradeoff between setting the
mean to a desirable level while keeping the variance low.
• Always try to MAXIMIZE a S/N Ratio
• There are three types:
– Smaller is Better
– Target is Best
– Larger is Better
Signal to Noise Ratio
• A nominal value is the best:
m-A m m+A
A
o
y
A
o
0 A
y
A
o
0 A
y
• The smaller, the better:
•The larger, the better:
( )
(
¸
(
¸
÷ ÷ = ¿
j
o j t
n y y SN / log 10
2
10
(
¸
(
¸
÷ = ¿
j
j s
n SN y / log 10
2
10
(
(
¸
(
¸
|
|
.
|
\
|
÷ = ¿
j
j
l
n
y
SN /
1
log 10
2
2
10
? Best improvement is early in the process.
? Use expert consulting help for full experiment and
implementation.
? Successfully used in automobile, airlines,
insurance, hotels and restaurants.
? Quality is a major feature that sets a service apart
from the rest.
? Foster, S. Thomas Jr. Ph. D.: “Designing and
Initiating A Taguchi Experiment in a Services
Setting” OM Review – Refereed: Volume 9, No. 3.
? Taguchi, Genichi: Taguchi on Robust Technology
Development: Bringing Quality Engineering
Upstream; Asme Press, New York, 1993
? Taguchi, Chowdhury, Taguchi: Robust
Engineering: Learn how to boost quality while
reducing costs and time to market; McGraw-
Hill, New York, 2000
? In addition to cited works:
? Visit American Supply Institute (ASI) website at
www.amsup.com
Customer tolerances for the height of a steering mechanism
are 1.5 ± 0.020 m. For a product that just exceeds these
limits, the cost to the customer for getting it fixed is Rs. 50.
Ten products are randomly selected and yield the following
heights (in meters): 1.53, 1.49, 1.50, 1.49, 1.48, 1.52, 1.54,
1.53, 1.51, and 1.52. Find the average loss per product item.
Refer to the earlier example:
The manufacturer is considering the change in the production
process to reduce the variability in the output. The additional
cost for the new change is Rs. 5.50 per item. The annual
production is 20,000 items. Eights items are randomly
selected from the new process, yielding the following
heights: 1.51, 1.50, 1.49, 1.52, 1.52, 1.50, 1.48, 1.51
Is the new process cost efficient? If so what is the annual
savings?
L = k(y-m)
2
L = Loss = 50
k = constant =
cost to correct
tolerance
2
k = constant = 50 / (0.2)
2
=1, 25,000
y = reported value
m = mean value (average)
. L = 125000 (y-m)
2
E[L] = 125000 E[(y-m)
2
]=61.25
L = k(y-m)
2
E[L] = 125000 E[(y-m)
2
]=23.44
61.25 – 23.44 = 37.81
37.81 – 5.50 = 32.31
20000 * 32.31 = 6,46,200
doc_202196339.pptx
The Taguchi Method
? Born in Japan, 1924
? Electrical Engineer
? Worked during 1950’s to improve Japan’s
post-WWII telephone communication
system
? Father of the “Taguchi Method” and “Robust
Engineering”
? Not a mathematician?
? You can still successfully apply Taguchi
Method concepts to your service/
manufacturing business.
? Basic concepts are simple.
? Just keep reading.
? “In the next century, the capability of
developing robust technology will be
essential to the competitiveness of any
manufacturing enterprise.” (Tsai)
? Substitute “robust services” and “robust
manufacturing.” You need this.
? “The product performance must be immune
to the noise variable”
“Being within specifications”
“Conformance to requirements”
“Fitness for use”
“Customer satisfaction”
? Taguchi defines quality as:
“the loss imparted to society from the time a
product is shipped to the customer”
? Taguchi is first to articulate that:
“No amount of inspection will ever improve the
quality of a product.”
Quality must be “engineered in” since it
cannot be “inspected out.”
•
• •
Off-Line Quality Control
Improving Quality and Reducing Total Cost
right in the Design Stage
Total Cost
it includes the cost of problems in manufacturing
and the cost of problems in the field.
Taguchi focuses mostly on
Off-Line Quality Control
? CUSTOMER SATISFACTION
? Design to the highest standards early in
the process to eliminate all non-random
errors
? Quality Loss = Loss to Society
quantified through “Quality Loss
Function”
? Variation (+/-) from optimal measure
results in a loss.
$
Design
$$
Service Delivered
$$$$$$$$$$
Post Service Delivery
? Ways to measure service:
1. Returning customers
2. Number of complaints
3. Number of compliments
4. Employee attitude
? Quality Should be designed into the product and
not inspected into it
? Quality is best achieved by minimizing the
deviation from the target
? The cost of quality should be measured as a
function of deviation from the target / standard
and the losses should be measured system –
wide.
Concept of Quality
• Traditional concept:
– Good in the limit and bad
outside the limit
– Step function
– loss off the limit
• Taguchi concept:
– Good only at target
– Continuous, quadratic
loss even within limit
– penalizes a product for
being “off target
m+ A m ÷ A
m
Loss
Pass
Fail
m+ A
m÷ A
m
Loss
This represents a paradigm shift in the way in which
companies measure the “goodness” of a product
? Deviation from
target results in
loss.
? Lower than target
? Greater than target
? Both lose
A
L
= k(y-m)2
A = k(A
o
)
2
k= A/ (A
o
)
2
L
= A(y-m)2
/ (A
o
)
2
B = A(o)
2
/ (A
o
)
2
o = B (A
o
)
2
----
A
m-o m+o
B
Classification of Quality Characteristics
• Nominal value is the best:
Example: Diameter of a shaft
L
= o * (y-m)2
• The smaller, the better:
Example: Impurity in drug
L
= o * y2
• The larger, the better:
Example: Strength of structure
L
= o / y2
m-A m m+A
A
o
y
A
o
0 A
y
A
o
0 A
y
? Quantify the Loss
? Warning:
Next slide contains
math formulas
? But give it a try!
L
= k(y-m)2
L
= Loss k = constant =
cost to correct
tolerance
2
y = reported value
m = mean value (average)
? Company C received an average of 10 complaints
per month last year. In November they received 15
complaints
. Management sets an acceptable level at 2 (tolerance).
? It costs the company $50 directly per complaint to
correct the problems. They determined the cost in
lost sales to be $100.
? Total cost per complaint: $150
k = $150/2
2 =
$37.50
L
= 37.50 (15-10)2
= 37.50 (5)
2
= 37.50 (25)
= $937.50 is loss for the
month of November
Case Example: SONY Color TV
• Ashi Newspapers on April 17, 1979 reported that:
– Identical sets were assembled in Japan & US with same
design, same parts and same process control
– US customers preferred TV’s assembled in Japan to those
assembled in US, because of better color
– No sets assembled in US was out of specs while 0.3% of
sets assembled in Japan shipped was out of specs, thus
defective.
SONY Color TV (Cont’d)
• Color density distribution:
Color Density
Distribution
US-built sets:
100% within limit
Japan-built sets:
.3% out of limits
y
m-5 m m+5
• The objective in robust design is to:
improve the quality of a product by minimizing the
effects of variation without eliminating the causes (since
the causes are either too difficult or too expensive to
control)
• Robust design is employed in product and process
design to improve product manufacturability and
reliability by making products insensitive to
environmental conditions and component variations
• The end result is a robust design, i.e.,
? a design that has minimum sensitivity to variations in
uncontrollable factors
Product Configuration
Material & Manufacturing
Variations
Usage Variation
Selected Values of
Design Variables
Performance
Variation
P-diagram
? Basic goal:
? Reduce variation in performance parameter due to
variation in noise by selecting the best set of design
variable values
? Here, noise refers to both:
? Materials & manufacturing variations
? Usage variation
? Taguchi advocates a 3 step,
off-line quality control method
for product design
Step 1. System Design
? concept design and synthesis
? innovation and creativity
Step 2. Parameter Design
? parameter sizing to ensure
robustness to variations
Step 3. Tolerance Design
? establish product and process
tolerances to minimize costs
? Goal in Parameter Design:
Identify design parameter settings which minimize the
sensitivity of a design to variations
? Step 1: Identify factors and ranges of interest
Classification of Factors
• Control Factors Design factors that are to be set at
optimal levels to improve quality
and reduce sensitivity to noise
• Noise Factors Factors that represent the noise
that is expected in production or
in use
• Adjustment Factor Affects the mean but not the
variance of a response
• Signal Factors Set by the designer to
communicate desires of the user
Product Design Process Design
Outer Noise Consumer’s usage conditions
Low temperature
High temperature
Temperature change
Shock
Vibration
Humidity
Ambient Temperature
Humidity
Seasons
Incoming material variation
Operators
Voltage change
Batch to batch variation
Inner Noise Deterioration of parts
Deterioration of material
Oxidation (rust)
Machinery aging
Tool wear
Deterioration
Between
Product
Noise
Piece to piece variation where they
are supposed to be the same, e.g.,
Young’s modulus
shear modulus
allowable stress
Process to process variation where
they are supposed to be the same, e.g.,
variations in feed rate
Controllable
Factors
All design parameters, e.g.,
1 dimensions
2 material selection
All process design parameters
All process setting parameters
? Managers’ job:
? Identify the Problems
? Brainstorm
? Contribute to experiment design
? Facilitator’s job:
? Design experiment
? Run experiment
? Analyze results
? Confirm experiment
? What do managers and/or employees see that
need improvement?
? Identify critical variables in the service that
affect quality.
? Open and honest discourse with all people
involved.
? Decide which factors are controllable and
which are not.
? Using results from brainstorming session,
facilitator will design an experiment.
? Management must understand this part, and
needs to fully support the resources needed
for it.
? Use of ANOVA requires managers understand
its use.
? Facilitator, although in charge of the
experiment, must assure management’s
understanding of the process.
? Factors closest to target specification
identified.
? Means to reduce controllable variation
produced.
? Set up new system using data from
experiment.
? Test and validate results.
? Full Factorial Design - the total no. of
experiments required to run all possible
combinations of all the levels for each of
the factors
? Fractional Factorial Design- a portion of
total combinations
? If orthogonality is maintained the
fractional factorial matrices would be
called as Orthogonal Arrays.
Orthogonal Array (L
8
(2
7
))
L
N
(2
k
)
Number of Factors
Number of Levels Per Factors Total Number of Runs
Taguchi’s Orthogonal Array Tables
• 2-level arrays
– L
4
(2
3
). L
8
(2
7
), L
16
(2
15
)
L
32
(2
31
), L
64
(2
63
)
• 3-level arrays
– L
9
(3
4
). L
27
(3
13
), L81(3
40
)
• 4-level arrays
– L
16
(4
5
). L
64
(4
21
)
• 5-level array
– L
25
(5
6
)
• Mixed-level arrays
– L
18
(2
1
x3
7
), L
32
(2
1
x4
9
),
L
50
(2
1
x5
11
)
– L
36
(2
11
x3
12
), L
36
(2
3
x3
13
),
L
54
(2
1
x3
25
)
Taguchi developed OAs to identify factors
influence without loss of accuracy.
No. of factors OA
2 to 3 L4
4 to 7 L8
8 to 11 L12
12 to 15 L16
For 2- levels
No. of factors OA
2 to 4 L9
5 to 7 L27
Selection Rules …
For 3- levels
Analysis
• Find the main effects of the process parameters on the
response
• Conduct Analysis of Variation (ANOVA) to separate the
experimentally observed variations into a number of
specific parameter
• Based upon the ANOVA result determine which factors
and interactions are significant
Analysis (Cont’d)
Taguchi uses signal to noise (S/N) ratios as response variables.
Signal to Noise Ratio
• A single response which makes a tradeoff between setting the
mean to a desirable level while keeping the variance low.
• Always try to MAXIMIZE a S/N Ratio
• There are three types:
– Smaller is Better
– Target is Best
– Larger is Better
Signal to Noise Ratio
• A nominal value is the best:
m-A m m+A
A
o
y
A
o
0 A
y
A
o
0 A
y
• The smaller, the better:
•The larger, the better:
( )
(
¸
(
¸
÷ ÷ = ¿
j
o j t
n y y SN / log 10
2
10
(
¸
(
¸
÷ = ¿
j
j s
n SN y / log 10
2
10
(
(
¸
(
¸
|
|
.
|
\
|
÷ = ¿
j
j
l
n
y
SN /
1
log 10
2
2
10
? Best improvement is early in the process.
? Use expert consulting help for full experiment and
implementation.
? Successfully used in automobile, airlines,
insurance, hotels and restaurants.
? Quality is a major feature that sets a service apart
from the rest.
? Foster, S. Thomas Jr. Ph. D.: “Designing and
Initiating A Taguchi Experiment in a Services
Setting” OM Review – Refereed: Volume 9, No. 3.
? Taguchi, Genichi: Taguchi on Robust Technology
Development: Bringing Quality Engineering
Upstream; Asme Press, New York, 1993
? Taguchi, Chowdhury, Taguchi: Robust
Engineering: Learn how to boost quality while
reducing costs and time to market; McGraw-
Hill, New York, 2000
? In addition to cited works:
? Visit American Supply Institute (ASI) website at
www.amsup.com
Customer tolerances for the height of a steering mechanism
are 1.5 ± 0.020 m. For a product that just exceeds these
limits, the cost to the customer for getting it fixed is Rs. 50.
Ten products are randomly selected and yield the following
heights (in meters): 1.53, 1.49, 1.50, 1.49, 1.48, 1.52, 1.54,
1.53, 1.51, and 1.52. Find the average loss per product item.
Refer to the earlier example:
The manufacturer is considering the change in the production
process to reduce the variability in the output. The additional
cost for the new change is Rs. 5.50 per item. The annual
production is 20,000 items. Eights items are randomly
selected from the new process, yielding the following
heights: 1.51, 1.50, 1.49, 1.52, 1.52, 1.50, 1.48, 1.51
Is the new process cost efficient? If so what is the annual
savings?
L
= k(y-m)2
L
= Loss = 50 k = constant =
cost to correct
tolerance
2
k = constant = 50 / (0.2)
2
=1, 25,000
y = reported value
m = mean value (average)
. L
= 125000 (y-m)2
E[L
] = 125000 E[(y-m)2
]=61.25
L
= k(y-m)2
E[L
] = 125000 E[(y-m)2
]=23.44
61.25 – 23.44 = 37.81
37.81 – 5.50 = 32.31
20000 * 32.31 = 6,46,200
doc_202196339.pptx