Presented by: Keerti jangid
M.Sc. FINAL
CONCEPTS COVERED
• Taguchi philosophy
• Taguchi Method
• Taguchi loss function
2
GENICHI TAGUCHI
• Born in Japan, 1924
• Engineer
• Worked during 1950’s to improve Japan’s postWWII telephone communication system
• Father of the “Taguchi Method” and “Robust
Engineering”
QUALITY IN TAGUCHI LANGUAGE
• “Quality is the loss imparted to the customer
from the time a product is shipped or
rendered to the customer.”
 The loss to customer sustains can take many forms, but it is
generally a loss of product function or properties.
 Other losses are time, pollution, noise etc.
CONTRIBUTION OF TAGUCHI
• Taguchi’s principle contribution to statistics is
 The philosophy of off-line quality control
 Taguchi loss function
TAGUCHI’S PHILOSOPHY
• 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 and the
loss should be measured system-wide.
TAGUCHI METHOD
• ”Products and services should be designed to be inherently
defect free and of high quality”
– Meet customers’ expectations also under non-ideal conditions
• Disturbances are events that cause the design performance to
deviate from its target values
• Taguchi divide disturbances into three categories
– External disturbances: variations in the environment where the
product is used
– Internal disturbances: ware and tare inside a specific unit
– Disturbances in the production process: deviation from target values
7
TAGUCHI’S METHOD
• Taguchi advocates a 3 steps of 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
1. SYSTEM DESIGN
•
All about
-
innovation
New ideas
Techniques
Philosophies
•
Application of science and engineering knowledge
•
Includes selection of :
- materials
- Processes
- Tentative parameter value
9
2. PARAMETER DESIGN
• The selection of control factors (parameters) and their “optimal”
levels
- The objective is to make the design Robust!
• Control factors are those process variables management can
influence.
- The procedures used and the type and amount of training
• The ”optimal” parameter levels can be determined through
experimentation
10
3. TOLERANCE DESIGN
• Development of specification limits
- Necessary because there will always be some variation in the production
process
- Taguchi fiercely advocates aiming for the target value not just settle for
“inside the specification limits”!
• Occurs after the parameter design
• Often results in increased production costs
- More expensive input material might have to be used to meet specifications
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The Taguchi Quality Loss Function (I)
• The traditional model for quality losses
– No losses within the specification limits!
Cost
Scrap Cost
LSL
•
Target
USL
The Taguchi loss function
– The quality loss is zero only if we are on target
12
CUSTOMER LOSS FUNCTION
• The quality loss function
L( y)  k ( y  m ) 2
–
–
–
–
–
L is the loss function
k is the constant = cost to correct / customer tolarence2
y is the reported value
m is the mean (average) or a targeted value
Note that when y = m (i.e., when the value of the quality
characteristic is on target), the loss is zero.
EML4550 -- 2007
Constant k
• Suppose that (m + Δo) and (m - Δo) is the customer
tolerance interval , represent the deviations from the
target in which about 50% of the customers would
complain (significant economic loss)
• This is essentially a definition of product ‘failure’. The
economic loss to the customer associated with
product failure is A(e.g., losses due to lack of access to
product plus cost to repair)
• Then A = 𝑘 ∗ Δ20
𝑘=
𝐴
Δ20
EXPECTED LOSS
• The expected loss is the mean loss over many
instances of the product . We have
𝐸𝐿 𝑦
=𝐸 𝑘 𝑦 −𝑚 2
= k[ var(y) + (𝜇 − 𝑚 )2 ]
= k(MSD)
• Here, MSD represents the mean square
deviation of y and is estimated as
𝑀𝑆𝐷 =
𝑦𝑖 − 𝑚
𝑛
2
MANUFACTURING TOLERANCE
.
𝐿(𝑦) = 𝑘(𝑦 − 𝑚)2
𝐴 = 𝑘 ∗ ∆20
𝐴 (𝑦 − 𝑚)2
𝐿 𝑦 =
∆0
𝐴 (𝛿)2
𝐵=
∆20
𝛿2
𝐵
=
𝐴 ∗ ∆20
𝑚−∆
m-δ
𝑚
m+δ
k = proportionality constant
m = target value
y = value of quality characteristics
A = consumer loss
B = cost of manufacture for m – δ and m + δ manufacturing tolerance
𝑚+∆
QUALITY CHARACTERISTICS
• A process has “several” quality characteristics
- Desirable qualities
Larger-the better ( strength , mileage etc)
Normal-the-best ( specified dimensions , uniformity)
- Undesirable properties
Smaller-the better (defects, cost)
• Determine the best setting such that
- Desirable qualities are enhanced
- Undesirable properties are minimized
- Process become ROBUST
QUALITY CHARACTERISTICS
• The normal-the-best case
𝐿(𝑦) = 𝑘 𝑦 − 𝑚
2
L(y)
Ao
L(y)
m-Do
m
y
m+Do
• The smaller-the-better case
L(y)
𝐿(𝑦) = 𝑘 𝑦
2
Ao
Do
• The larger-the-better case
1
𝐿(𝑦) = 𝑘 2
𝑦
y
L(y)
Ao
y
Do
EXAMPLES
1. 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 $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?
Solution:
Note that this is a situation in which target is best.
The target value m is 1.5 m.
The loss function is given by L(y) =k(y-m)2 , where y
represents the height of the steering mechanism and k is
a proportionality constant.
To find k we have
𝑘=
𝐴
Δ20
= 50/(0.02)2 = 125,000
The expected loss per item is given by
E[L(y)] = 125,000E(y—1.5)2
where E(y — 1.5)2 is estimated as follows
𝑦𝑖 − 𝑚 2
𝑛
=
[(1.53— 1.5)2 + (1.49— 1.5)2 + (1.50— 1 .5)2 + ... + (1.52−1.5)2 ]
10
=
0.0049
10
=
0.00049
Hence, the expected loss per item is
E[L(y)]= 125,000(0.00049) = $61.25.
2. Refer to above Example concerning the height of a steering
mechanism. The manufacturer is considering changing the
production process to reduce the variability in the output. The
additional cost for the new process is estimated to be
$5.50/item. The annual production is 20,000 items. Eight 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?
Solution:
Here the loss function is L(y) = 125,000(y—1.5) .
For the new process, we estimate the mean square deviation with
the target value of 1.5.
𝑦𝑖 − 𝑚 2
𝑛
=
=
0.0015
10
(1.51−1.5)2 + (1.50−1.5)2 + ... +(1.51−1.5)2]
8
=
0.000187
The expected loss per item for the new process is
E[L(Y)] = (125,000)(0.0001875) = $23.44
The expected loss per item for the old process is $61.25
Then by comparing the loss of old and new process we have
a saving of $61.25 - $23.44 = $37.81/item,
But here manufacturer have also spend cost on new
process is $5.50/item.
Thus, the net savings per item by using the new process is
$37.81 — $5.50 = $32.31, making it cost-efficient.
The net annual savings (20,000)(32.31) = $646,200.
3. Refer to above Example concerning the height of a steering
mechanism. The manufacturer decides to rework the height, prior to
shipping the product, at a cost of $3.00 per item. What should the
manufacturer's tolerance be?
Solution:
The loss function is L(y) = 125,000(y—1.5)2
The manufacturer's tolerance be given by m ± δ i.e 1.5 ± δ. We have
𝐴 (𝛿)2
2
𝐵=
=
3
=
125,000
𝛿
∆20
δ= (
𝐵
𝐴 ∗∆20
) ½ = (3/125,000)½ = 0.0049
Thus, the manufacturer's tolerance is 1.5 ± 0.0049 m.
For products with heights that equal or exceed these limits, the
manufacturer should rework the items at the added cost of $3.00 per item
to provide cost savings in the long run. Otherwise, these items will incur a
loss to the customer at a rate of $50 per item.
TAGUCHI APPROACH
• The Taguchi Approach can be used at the
system level to interact with outside
customers, but it can also be implemented
within a company
• Each successive step in the manufacturing
process can be seen as a ‘customer’ of the
previous step (manufacturing, purchased part,
service, etc.)
REFERENCES
• FUNDAMENTALS OF QUALITY CONTROL AND
IMPROVEMENT
- ÄMITÄVA MITRA
• A PRIMER ON THE TAGUCHI METHOD
- Ranjit K. Roy